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>> endobj 1088 0 obj <> /Annots[1091 0 R 1092 0 R 1093 0 R]/Contents 1089 0 R >> endobj 1096 0 obj <> /Contents 1097 0 R >> endobj 1101 0 obj <> /Contents 1102 0 R >> endobj 1105 0 obj <> /Annots[1108 0 R 1109 0 R 1110 0 R 1111 0 R]/Contents 1106 0 R >> endobj 1114 0 obj <> /Annots[1117 0 R 1118 0 R 1119 0 R 1120 0 R 1121 0 R]/Contents 1115 0 R >> endobj 1124 0 obj <> /Contents 1125 0 R >> endobj 1129 0 obj <> /Annots[1132 0 R 1133 0 R 1134 0 R 1135 0 R 1136 0 R 1137 0 R 1138 0 R 1139 0 R]/Contents 1130 0 R >> endobj 1142 0 obj <> /Annots[1145 0 R 1146 0 R 1147 0 R 1148 0 R 1149 0 R 1150 0 R]/Contents 1143 0 R >> endobj 1153 0 obj <> /Annots[1156 0 R 1157 0 R 1158 0 R 1159 0 R 1160 0 R 1161 0 R 1162 0 R 1163 0 R 1164 0 R 1165 0 R 1166 0 R 1167 0 R 1168 0 R 1169 0 R]/Contents 1154 0 R >> endobj 1172 0 obj <> /Annots[1175 0 R 1176 0 R]/Contents 1173 0 R >> endobj 1179 0 obj <> /Annots[1182 0 R 1183 0 R 1184 0 R]/Contents 1180 0 R >> endobj 1187 0 obj <> /Annots[1190 0 R 1191 0 R 1192 0 R 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SKTBӉYI1!2:ϱq;9 Ӊ(qi8dA(:p^i\Vsa|vmߚOƍ3 uݔAʊĆؕiwdi:4qvbк3Ҩ$3,#?Z_\g{Fnj倳b8Bz bͰsEI.޽mW]*M)iy>YXf,]ZuK8d-&`{Ղ"inEMmma'8AsEZ"STW.)Z[" ʕ|R s[FR\\[Im#Xԙaթnl* }QLҤ!I 15 %L*jas];^8Ri=os] c8ЭVkM tTًmQTfIWĴfT^p\\2pJb552rSS[H@Ñ2}YVGs01O7Y7Mf9X6b;he %#1@!@!@!@!@!@!@"'ohIQZO *ȱ"08N,pm↊Х%nJLsr;"VYbI2[)R)I@ĜxU_0RT Rj[ $)1ң}[RLGĎ4~2"Sg}r?\eRORPH(6*R))+J&y\ $qgj?Wۋl=OnL-wXyї8NDO%IBgLMiC{ZiwzQqrRU)> stream xWr0 +xfbҙ^NC:Jr}AReGMu1 xMɔP WwܡDhV( 5<9?:v )k Lpir2YĄ00pܵ=-f19Dd|FN#lw%xW# h)B'R,2dA.}yKz|s/M9IMuIZXPe߄Ral6%[y+l*p Fu)Xؘ6c1%5bt,,TAJ N,y?`%G˝K}ӣJә=J Z`~VyDB_^"ch4$aƞEeU y{=Q/Ftsh[]I1OmW)slUOUjݬ꫺ArX@aI1{@}3.L/k$yV%1?Kt.rXW(60RHb7&>:?|6PEAxhPKa_Vg%GG|2\]!>蠬,SԷ|G³P}z$k8,@;0~#~"6"5ޟխRjޠ" yT Sʓ?kE>$u;ם zq1 A9П~{\-txP25ȅΪb3o5rm8P̧xZ6Eer`>/, endstream endobj 36 0 obj << /Length 934 /Filter /FlateDecode >> stream xWn0+xx})KWt94oiBU;$%[v4[0&yoGS2%9+Õw(pÁqM*OΏN}](C(0k_>lFpF8`!\L&a W]ǭyoo||53ԜωE%B %3rg> fW/^~+ܟW]l@B39ڞPJ1mʸZzM-2x)6 K|_˲)W^̙&C``J_S^%&Lɹ~fGCl##@0E*ulC> stream xWKS0W,zk:=:AC\$tU$J 9jݕ"|谭p #Bsj"p \ے\vNmz#5FZ0\7y ¥xH@XUPW=o/w` THIX5̒9ˎus6{_3c94ubrUv??{c.∐&qTa,ݲjӘ%rD4A۬!rBdjPO0כwhۀ6NnG664ҡ #L I j\\,lwW:j4֑HM7mF)Ri75n(DVi(8X*3K`8;KqC稿H--(W c 2.N0ksydoQA6C`qԒj1AZefO f X1$s쁣H$3yi1B>ηt^}0eO3Srݪ1eU+=OQhxGz kl% <_yē5><@Ut|s7/gVyX,v vŦ/|ަt0> stream xWKs1 +|\X~{:=6딖dCi}e!fL_ز,}$ی #:lKJ@GS+Sܕs`o+Q0 _ăq@|@8j!\8t%\s5i暽~ @ԜI QS,_E7`_ѸAtO}p]LeS8"-rI4uFXG4ɍ `Л&:U(GDsRug ";Uʬ\s.s hmQr!!tb XPF.unjʼntƻ+ Z 3JH6Y"pL7 P4C, `%aHa`زġs_w$떀 ;j1MJdG!ri5G>-F lZP@-wQ]|٬,!, Lb :Em>Q $ҙOź#;R}V|XUV=oٖdF~L%)` &$Ihs y9 i5ǛAnrۻA|l0L7GHjo򧨌'Q6D]㳛 i5Ȋ]g0fT olɍM}%*:۾"Y@׶(tDRgA,JS-b30(FEW.ߏ-vb^M-)ɊpYy.HRx)1/?ZKe endstream endobj 52 0 obj << /Length 779 /Filter /FlateDecode >> stream xWKS1 W9,?imza-yP:oMp $3KeYId $O 5Vrݖsro+Ֆ ΅_AĽͰI@neRY.$怀cRGs5ٽ5{1X2/Z( piv#mu&Дr80h4Y')ewkkKR1ýEa\S؁5so(KhhNB봼rSe<&U#]DoǮ*O>79ZD%rgBV8wWQ0ap $ hz)6,.pWɅe` "-gT-5xj]>ͫZ!PhNG&Q|lZԁl8!J ۋN%*x,zM> stream xXێ6}߯ࣄ\/ ݴ6ۗml [e- %J4lx]tJ!ᙡ)#g#/HhNPNרW; YR>!8C bA\B9j@tE\5gso9ϐ%JQA-O}2,֛,S,Mv|UeK?';"~g{i⌰ Ph#$~o}@#Nqyan,&9`'DvA&)IԼfE}ٞ'}CmLbjmF:vq3ټM1&q8PC<ڡC;gC.M f@jQNf•}-F/Nψ CqA Cሂs,\ Gc:0 Oj3/%iTf C˯[SAw( `=NV"o|/WC01͈zJ@VߤXJ׹̪.y6}%:3I  ]9B9:bȗ}((F:/GN`!AMEB6$ l)KO Q`3NczP]FIKL?X1s<;-^5B5q2͉|X"BN WroLOkrʳhs.> stream xXMo6W(owC 4.hw.-B;(Yip\ts iy34#sȻ+d8r7H#(HM C̮>LnGj%r姾ۜx9\R,R&dU•C">N^;? 2)tPɀ6MM*lRUi&9$rwUM?'; '#]E uVgB dQOV@ q,9H]2ͼ@L?.< '_Ӭ1g#)Xsߍr*&c3ټM3nl1!>d\`fXƽ06TӢjwU`Ҫs!3a5(p!j`B(SXE 2<+l|諪*E+W}Q}-y%V8ۻkM f#_4Iy}oɔIoxYmIn3)LTTGc C1 endstream endobj 68 0 obj << /Length 1073 /Filter /FlateDecode >> stream xXێ6}߯ࣄ\/ ݴ6Ml [e/%J4hSF3ggHQ4CF#CМX70QUՇۑe%ZK!xppc?l| q&qi(_ք0j'syOu|u} @E%'6:& fm9[eئ_.H7\"M3 pMf 5riXcu,ʼH_.6)ljХ|(_{60 3WxSCT'!czqpa Ex]V.A/-^͑fp kSbcOQm7{ سc@lo #C/&$ty]w7v`,Ak8G,R #Q>~?#GyZuW+-ƥ* N=K8{RJqT*J}6hd,:~+72$bVih*łȨҶ#d_>B endstream endobj 73 0 obj << /Length 1160 /Filter /FlateDecode >> stream xKs6ޏ;۴=ni K(%]H=hyl'"X% Z ~"G G ǿ A\1lDL3LBCwW=L7.>^6E~1ʱ&11a(_PaA E=={xW5`.C;d$0'o]ٌ餙d),+jO J^_3/5J%J-ކL"*dUx) ZRfzՂ'eg"2\uo/ڵr6\ ;x@G(|D=O9t|x,  !@Hm5zR18]:t/$rA Ş}e+x>Ru뚠r!~o&;!Xh bI$5EK * 5 UtP`{_ϘMjD$_8Y5=p q>B[#0nE!F&:h_HŔҭ]|>Nk7J`Pdt C%䙦D"\+uV8qKW6zX7(5hArW|.\z|e4!f 4S LSáB ^b-.5t n<% ZbRjTA=.˾_of g٦-H> stream xKs6ޏ;۴=ni K(]I=h{du&i}Ep ,b •Oh!+ i)Sh/G/}WFSc/ _ӦO"F9D#&4& N*,aǓǹOf~jB14CK"` sbOY͘N6Se[ܗEE]~8wA k&Vs`BX0݃@D, ^3/ὟYLRА,V3wN$YYv6ҭ] *nCs^mP{Ty:Fo+nMc@7nnQK !b@j;Qosqkp)Al=s\U\6[ ˓(mJ~5N-Z~^>A%ʽ0RcC-`BÊr9*0(\w #zlR{l%!>ܦo""<qŢjǜǡ}H' hQ4D hoŔҝ]|\Nk7LJ`PbK0"O W"YnKpeΪ@tmY^s0&l\.Ye ^46!+zjPp+HqӎBJ$G?=ܩd}kBgDwa%FxfJNsD sc}czac]B*)Un7qSEZLS7,e$U4aHBq" 2ʪ`EOtHr09ѕƈ]QW Sk]}}b<Oq]m6\ ^k"}0{,HZw/UE:〓Tr_:?Npf,HE_0lg22gBUgޘQL6y~q~@~~֘K4|DI%0wlńh/l>@QY{ĦF9N H*jf ! 6-m _4ˣS>+*٤^*NrQwOvnO9<'tj@ endstream endobj 86 0 obj << /Length 1165 /Filter /FlateDecode >> stream xKs6ޏ;۴=ni ˬ(%]Il,(K`oK@xAvC A\1lDL3LBC7^L&N"?qXИ0zA AL?Ka ,)*̉Ak>yge6c:if)&Yˮ+<늺9Y;%Hab0PCTRDm B[QEޯ,e&-hyR;',CswZ[6T]^ݭ|.t ~ݒh)ǀn4~bBĀv7_";6R:xk8',5{⺹d]A'Q֭kJ~5-Z~Z>A%ʽ0RcC-`Br9*0(\ #rlR{l%! 7 Wo#"<qŢǜOǡ}H' hQD h_Ŕҍ]|\N+w,ٖ0"gD3}(rU<w81=&`m0h\.Ye ^4uuyB`E zϋިq8d+A/nF&O3@TK0ٗJ~uA]C Uaɇ4؆ц@jĝ {31zRW[J_}VrGžF I3fͶXTYnNq`c+ ؘoXz47$Ih2R !<+="A@W#vE'])Lv,fTqfB0WQGf}>~oc,M iݽuTѼ:ܒr]:aNv.o\wDcA*: f> stream xKs6ޏ;۴=ni K(%]Il-(K`oK@xAC A\1lDL3LBC7^L&N"?qXИ0{A AL?Ka ,)*̉Ak>yge6c:if)&Yoʮ-<늺9Y;%Hab0PCTRDm B[QEޯ,e&W-hyR;',Cst |֮ sס9׷.(?oKxc~_*x1p?#cX@o1 hH'cqkp)Cl=q\M\.[ ˓(5a%J`G -?-AG l ^Qe0nE9bP`{Et9c6=^6\7܂bQucΧPȾ| r$}V(`"Bzp/aObJ.{>.E;LJ`PlKrO W"YnKreΪ@_tmY^s064.w~֬2vͦ+ʧezaO#]BҌY-UmX؊|B6&z2 ^R*0$}9{ʪ`EtHr4:ҕƈ]IW Sk]}{d<c٩15 ʧC0\/Dx-|g{yTMvJtn9ݺq Z (IVB?>V-.7"~ý&3۲|6\rQ/xk+,&DEg{أG5|{ErSe_ST7T)nS]FY *šp9=ױ8ts8D$Ê+ı!|zUҤ{i*NrQOnnwO9> stream xKs6ޏ3۴=ni K(]Il-d<"vA3DЏWdJJ7ÆK4Ô)r귽+R#1^iS'Nke'0][^怹P Mœ4EOyVf$$uegmQW??ŹJ^3/5J%J-> "*dUx)\ ZORfzр'ew"24s׸n`P9wzynݣλБ0<6 |_uKnݖ wsa:o<ZO!R|ztԞ<'7ґO[!>a ͵%kN. {yf̚M1v;מeGD{`cB_a-_o'u. CHݕX V@G -]Il8u0vƳQ9Sfs QS=k*Q0{smTkYUϛH2P*6*)gE<#ntkj,HE/A䣬B~& }] nE1n96n9|oq{M(g6e l&{8iHçdxc+,&DED%c.Ǔj洅.ˮFf&|ݺeW3;̳5{!B%fP(ťy!u+x;ʑL2B'\%tMIViΗ sʙ< endstream endobj 102 0 obj << /Length 1019 /Filter /FlateDecode >> stream xWKo6W(#.ZzH{\[[=ȿPvƱ"zYjG o>R)C)*= ƿ"&)L (&T΢o'+P7ʼne a*D)EE=B 4» x<93gWo0㒢l4)%fF }nl!NѶISm۪,]E}WyLe_/_e=Il HZzt~EX%2HhXGg~]vo:Ƣ7e8W,V* =8aAi.a6Vv'6ޯEpp z(1/3h]nhtȋI:QʛVv5df"q8+>+ĩTBrY&,A(n+)2qk2hJY!w޲zqC`jo(6S :׳_oBn; O Pxt"h@=<`PeԻvE]qwCst8#Ah]/3mpH&u9.6d'G~L1AͿGuDc Sg<rq5[ %at`US3GFFOg endstream endobj 107 0 obj << /Length 1026 /Filter /FlateDecode >> stream xWKo6W(#.ZzH{\[[=ȿPv7Z_9曏TP~JF#oI5* h}ɢ숕P(DkB2m\Q°J\ᔢ!Q<;̏ջk ̸([#E!EYQBvFtc8G* gWQ_USu}Ww1}wה#bڡCTK>ߣD -L`¯-@XTfl VJ% Ӣv); gX|;0:A'%#n|f523HHA`&m4? pdy0iI3*y?vYyʮ"=L0Q;g0pW%?5gJ%r7BaM 2+#_XPXWKeG+sve0Д׳BFem=`Pm>/@u(9gބ>v&G!8С9Թ lY˷sh\{{xAQiwmsYuPȎkLn£svsd[PM?e%ԻؐD 1ܧ >O4?rlU=%Kl(:l7xx,c> stream xWKo6W(#.ZrH{\[[=ȿPv'ԎC7|RtRUz4 %ELR@TQLDEN&}#VBo ˴ rD *UrSzp@hDx:=gWo0㒢l4)%fF }nl!NѶISm۪,]E}WyLe/n/#Il HZzt~Jd"0L.tEE[o!ʶq`&YT2sЎ>$WߎGϷ:<ODc56:]ya>;Pb4" {BDsqK;"q{8,<=9yIQŞ9 9a0셬eֵGu_?UKy31&1|S8 _K0g3%^'[OlB֓ȼ=?D860Wpb ,HإBS ܄nI8y|KjЩrrznս-Hɽƣ0|R)]1m&N mV3+3cP^ flP1U^!/&-|FE6c7+oZX'> stream xWKo6W(#=d-,izȿPvR;9|3CtF _ !+ i)Ssh}ɢvZjD05p&N/ݦ;Nkf @d0x>k~/]R >`.C,Ġ|$WܐfOiL0l*\'}YET/䴯-d)l57()QG; Yl33AȰ.uIiP զ`%]`sZtN>EVVU~[Od7&~uO37)3I kY ΀2Keࠕ>f|_ƳQ!ϯ !8.?4<;yNVÑř9 rb3YSaO1!~:v¹\X7!Fp1T"ok0gs-_VO>u5qڛ)LE SIH`k(GX ='^ |\6p `ɺ=M:Um&Z9MH %AЍmPM8bRp Nc XmM׮f̜/)a1{1X@bwy fhCQM Em\я;ƦhWAr@$;)j^X&ٌ0\%XwVg Pڪg)c76x* Tɇ Yqp&mh_#1!*gmb>cjN'wao=ȏXà|C z-ӓd7ƒ7KO* <-(7m?(ةu)bt:yз5I'-Z\ {$Ê+ı!p5]\:sqL=ї3uG29Α endstream endobj 122 0 obj << /Length 936 /Filter /FlateDecode >> stream xWMsFWLNO7{u֩\'mEE ;_= BHk;UުhF0rG퍀#^aDhNPNkJH2Q2<8g@p0C4q2-@@%\t-O+z<Rs2%*& fdF>H vL,!LoKy3]pI4xhFc<8jXcO:˴Be\שKtva{˰1a! 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CR?M1F1m?ַouKw짳KoΫlVWw6$Ɓ4:[õ-Bz 0 ܓ) |5k%/+@ /26EǞ-t&K˴OU-"iv 7 (?t !UBfܘmQP.҆hM>'zhr'9^;Yk];Cq9q9Jca*鿑9=''(g1 %XS".>8 EjƜ)E> #-zm< endstream endobj 194 0 obj << /Length 947 /Filter /FlateDecode >> stream xXK6`n2P1|ȡA>i[V!<}^ʱi o>~C5"+7R)dXsb26 LvíiSQQE ҲF1~sO|z*H2\! E9h76)y9UArj{]0Yd{ @,BNJk L$ rɯ>߽78p.`! ^ƭG:uؽxyL1׋@8.BlKgTٸ/z˰|inRw+M8"c}G_|e>AP@s}$4zwYBgl 9(*D\N. Dx:MK4x]ՇNbj%`~P>"# %ra }[rA{[%|>t^f*. \{\#ʇ9i,%% J`Jk?Fa+o hBF/#G31w(h6<ᘀݴq: xW-ަ.U&65?L.1iUlđxo,3[\x:i$僜)J'@/zy˰5t:M7ۢo<6C )3.PEWzk M^/:ia|ɋ/4Qְ{%OTy)Wm3t㿏 N/Q{GՏ4@u8r_Ga.pLo%BL08֤قe NkAb]ּy_;AoBY>#ozj endstream endobj 199 0 obj << /Length 946 /Filter /FlateDecode >> stream xK6)؛ T CzhѦhhGDm-9m}"W5Z{1 qH eoQK Oaba$ޤmP`%|S(NJ( Cy BЈ \<[~y*dhA %DuF_۬ؖ*TEƵ:*meqV??]'^b 8U\;Ih"Q,|ʽ$?(ũs( 4IL0sCݫbT0| {:vh_A{PmٵWZ?235pS+p E ?Cʼ]28J&3i B>z ]1破ޛSP!2ubB*wy|dT6]g>) ~>"{0e~c^a|^HaJu^". 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TdyEmKQ\eLc6'1pN2K XpG>?92_G5S92/ɇnKL2߆Ϛ mqj60E@ի__Owzq.1["N2$7Z+N`C<qNC ; gIUbd #nf% ?EQ3aq̮g9XW%.|ꁑmO&#'we;\ԡ<+6U\XEqƕEY>l\Qєivt:ڬ#o燲sචXvT~XE>o#[7 ӺnrӮE]RGjpMkJ0x[r=M4)tAyM^hȟP inÃQ"/GMu c_jsAe HRǒlߤd|=}â@Pvx5> stream xWKo8WKbRt׋={P,9&"K%ͿPCri\D|͈b09ϰˆ4:raȦ"˓~ڑZm ܹdlZc6'1pN2K XpGFs ?\ɫSn!*d$j DC%sd^nKOLUoÌgM΄ɶhXqO-:t'@G ' !zzS0(z36>6TYU,VMf0Fa]z[u1Uev5A,:FB!><}DIp^#fITQⱊ2kEY>lTl(C|idOtDPv.TznJO_k' ǴUt)4C$t ל)~"]K !#N(P&zetS U H]$jOvD =0"Q2 M!(@ٵXer({[w-G{b=5lIdꮥښ ]=5O?1 #] uq˽Y*D(%nio5´IUt))MݛEnR*V[#-c͗4VE2OLUhטa!-j ]]c/Ἢs:'(S"iK CQM½n,Uni ]⼮R#Æ:v3<|J%=e}O?~=?+OAk-,7mf9\M5(yI3$ pc;o1s?+@HRR{sKmP"^I+͢g jRXqwE*oAE endstream endobj 387 0 obj << /Length 1276 /Filter /FlateDecode >> stream xXK6Q"/MѢE@YmߡH,)5XC73?";r Za#ÔIThlW*R`%tߎݦ:N+  @h"gq:#޽|C mHpQbN4}:NidyV6!*&N͇_d_7DbK/0$6k $ 9x~rJdP 0R"r0w[<6#Sc ֏,Fpo~D8{,b.f=z4kJIDl10 P#I%,^xdFSp7|%C>` fXI([XpF2B19`iu=KqnMHw6*%`spKi:MY7}fI|rkpҭہHDZ K}!6A^=/ko#.ZaJ,_˺/E%$i o vqwʧñCﴊO#cgۂl}Ӣau 960OѺSVE ,ӕ`%oZxV]O0u{͟>ʇᶪCS{H}7FX">$\ݿg)aTk/\U?%m"eۛ5Ǽd ԸY _h endstream endobj 392 0 obj << /Length 1277 /Filter /FlateDecode >> stream xXK6Q"/MѢE@Yc+iw(R/K4@.Do?";rZa#ÔIThv1*R`%t,MæN+  @h"q<_?n^ b\H{qD(1'mw>x'4l"+Sm'ׯwo@ŵŁ`f<xOf%2H 0R"r0A^;ƃ}]? ĕXC.[ĭ aªڬ*WBqԣW)| Ye+a+Q .3P!H%,^x32H`)wFF1D1|^$1#'~e +eK/ ?BF( "t-]S i]틢ڻltn)͇ݤI+t&s7 绩\q޿~ڎD- jZX"z!oh'sHNԑ,x_ D”^I WͰ] n I~$|۸Oa]==u$NlS?nڶBZ>U EL䋲H3߭Qj4GBtqc9YXlm Df? kf[oS=;TĞpB6|K @GbAɻ}v_xlTV3(Y౲ߖ[Јy''u<ʟær jj !< `x8Y OdY02]STέqz@۷4“;ČB'S83і hǾpk'OO4 W 9NN-tcXď,VAxDɤ.,0P0ʙJ!ahw9]v`q`WB0i_r@JKM/kR=Jҕ$$I4I -/F"A}A?![3{!CEGҋ7 I+gds5=Gx> _)?+t 6m :+H;`ufUaڬH$>(nl* k CO7mUCS{HfoMSwM;qZ#E}b!̷X$w7Cǘp?;jsac%m2燪c̪\ Y̍?l, endstream endobj 397 0 obj << /Length 1279 /Filter /FlateDecode >> stream xXK6Q"/MѢE@Yc+iw(R/Ku1)r8|qfhIK#qɰba$S{Xm"jm wS)S(NJ(Ą„ȩx\O~ۻo0i&J̉F^1 ۬&TqC]&Fqmq`D!'ޓ@ 6.3.FDno"ȫxg{"k+7[hv7ߧjD|Xʟc)ar x O>` >*emZ4/|˒1uCuv8IL_;4^LVb^ bCWrf 1!m2PWt:ՆӠ^"xГb+cXu]7i86Cy )J&шA#UR34C;J}.z'v*( 3zJ|ncٺ$({Ҧ]Xgf[,']h'o z?&;AOy=YNPuY{,K=' Z endstream endobj 402 0 obj << /Length 1279 /Filter /FlateDecode >> stream xXK6Q"/ MѢE@l Vw(R/KNk/ŤǙ #!'-B;%ÚG))NŢmUTkKX M5"F9VD!&& %EЈEN\䏗f{-U`B2!#"D9h{n7qrH6+r 9UAܶqrl>nxs]Gkz $Q\[!Q fdP"( [ۆ *=p6V7Uc NK6#8[a†UYUqՃW ڔ>1_pς h0R 0/ hʝQ Ql w2;IL(]90JDR ǂ~ORŔ Hc.6! ?[՞=x6܆4ov&uڮ),&s ^qFM7n@mA(t!A"ߤh'S|) 3?rR  S ו5 w/6]XWGsĉ%!ml<ҲM8mQDEZTm,FKlp$lWd']J!: Q6̀e9lFqgSBچ+uEcWm8 :(=+fJaoQ{0PqZjj37d T9Y%5CN98`rwr`qzAZa=Ҟr CO/׭z,[W2'NN?`h6@pzFȕCBO 6\=s"H<:0qZq+ 8$nJ sOϚ>FfH0_XRWO]%"Lش1H}+T\ub+ڪY {]`Xegf[,zf&E^w~.:,y=YP|_uY{(K- } endstream endobj 407 0 obj << /Length 1278 /Filter /FlateDecode >> stream xXK6Q"/MѢE@Y$7P^k/H9r83A;D/wMM%ÚG))Jl7*R`}0ffSd QQ CIB 4bSxr뻗o0i&J̉F > ,ϊ*TqCYuC.-Hb80B̌Wg D QKDn+"8ƶxܵ!AkqZ^bD8},bA/W  2OM#Ȃ.C;هG(N@#x bN p'ez" 3v͵p,8?M=T.PL9l"4::钟ۮlҠñ]IQn/mHfiRߘ‚̨xtץ[+>tA!jn5 k-l G!7j&9%Qx" iu[ G{jďj)2(Qqe*J{̂$:8ċMĝ wV}$qb Ol{h*.jυhqݺvB1'ee+_wZ  Qٯ $"#l.D7bm@3``ά;ۺLy,6p]pB`5s @Yb PZ}q_v^WJ8*07 |hpTa~<4!KbWd i|ؕhz#tk)%fz:JV0 endstream endobj 412 0 obj << /Length 1042 /Filter /FlateDecode >> stream xWn6+ђK"]2vѢfPlFRIA"%Kܺ Ln,sh(N E"Dq ,|r}+D R6Na3g3AUKE(GC Ј^]b;rɇ)p"Mb*!B z+I7.~[pLLbx2c[ȿXKvb0Dr#G<(%@&9C !-lC:Elϼ\ɨX2-\ߝBpo FɕNĔ]D"  `Cʊ` u9IM4 1Nd/ M2c6%Ǎ Gkz׋'+3#> \mҏ ">7*znſ˨ oˑ-!ڬ"HS%$x$'[xI{.NAM_S*h"qZb `x봃JQ*1o6nѓHwYM^`!|:l:([g;Rh1du}@Nၽǎ0>$P Q\-~yɚ)ZYsۮpwI:-)Yh-J(Q%TQɾ]ꑿd=*u A yަ^3l\TjNC7/I٤Rw.-|rr*$%o<[mwXMv\5{}~ ͪjF1o&~uǎ3O? t,$TB@KwO]d?]nzn 瓲AAՠb> stream xXMo6W(O-E{hv{PlVRIE}"%K\ t^"g׏rˇ*s0"%b}ޕEݤE7.~_tfFbi5϶f^%ڙ+)]=.@ 6kj(Q4OdIH3 !_w9Js! 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AxW4yUeF60R9@Ð} ($)T.Gʀ((Sl8"=H|i-~;AK*T٣C'TPr$n&rT@uqe$Am m%}A? zMg E]m=DAO+{Rv%v-:> stream xYKs6WHMK3t&iC6P E"e> $A=2M^ X.w?|؅qp3  H3QE2)"/``mYID C r0u N9受Kĸ"H`.JİϺ3LfE^5nʗiSl_gњ<(-(PQ)J:P^9|ДAFBd{ (&0p{xgx_f`y1&7[kJXVGvE林~kx`%Q%ֲ!CZN֋1$O; ")!iix(btPd{ X|_^׹UYﳕx0_@|w&{ˁ&\̿wajK@c\"QϳOyC]D &Ythf'<)9tdzb: LG9rUq^仺٥um_Æ3iZ70j8MӀFRp{+IBgz$OP=|0<$5U!yBյtf}mOcW)-3e QAaA/]KU#"Wԅp yDZ!Ci` xӎܗ0m+!6fڍi >=.vy1:\ƀe7h|񐞔B}G@(@`BqkHKW[3q(!œF_6v[qϋ]hڸm;K+> stream xYKs6WHMK3t&iC6P E"e> $A=2M^X.v?|X@8ZF8i ڿGLRPhqG_mPFDk8#tDqQ*\!LlB tDSxZӳGŴ*2J8EXI+Md$D|Gb 7xΨwumVfcs~vcMiu۬%$.2m[k.X(* DҊw't(t7^!y* eQLl IcNEYۦ"[`v>ծ{^˳g+a?(`LvM<>m .|/'00I1D>BgRŷ@L@%TN OxSrHt2 s:H1#Å[ 'C&9yHՐmnf5?1 DűR"\2( mk8[ -V:`/=:t^ A;5̈́ n _C;(F\'"F``#~DI_O8΄FA\".6B}"ΠzW9hk+-A Q^if er"o;y=t$ɽL]b j8X9?@CzE!1^ѹ}!Ȁe,SXi(~ #@)zP✝'TQ1+e QAaA/]KU#E  򢉴B9-m/cVB>mv/jצ%I\7u3e [~|Sy ;D+ؼ GXCZQ*8si.PnE/ҖܞT,PxN #nd#p^~ PI?+#{KZwDĨ$Gp&> stream xYKs6WHMK3t&iC6P %"e $A=nmQLXnnCvEޗjt< x+ʓ!xGvBJwPƐ44_em:(f^|ۧM=<}r~DwgҸ ;חt-yڅq 0ƎJ=D#nٗT!/",`Ff U: GS MzJ񱚘fB: ӑp h@blqgFUnvi]OL_ iPH n PAMʄ:)`>Cqu"%LmQ7z)9TxOu7<%x_-|\{o]F[Y[٬2u G`Qγq9# (w$7g=^a쇠Qނhf%Dw{I{] (@'przp9 S I1Bbh={B.cJCK) i9BBsvPuGy8tVco[Zw8G t9lU@:.[(ȋ& O״\LXU;rĶ|0_nLK8蓸nb'fB`z|?[ݓRH7 W(G\e8b` iIGgNl"iN{ww_D"m]ۓjڸ#9K7ny?(eզnM4XV1"ɑܿI9DP9@aa+d]  ljuQCN6CHۛmy>o'벘eW`Tz-Z!G=d@e;۲5`;' ˪]K>lb*L_ endstream endobj 547 0 obj << /Length 1388 /Filter /FlateDecode >> stream xXKoFW%}?ZZ7n{Hz%b#H@~}g(j: @/"\|73$La 6\"LMgW/}WFSc/c)rS(ǚhĄƄB b2x|\(`I0']ѻ췶osNMts|OUe5<7朩lsu{/ޟG[d)l57+`) X +dUp`=J1ps{ ]z:?g9En]a3uqiF {"IF~ա 63 ؔ?M=uMb}űtW(8\]%"^U,Әs9񋊱I {&[13Do4*πw8FTZ4uhxB$lq|{>!ctFg!ݶerUlQ][/SŪ=_oW]ufEW5u0 ]݋0u:^ a<;EvM]V?DQꖽwogM޶8-9I$5;T-B{u0ҾU`}4C4l:pz\a(np>t4Cc5 kf3"!$6҅&Q awɵU_K9㵜ycl b{E&so3crbpta& Y-Eb3Bk6s9șNi'M%m;ۼ>GOfU棃'Ğ4IU^:JCI]LʔTGp(S ܞHbFB->E^#@K00).P^Ұ|D>Ye9u pÁ=r<AB 'ȳPͮayC Bbq_\Ǥš cY nkr=߈rIvsA=`+z\_2(2׆86$Uɧ MOA_;&m, endstream endobj 552 0 obj << /Length 1386 /Filter /FlateDecode >> stream xXKoFW%}?ZZ4n{Hz`$b#H%@}gHj8 4@/"|͋"^\ٕ•#ÆK4Ô)+K+R#1hױ9)bcM4bBcb1E<o.02X&*̉A7K6˜S5f.+UYw Ͷd*ݭv^y˿rGD@ [͍ÊX b"#V?{g; Yl G)fn!{sk@Og/ k6\_nu%vn]dݺD.wqp><,&3ɋ5;>9#ZVn6]W- \h}*۩hp=Ɨe4RGmPCA;Nǻ[ap0GB}t4;mg9KauumF KH;"IB F^ H:D eAhY$W[J0:9NZÑљ|}J ;(} ۲τUM*ڮOeŦ=7]uEW5uP8Qݳ \>eH1bw*횺|8cb}./nxftmyL"ܡjg`_'X ,{CX1xfs 9.V !JБjȬ?&4X+`HϴX..4KŨXhL%RckCz Ha4eH fOEۭх%fSַ`_lV( 8ș.-"UK4̳ 8k;Zl7e> Gk--3+cl*_\c7Mjv%YzjQOq<@wQ"1CX؝/mY ?>8@z:P/EsL[y>O /O?Fйy u旙Pǵ> 0K%=.& X<(X(ڐ~L*@?&$ Û=rc'|ƻ>qD9뒰vu !u-&vTTlc*s HMO!cm[1P)9 endstream endobj 557 0 obj << /Length 1385 /Filter /FlateDecode >> stream xXKoFW%}?ZZ7n{Hz%b#H@~}g(j8A/"|͋"^ɕ•#ÆK4Ô))kKxpm1ʱ&11ahPa "-볋K̅bz D sbhb|]uݪ]A+ DQw/bsI eƈө,kE)\^Tݲ]۶ D[CCb)dx@k`]`94ilSu~R`6܊!:?D :X 53S I|XCHl Ml 8t{1n/rSI{,Đ^ ]"L>C1663|qeZ80׷ެ\"a0~=cN }Ғ<-ބDM<6oyY(P$NCabO~})ۏciNMb*WsnB #1XŤ$eV(Ĕ@08nOLq$1#"v,J @h ^&%Z>K\XY}oycj!`y@U#HHBKCY"Pͮe<8DnڧOS4;lʘW #tkiSm<)G ܱN$ Cj]-$qH1Zr֬V}-HpX32xA* ډ߀B0>nxSK> stream xj#GVd93#-WeƴxF'%Va:  D<)aA bHEs gA/6gk>4Hg [QX_ sjAXF@FsF*[U kCiICv6F֫gЬ.Xѭv$aet,ˎכ˻"mYQؿzwzKZ\ a?Bކ?؍ 4lL'zv*~->own+Z|ta[Y|{owjۯp6[|?6wsewo_֏tc>1! makZ< .~ۇ?ҍ}rϿ ibˬ~;`"`q$ZdTn#vsfFpP D2 ghLNqV8 8O))n pwq\Ip6iyT3MԦ4$:$LmL!"ǻQ͵$bmb~3Sk'*:mɳvtJ?w{WtJM'MB'{1$-HGk$6h IԣmY=<*Sc< n O“zz1ă;sLJ)s}OOiSf<> stream xYMs6WViX|#394miS:Mz`$b+H' )Rlղd&"}o]K5?9Bn8:#';>ۑe`Mm q 5. eLu@@: %\uM<+?\ @ԜL.ItQS,;&DVU.Ɖ3JgʋO Nϸ$:#XhH 1ecNc><1v Ry2ek lQQ~UfzṸU,(܎KoMAߔht$y5NAs˝%jhVă)3 C˘IFXkKQdߔ5b`YĔo?Epp[|˫Fyp_%+q~)Ve77* FքfG'wzVUjxms$zrhԒiQ+ g*}Z:p&4N0)j0]^DcPDRgAԕDc0%}potuSG_fkx|39a` *ʹ`6XQ&IZu9ctUCvٿMhz-]$1-z7|.p]XӦO)J=؄g/1,Ey`ZuYq7 ԑAtioIz3Gu]ڗYkϼ+EAtJ +Y}D % 58#d25$P19wtEV}S_ٴr[C "ԚwGcEG:R"7坎y5>ۗT}CSԶ kQ`BybHiO/ ư ڻNWr9 7.F7,ӱУuA_-isHs,ynĈa3",7 endstream endobj 568 0 obj << /Length 1364 /Filter /FlateDecode >> stream xYMs6WViX|#394mi'S:Mz`$b+H' )Rlղ[g&}o]K58ÈМZ7d󝗞H2Q2tؙ|wwA 3KC'ea WA]<|599=>P!5' bb]T0K&3n} Uq",b5cӣ,x3.C1$R C(~ nYjӘ{2ek lQQ~U03^\\Qy&.1FS7%-5 f^F7A\Arg d{ '2fQ6?RT;7%vMiz1DkQ@;:jjpCܗa G ǭEGUuY,MM D75K9d0NoUEƉY>N'F-Ҡq*K>%D_Rp|`)^JkἚ/3L+Yu%LF_0;Aї^3p)̭C!D0UVZ\ |\Vܨa$V1*I!uDl;߈&k K~fϖ>X LbH8.b]p{%pG0:kQ“lOЧ[ z j3ƢҷvŨa,FlɨbN~lJb[/k$,_PVʸtI:7lܧ\o%%5eP ׍ǧsZ,+_Ig/QhIFXzSzx2%6!al]aF ?jOI˦-oevQjN?D~CCzZ 2@㨎j'i(Gt%JMMͶV|uжF1l-Kay38deyi~U!Ii pۭ\/r= ܟ׽;> stream xYMs6WVi\|#394mi2Mz`$b+H' )Plղn'}o](%$%Oҭp™pŨ0(0E989yɎTKMR Ƹv&߄nqaN5aBӔ 0Iv~KF(1T]TLfCyWu- =f.O NϘ Z͍ X(ecVa>{a}Wb1xFFU]Lz)syF1繟(̌KgMAhJ:ͼ'2xAeN+b^4e\$z3RڒTY⻦UL=rO헨[nnmy5@ջ !˰!~Fr#/媾,Xy"h7l>릚ҏWĉocE'ѓCLF8+VY' ׁo/VQ>J_ᢞ/sL#$u)LF7Zv& n/l5.>.7ۄn1UVZ%ee]lVܨa$V֪*H!Fl[߈&k O~fϖ8&qjIbP8.`]p{pG0zkQ2ܑlNЧ[ j 8tj>iդ -FsXd1|KFsdSf)MS#aIJچ%%`>ْOiKJ55eRS׍ǧ4sZ.kW g/hIDXzBЩ=}fzE>LQg@j`gHǧeӖwX;rר >N٧`Xrl#<̋yM—g(Lm꠵u,Z}" #yՒ"Gմ]ɰ@\/jЃKAyLXM-!u# &<{aȻl_hKwc4. %vv+Wgz;[6&%nJ9fs5%T78d '6ٸGKQ=.jPe/ȧug5fV֝û;Ж*4L2pS{޽hjҞ/"$'oQ > stream xYKs6WViXδԉ&=0mDWwA)AjSq(h[`b0m#0"4V( 5Yg|';R a v&AP PtY!p5xlW~ 9\K袦Y2oLl<]ffyeiNϸ$:##$R , 84@9b UxbUl 1"*SVrTͳ0qQ6)iH0j(6 2;KЬ!Sf($=1*teזɾ)kJSmԳ)$ZK_ZW:}p5\ḵHS.e WH0&|)5>lک8"IPԒiQ+ g*cZ:Mi*FrᥴΫ2ty/@I$R({+ $F_fkxN9`Dc4w2ϛ)r4MPVT dlWmdf'q:Ǭl!4|YܐIG&m_tHA~.$XXӦ*p/u,yBH?x/e]v!X lʆ%T{kG?׾N%_{Bl$\) =SjX{*j(nA1 @:{Gafqs6%/.rP핔/~˦U g %fVڞ@0jkpGPk:޽hjY *ё[Do0;j=n}CmT FkmJVϑ2l/^)gXaLCt.'ß*mr騔ڶwo@MB VU~ȧY Ⲩ Dp#FƯB' T endstream endobj 584 0 obj << /Length 1359 /Filter /FlateDecode >> stream xYMs6WViX|#394mi2Mz`$b+H' )RlղL.-wo#'lkp9Bn8:#';/=ّe`d368f2N`;%_MNNTHXD5̒Ɍ`BdlUb0t6˫X(K{@tz%a=$9e1Q1={?2ekOQ@a_U4Lן2<~jbhMIKFGWDM4=WY"fE<ٞ2C0$ dT/NM]Sj+EL'ZK-ŷD5!˰c ǭEGߊUuY,MM D75K9d0NoUEƉY>N'LZi8Wi%ׁo/NS)8>0 /p^͗ˋ(6)H,u%D[ FNP'055[S !zhUs1y\ VD+n԰IVD]j$AH]ێ"7" B$bp?h&1s$qTju\. E]ẕ<.< Xg<0#SlOЧ6A@J h|`E5o }.F sxd1bKF sdSz) l]#aIJVKI$dK>z5,)魩.sTZpn<>=byu]ZM={B3WN &J'ң'tZ=0У\ۗQ.n [d`zz?%R;3}@:>%-QFO,!t!&cqTUy4OaiX z)f&fۭ-:hm#{6˖z:@O8G_!ND*cyr]֥l4ʦH[ҵwCe؏[Kήz틥_F• yW;׾Zl!<4@{PagqYx6ђ./,r/ʦU g %gVûF0jk0PPk:hjY *QU[Dr^WqܾæO0Z28ظP^9RFT`,KlBՂlP ^˥R;s7b9 =Z'XT"6gD§ˢ$$qmF ܿ_$ endstream endobj 589 0 obj << /Length 1120 /Filter /FlateDecode >> stream xYKoFWQE (P4ju(l Ȳc@D w(R\\r%r4o F]@tG0i;Z䀆gfO{V[&88 4n ,VXrl.ԕxtӿ%?o}K1p s\ E!.cGv?s9frZAOgf7?T}Ry QFϝ,CǥEuBA(krHZvRB1sT /.BNثs*oIIDt\%Lq_B4 %wVy\SxZD)t;`9l^V*eQ UҞi%}o F Ү)%3[ P+2ϕWԨhL!"Hm%9FIX36 j~r_JktQ3\!lڗnBU@( :Z u-7VҎ@6bj2u4 %SN57n' -`.C k /_ Sc]SœhqT* X. 0n^70!cAGJ VkS؟9&$\P#=(Gce|lpљxКfK-: eb{qt`$¸))X*zֲmcɶ())(@Mo`s$kRC w. Va{IMꤽ 40mM['VG3RA)#l]/f$p>e{y z?OѶ M@1~Am>s.u'5,WxN;_ԗܽB!T"wl_O'P:[l盗o%Ðv0?vO_6_5>hZgE'>r endstream endobj 594 0 obj << /Length 1093 /Filter /FlateDecode >> stream xXKoFW:p3nC  pS9IGw$+ZrmzJ7<=2hZ??II"4lOG+2 џf Ar+,Ce@#'"C]q9G~wӫd .Z(2p)]2MR .,)[ml>VF7dxT.4ƽ>mUMmE} v|KKfm#Ƶ6HÍQ jIXno !{Dh\#{D8׽}kfż"㑊;3MsU#>]RNc5ϋYJZ3[ZS%QO^TFp۷xQ-Z;qurZH l rޑa"!I^䴵(pʇ11-ƛI 6A>XBٝL.H$Y>YlB2/c2p6k;hv|V[-Ev`@iERb.FOq./4p]QZ֒wHÅa?H8{N(-7tJ$I,4!H ې w΁d#$;e,_ƴmUfU^TMfr4>>;TE oȻ߃R endstream endobj 600 0 obj << /Length 862 /Filter /FlateDecode >> stream xWKo0WFV"߱ eŅr0Y6"//8vv $.'}xB8!{-BFa%bÔ)48g)l S R(W]z}V``2J1fsh>̘"sg0JՌfЩm6a]w9;Um?+}bWjGfUMծ{[~[H$єtKQ8N ٌRbb+$V]_2@βj[8G]|յNsnl]W!,@=Kʨ[S+y> .] 7Kmp ֵ5Lf[6N2Mfgp-oԡ}!?2HbSmvÔ704Qbѵ>i{=|_X \UHA@72)Et:s÷uʷY˿CՆyExo^]n%Ẻqrrp{#)Rj,)LW~+LRޱ 5}ϑ;"܆i)Wߤj^I1~ Օt҇kǫB΁ѹ8~8E]>24u&%5Fglo~m9F17n l݌ cMx}iU6ͺU_WS@WdSٽΠ9g8=|Qz~r( endstream endobj 605 0 obj << /Length 863 /Filter /FlateDecode >> stream xWKo0WFV"߱ eŅr0Y6"//8vvEiD%.kvf" )ƯBW k.+Lɻ_^gG\L/۰) )bf" Dhd4ܿ7?y6?9}N P ͗HcI@T 1{2cEf[oWn[_0)]W]qf->g)l S R(W]z0FAkb00c:q (V3äaw{֥_qxczwqӝwGVөUޖ_ƃ>) l4Rb! 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Structurally, it is based on the ref10 implementation in SUPERCOP (see https://ed25519.cr.yp.to/software.html). There are two internal implementations: - A port of the radix-2^51 operations in ref10 - fast and constant-time, but only useful for Ed25519. - A generic version using BigIntegers for calculation - a bit slower and not constant-time, but compatible with any EdDSA parameter specification. To use ------ Download the latest .jar from the releases tab and place it in your classpath. Gradle users: ``` compile 'net.i2p.crypto:eddsa:0.3.0' ``` The code requires Java 6 (for e.g. the `Arrays.copyOfRange()` calls in `EdDSAEngine.engineVerify()`). The JUnit4 tests require the Hamcrest library `hamcrest-all.jar`. This code is released to the public domain and can be used for any purpose. See `LICENSE.txt` for details. Disclaimer ---------- There are **no** guarantees that this is secure for all cases, and users should review the code themselves before depending on it. PRs that fix bugs or improve reviewability are very welcome. Additionally: - The unit test suite includes tests against [the data from the original Python implementation](https://ed25519.cr.yp.to/python/sign.input). - The code (as of 97cea3f0d910fc627c7b57b1bc4d783cdd0c2a4a) was reviewed by [an independent developer](https://github.com/BloodyRookie). - The code (as of dc9f58f2c874463c15465326efc040d17a627b3a) was audited by an independent third party, and the one issue found [was fixed](https://github.com/str4d/ed25519-java/pull/31). Code comparison --------------- For ease of following, here are the main methods in ref10 and their equivalents in this codebase: | EdDSA Operation | ref10 function | Java function | | --------------- | -------------- | ------------- | | Generate keypair | `crypto_sign_keypair` | `EdDSAPrivateKeySpec` constructor | | Sign message | `crypto_sign` | `EdDSAEngine.engineSign` | | Verify signature | `crypto_sign_open` | `EdDSAEngine.engineVerify` | | EdDSA point arithmetic | ref10 function | Java function | | ---------------------- | -------------- | ------------- | | `R = b * B` | `ge_scalarmult_base` | `GroupElement.scalarMultiply` | | `R = a*A + b*B` | `ge_double_scalarmult_vartime` | `GroupElement.doubleScalarMultiplyVariableTime` | | `R = 2 * P` | `ge_p2_dbl` | `GroupElement.dbl` | | `R = P + Q` | `ge_madd`, `ge_add` | `GroupElement.madd`, `GroupElement.add` | | `R = P - Q` | `ge_msub`, `ge_sub` | `GroupElement.msub`, `GroupElement.sub` | Important changes ----------------- ### 0.3.0 - The library has been extensively profiled for contention issues in a multi-threaded environment. The only remaining potential contention is in `EdDSANamedCurveTable.defineCurve()`, which will be rarely called. - The public constant for the curve name has returned as `ED_25519`, and the curve specification has a public constant `ED_25519_CURVE_SPEC` to avoid repeated lookups when converting to and from encoded form for the public or private keys. - `GroupElement` is now completely immutable, and all fields final, to avoid the need for `synchronized` blocks over mutable fields. This required some new constructors and paths to construction. - `EdDSAPublicKeySpec.getNegativeA()` and `EdDSAPublicKey.getNegativeA()` now evaluate lazily, taking advantage of the immutability of `GroupElement.negate()`. This boosts the performance of the public key constructor when the key is just being passed around rather than used. - Support for X509Key wrapped EdDSA public keys. ### 0.2.0 - Ed25519 is now named `Ed25519` in `EdDSANamedCurveTable`, and the previous public constant (containing the older inaccurate name) has been removed. Credits ------- - The Ed25519 class was originally ported by k3d3 from [the Python Ed25519 reference implementation](https://ed25519.cr.yp.to/python/ed25519.py). - Useful comments and tweaks were found in [the GNUnet implementation of Ed25519](https://gnunet.org/svn/gnunet-java/src/main/java/org/gnunet/util/crypto/) (based on k3d3's class). - [BloodyRookie](https://github.com/BloodyRookie) reviewed the code, adding many useful comments, unit tests and literature. str4d-ed25519-java-7c26a63/eddsa.iml000066400000000000000000000020661327341674300166230ustar00rootroot00000000000000 str4d-ed25519-java-7c26a63/jitpack.yml000066400000000000000000000000241327341674300172000ustar00rootroot00000000000000jdk: - oraclejdk8 str4d-ed25519-java-7c26a63/pom.xml000066400000000000000000000152011327341674300163500ustar00rootroot00000000000000 4.0.0 net.i2p.crypto eddsa 0.3.0 EdDSA-Java bundle Implementation of EdDSA in Java https://github.com/str4d/ed25519-java UTF-8 CC0 1.0 Universal https://creativecommons.org/publicdomain/zero/1.0/ repo str4d str4d str4d@i2pmail.org scm:git:git://github.com/str4d/ed25519-java.git scm:git:git@github.com:str4d/ed25519-java.git https://github.com/str4d/ed25519-java ossrh https://oss.sonatype.org/content/repositories/snapshots src test test **/*.java org.apache.maven.plugins maven-compiler-plugin 1.6 1.6 ${project.build.sourceEncoding} 3.7.0 org.apache.maven.plugins maven-surefire-plugin 2.21.0 org.apache.felix maven-bundle-plugin 3.5.0 true net.i2p.crypto.eddsa, net.i2p.crypto.eddsa.spec net.i2p.crypto.eddsa.math.* net.i2p.crypto.eddsa org.apache.maven.plugins maven-source-plugin 3.0.1 attach-sources jar-no-fork org.apache.maven.plugins maven-javadoc-plugin 3.0.0 UTF-8 UTF-8 UTF-8 --allow-script-in-comments

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attach-javadocs jar org.apache.maven.plugins maven-gpg-plugin 1.6 sign-artifacts verify sign org.sonatype.plugins nexus-staging-maven-plugin 1.6.8 true ossrh https://oss.sonatype.org/ true org.hamcrest hamcrest-all 1.3 test junit junit 4.12 maven-plugin test zzz zzz@mail.i2p mbakkar Mohamed.b.bakkar@gmail.com Philippe Marchesseault pmarches@gmail.com BloodyRookie nemproject@gmx.de Jan Willem Janssen janwillem.janssen@luminis.eu Lyor Goldstein lyor.goldstein@gmail.com Ilya Maykov ilyam@fb.com Mark Raynsford code@io7m.com rick.parker rick.parker@r3cev.com Christian Sailer christian.sailer@r3.com str4d-ed25519-java-7c26a63/src/000077500000000000000000000000001327341674300156235ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/000077500000000000000000000000001327341674300164115ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/000077500000000000000000000000001327341674300171035ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/000077500000000000000000000000001327341674300204235ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/000077500000000000000000000000001327341674300215035ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/EdDSAEngine.java000066400000000000000000000417741327341674300243710ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.io.ByteArrayOutputStream; import java.nio.ByteBuffer; import java.security.InvalidAlgorithmParameterException; import java.security.InvalidKeyException; import java.security.MessageDigest; import java.security.NoSuchAlgorithmException; import java.security.PrivateKey; import java.security.PublicKey; import java.security.Signature; import java.security.SignatureException; import java.security.spec.AlgorithmParameterSpec; import java.security.spec.InvalidKeySpecException; import java.security.spec.X509EncodedKeySpec; import java.util.Arrays; import net.i2p.crypto.eddsa.math.Curve; import net.i2p.crypto.eddsa.math.GroupElement; import net.i2p.crypto.eddsa.math.ScalarOps; import sun.security.x509.X509Key; /** * Signing and verification for EdDSA. *

* The EdDSA sign and verify algorithms do not interact well with * the Java Signature API, as one or more update() methods must be * called before sign() or verify(). Using the standard API, * this implementation must copy and buffer all data passed in * via update(). *

* This implementation offers two ways to avoid this copying, * but only if all data to be signed or verified is available * in a single byte array. *

*Option 1: *

    *
  1. Call initSign() or initVerify() as usual. *
  2. Call setParameter(ONE_SHOT_MODE) *
  3. Call update(byte[]) or update(byte[], int, int) exactly once *
  4. Call sign() or verify() as usual. *
  5. If doing additional one-shot signs or verifies with this object, you must * call setParameter(ONE_SHOT_MODE) each time *
* *

*Option 2: *

    *
  1. Call initSign() or initVerify() as usual. *
  2. Call one of the signOneShot() or verifyOneShot() methods. *
  3. If doing additional one-shot signs or verifies with this object, * just call signOneShot() or verifyOneShot() again. *
* * @author str4d * */ public final class EdDSAEngine extends Signature { public static final String SIGNATURE_ALGORITHM = "NONEwithEdDSA"; private MessageDigest digest; private ByteArrayOutputStream baos; private EdDSAKey key; private boolean oneShotMode; private byte[] oneShotBytes; private int oneShotOffset; private int oneShotLength; /** * To efficiently sign or verify data in one shot, pass this to setParameters() * after initSign() or initVerify() but BEFORE THE FIRST AND ONLY * update(data) or update(data, off, len). The data reference will be saved * and then used in sign() or verify() without copying the data. * Violate these rules and you will get a SignatureException. */ public static final AlgorithmParameterSpec ONE_SHOT_MODE = new OneShotSpec(); private static class OneShotSpec implements AlgorithmParameterSpec {} /** * No specific EdDSA-internal hash requested, allows any EdDSA key. */ public EdDSAEngine() { super(SIGNATURE_ALGORITHM); } /** * Specific EdDSA-internal hash requested, only matching keys will be allowed. * @param digest the hash algorithm that keys must have to sign or verify. */ public EdDSAEngine(MessageDigest digest) { this(); this.digest = digest; } private void reset() { if (digest != null) digest.reset(); if (baos != null) baos.reset(); oneShotMode = false; oneShotBytes = null; } @Override protected void engineInitSign(PrivateKey privateKey) throws InvalidKeyException { reset(); if (privateKey instanceof EdDSAPrivateKey) { EdDSAPrivateKey privKey = (EdDSAPrivateKey) privateKey; key = privKey; if (digest == null) { // Instantiate the digest from the key parameters try { digest = MessageDigest.getInstance(key.getParams().getHashAlgorithm()); } catch (NoSuchAlgorithmException e) { throw new InvalidKeyException("cannot get required digest " + key.getParams().getHashAlgorithm() + " for private key."); } } else if (!key.getParams().getHashAlgorithm().equals(digest.getAlgorithm())) throw new InvalidKeyException("Key hash algorithm does not match chosen digest"); digestInitSign(privKey); } else { throw new InvalidKeyException("cannot identify EdDSA private key: " + privateKey.getClass()); } } private void digestInitSign(EdDSAPrivateKey privKey) { // Preparing for hash // r = H(h_b,...,h_2b-1,M) int b = privKey.getParams().getCurve().getField().getb(); digest.update(privKey.getH(), b/8, b/4 - b/8); } @Override protected void engineInitVerify(PublicKey publicKey) throws InvalidKeyException { reset(); if (publicKey instanceof EdDSAPublicKey) { key = (EdDSAPublicKey) publicKey; if (digest == null) { // Instantiate the digest from the key parameters try { digest = MessageDigest.getInstance(key.getParams().getHashAlgorithm()); } catch (NoSuchAlgorithmException e) { throw new InvalidKeyException("cannot get required digest " + key.getParams().getHashAlgorithm() + " for private key."); } } else if (!key.getParams().getHashAlgorithm().equals(digest.getAlgorithm())) throw new InvalidKeyException("Key hash algorithm does not match chosen digest"); } else if (publicKey instanceof X509Key) { // X509Certificate will sometimes contain an X509Key rather than the EdDSAPublicKey itself; the contained // key is valid but needs to be instanced as an EdDSAPublicKey before it can be used. EdDSAPublicKey parsedPublicKey; try { parsedPublicKey = new EdDSAPublicKey(new X509EncodedKeySpec(publicKey.getEncoded())); } catch (InvalidKeySpecException ex) { throw new InvalidKeyException("cannot handle X.509 EdDSA public key: " + publicKey.getAlgorithm()); } engineInitVerify(parsedPublicKey); } else { throw new InvalidKeyException("cannot identify EdDSA public key: " + publicKey.getClass()); } } /** * @throws SignatureException if in one-shot mode */ @Override protected void engineUpdate(byte b) throws SignatureException { if (oneShotMode) throw new SignatureException("unsupported in one-shot mode"); if (baos == null) baos = new ByteArrayOutputStream(256); baos.write(b); } /** * @throws SignatureException if one-shot rules are violated */ @Override protected void engineUpdate(byte[] b, int off, int len) throws SignatureException { if (oneShotMode) { if (oneShotBytes != null) throw new SignatureException("update() already called"); oneShotBytes = b; oneShotOffset = off; oneShotLength = len; } else { if (baos == null) baos = new ByteArrayOutputStream(256); baos.write(b, off, len); } } @Override protected byte[] engineSign() throws SignatureException { try { return x_engineSign(); } finally { reset(); // must leave the object ready to sign again with // the same key, as required by the API EdDSAPrivateKey privKey = (EdDSAPrivateKey) key; digestInitSign(privKey); } } private byte[] x_engineSign() throws SignatureException { Curve curve = key.getParams().getCurve(); ScalarOps sc = key.getParams().getScalarOps(); byte[] a = ((EdDSAPrivateKey) key).geta(); byte[] message; int offset, length; if (oneShotMode) { if (oneShotBytes == null) throw new SignatureException("update() not called first"); message = oneShotBytes; offset = oneShotOffset; length = oneShotLength; } else { if (baos == null) message = new byte[0]; else message = baos.toByteArray(); offset = 0; length = message.length; } // r = H(h_b,...,h_2b-1,M) digest.update(message, offset, length); byte[] r = digest.digest(); // r mod l // Reduces r from 64 bytes to 32 bytes r = sc.reduce(r); // R = rB GroupElement R = key.getParams().getB().scalarMultiply(r); byte[] Rbyte = R.toByteArray(); // S = (r + H(Rbar,Abar,M)*a) mod l digest.update(Rbyte); digest.update(((EdDSAPrivateKey) key).getAbyte()); digest.update(message, offset, length); byte[] h = digest.digest(); h = sc.reduce(h); byte[] S = sc.multiplyAndAdd(h, a, r); // R+S int b = curve.getField().getb(); ByteBuffer out = ByteBuffer.allocate(b/4); out.put(Rbyte).put(S); return out.array(); } @Override protected boolean engineVerify(byte[] sigBytes) throws SignatureException { try { return x_engineVerify(sigBytes); } finally { reset(); } } private boolean x_engineVerify(byte[] sigBytes) throws SignatureException { Curve curve = key.getParams().getCurve(); int b = curve.getField().getb(); if (sigBytes.length != b/4) throw new SignatureException("signature length is wrong"); // R is first b/8 bytes of sigBytes, S is second b/8 bytes digest.update(sigBytes, 0, b/8); digest.update(((EdDSAPublicKey) key).getAbyte()); // h = H(Rbar,Abar,M) byte[] message; int offset, length; if (oneShotMode) { if (oneShotBytes == null) throw new SignatureException("update() not called first"); message = oneShotBytes; offset = oneShotOffset; length = oneShotLength; } else { if (baos == null) message = new byte[0]; else message = baos.toByteArray(); offset = 0; length = message.length; } digest.update(message, offset, length); byte[] h = digest.digest(); // h mod l h = key.getParams().getScalarOps().reduce(h); byte[] Sbyte = Arrays.copyOfRange(sigBytes, b/8, b/4); // R = SB - H(Rbar,Abar,M)A GroupElement R = key.getParams().getB().doubleScalarMultiplyVariableTime( ((EdDSAPublicKey) key).getNegativeA(), h, Sbyte); // Variable time. This should be okay, because there are no secret // values used anywhere in verification. byte[] Rcalc = R.toByteArray(); for (int i = 0; i < Rcalc.length; i++) { if (Rcalc[i] != sigBytes[i]) return false; } return true; } /** * To efficiently sign all the data in one shot, if it is available, * use this method, which will avoid copying the data. * * Same as: *
     *  setParameter(ONE_SHOT_MODE)
     *  update(data)
     *  sig = sign()
     *
* * @param data the message to be signed * @return the signature * @throws SignatureException if update() already called * @see #ONE_SHOT_MODE */ public byte[] signOneShot(byte[] data) throws SignatureException { return signOneShot(data, 0, data.length); } /** * To efficiently sign all the data in one shot, if it is available, * use this method, which will avoid copying the data. * * Same as: *
     *  setParameter(ONE_SHOT_MODE)
     *  update(data, off, len)
     *  sig = sign()
     *
* * @param data byte array containing the message to be signed * @param off the start of the message inside data * @param len the length of the message * @return the signature * @throws SignatureException if update() already called * @see #ONE_SHOT_MODE */ public byte[] signOneShot(byte[] data, int off, int len) throws SignatureException { oneShotMode = true; update(data, off, len); return sign(); } /** * To efficiently verify all the data in one shot, if it is available, * use this method, which will avoid copying the data. * * Same as: *
     *  setParameter(ONE_SHOT_MODE)
     *  update(data)
     *  ok = verify(signature)
     *
* * @param data the message that was signed * @param signature of the message * @return true if the signature is valid, false otherwise * @throws SignatureException if update() already called * @see #ONE_SHOT_MODE */ public boolean verifyOneShot(byte[] data, byte[] signature) throws SignatureException { return verifyOneShot(data, 0, data.length, signature, 0, signature.length); } /** * To efficiently verify all the data in one shot, if it is available, * use this method, which will avoid copying the data. * * Same as: *
     *  setParameter(ONE_SHOT_MODE)
     *  update(data, off, len)
     *  ok = verify(signature)
     *
* * @param data byte array containing the message that was signed * @param off the start of the message inside data * @param len the length of the message * @param signature of the message * @return true if the signature is valid, false otherwise * @throws SignatureException if update() already called * @see #ONE_SHOT_MODE */ public boolean verifyOneShot(byte[] data, int off, int len, byte[] signature) throws SignatureException { return verifyOneShot(data, off, len, signature, 0, signature.length); } /** * To efficiently verify all the data in one shot, if it is available, * use this method, which will avoid copying the data. * * Same as: *
     *  setParameter(ONE_SHOT_MODE)
     *  update(data)
     *  ok = verify(signature, sigoff, siglen)
     *
* * @param data the message that was signed * @param signature byte array containing the signature * @param sigoff the start of the signature * @param siglen the length of the signature * @return true if the signature is valid, false otherwise * @throws SignatureException if update() already called * @see #ONE_SHOT_MODE */ public boolean verifyOneShot(byte[] data, byte[] signature, int sigoff, int siglen) throws SignatureException { return verifyOneShot(data, 0, data.length, signature, sigoff, siglen); } /** * To efficiently verify all the data in one shot, if it is available, * use this method, which will avoid copying the data. * * Same as: *
     *  setParameter(ONE_SHOT_MODE)
     *  update(data, off, len)
     *  ok = verify(signature, sigoff, siglen)
     *
* * @param data byte array containing the message that was signed * @param off the start of the message inside data * @param len the length of the message * @param signature byte array containing the signature * @param sigoff the start of the signature * @param siglen the length of the signature * @return true if the signature is valid, false otherwise * @throws SignatureException if update() already called * @see #ONE_SHOT_MODE */ public boolean verifyOneShot(byte[] data, int off, int len, byte[] signature, int sigoff, int siglen) throws SignatureException { oneShotMode = true; update(data, off, len); return verify(signature, sigoff, siglen); } /** * @throws InvalidAlgorithmParameterException if spec is ONE_SHOT_MODE and update() already called * @see #ONE_SHOT_MODE */ @Override protected void engineSetParameter(AlgorithmParameterSpec spec) throws InvalidAlgorithmParameterException { if (spec.equals(ONE_SHOT_MODE)) { if (oneShotBytes != null || (baos != null && baos.size() > 0)) throw new InvalidAlgorithmParameterException("update() already called"); oneShotMode = true; } else { super.engineSetParameter(spec); } } /** * @deprecated */ @Override protected void engineSetParameter(String param, Object value) { throw new UnsupportedOperationException("engineSetParameter unsupported"); } /** * @deprecated */ @Override protected Object engineGetParameter(String param) { throw new UnsupportedOperationException("engineSetParameter unsupported"); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/EdDSAKey.java000066400000000000000000000014361327341674300237030ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import net.i2p.crypto.eddsa.spec.EdDSAParameterSpec; /** * Common interface for all EdDSA keys. * @author str4d */ public interface EdDSAKey { /** * The reported key algorithm for all EdDSA keys */ String KEY_ALGORITHM = "EdDSA"; /** * @return a parameter specification representing the EdDSA domain * parameters for the key. */ EdDSAParameterSpec getParams(); } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/EdDSAPrivateKey.java000066400000000000000000000246761327341674300252510ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.security.PrivateKey; import java.security.spec.InvalidKeySpecException; import java.security.spec.PKCS8EncodedKeySpec; import java.util.Arrays; import net.i2p.crypto.eddsa.math.GroupElement; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import net.i2p.crypto.eddsa.spec.EdDSAParameterSpec; import net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec; /** * An EdDSA private key. *

* Warning: Private key encoding is based on the current curdle WG draft, * and is subject to change. See getEncoded(). *

* For compatibility with older releases, decoding supports both the old and new * draft specifications. See decode(). *

* Ref: https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 *

* Old Ref: https://tools.ietf.org/html/draft-josefsson-pkix-eddsa-04 *

* @author str4d * */ public class EdDSAPrivateKey implements EdDSAKey, PrivateKey { private static final long serialVersionUID = 23495873459878957L; private final byte[] seed; private final byte[] h; private final byte[] a; private final GroupElement A; private final byte[] Abyte; private final EdDSAParameterSpec edDsaSpec; // OID 1.3.101.xxx private static final int OID_OLD = 100; private static final int OID_ED25519 = 112; private static final int OID_BYTE = 11; private static final int IDLEN_BYTE = 6; public EdDSAPrivateKey(EdDSAPrivateKeySpec spec) { this.seed = spec.getSeed(); this.h = spec.getH(); this.a = spec.geta(); this.A = spec.getA(); this.Abyte = this.A.toByteArray(); this.edDsaSpec = spec.getParams(); } public EdDSAPrivateKey(PKCS8EncodedKeySpec spec) throws InvalidKeySpecException { this(new EdDSAPrivateKeySpec(decode(spec.getEncoded()), EdDSANamedCurveTable.ED_25519_CURVE_SPEC)); } @Override public String getAlgorithm() { return KEY_ALGORITHM; } @Override public String getFormat() { return "PKCS#8"; } /** * Returns the public key in its canonical encoding. *

* This implements the following specs: *

  • * General encoding: https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 *
  • * Key encoding: https://tools.ietf.org/html/rfc8032 *
*

* This encodes the seed. It will return null if constructed from * a spec which was directly constructed from H, in which case seed is null. *

* For keys in older formats, decoding and then re-encoding is sufficient to * migrate them to the canonical encoding. *

* Relevant spec quotes: *
     *  OneAsymmetricKey ::= SEQUENCE {
     *    version Version,
     *    privateKeyAlgorithm PrivateKeyAlgorithmIdentifier,
     *    privateKey PrivateKey,
     *    attributes [0] Attributes OPTIONAL,
     *    ...,
     *    [[2: publicKey [1] PublicKey OPTIONAL ]],
     *    ...
     *  }
     *
     *  Version ::= INTEGER
     *  PrivateKeyAlgorithmIdentifier ::= AlgorithmIdentifier
     *  PrivateKey ::= OCTET STRING
     *  PublicKey ::= OCTET STRING
     *  Attributes ::= SET OF Attribute
     *
* *
     *  ... when encoding a OneAsymmetricKey object, the private key is wrapped
     *  in a CurvePrivateKey object and wrapped by the OCTET STRING of the
     *  'privateKey' field.
     *
     *  CurvePrivateKey ::= OCTET STRING
     *
* *
     *  AlgorithmIdentifier  ::=  SEQUENCE  {
     *    algorithm   OBJECT IDENTIFIER,
     *    parameters  ANY DEFINED BY algorithm OPTIONAL
     *  }
     *
     *  For all of the OIDs, the parameters MUST be absent.
     *
* *
     *  id-Ed25519   OBJECT IDENTIFIER ::= { 1 3 101 112 }
     *
* * @return 48 bytes for Ed25519, null for other curves */ @Override public byte[] getEncoded() { if (!edDsaSpec.equals(EdDSANamedCurveTable.ED_25519_CURVE_SPEC)) return null; if (seed == null) return null; int totlen = 16 + seed.length; byte[] rv = new byte[totlen]; int idx = 0; // sequence rv[idx++] = 0x30; rv[idx++] = (byte) (totlen - 2); // version rv[idx++] = 0x02; rv[idx++] = 1; // v1 - no public key included rv[idx++] = 0; // Algorithm Identifier // sequence rv[idx++] = 0x30; rv[idx++] = 5; // OID // https://msdn.microsoft.com/en-us/library/windows/desktop/bb540809%28v=vs.85%29.aspx rv[idx++] = 0x06; rv[idx++] = 3; rv[idx++] = (1 * 40) + 3; rv[idx++] = 101; rv[idx++] = (byte) OID_ED25519; // params - absent // PrivateKey rv[idx++] = 0x04; // octet string rv[idx++] = (byte) (2 + seed.length); // CurvePrivateKey rv[idx++] = 0x04; // octet string rv[idx++] = (byte) seed.length; // the key System.arraycopy(seed, 0, rv, idx, seed.length); return rv; } /** * Extracts the private key bytes from the provided encoding. *

* This will decode data conforming to the current spec at * https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 * or as inferred from the old spec at * https://tools.ietf.org/html/draft-josefsson-pkix-eddsa-04. *

* Contrary to draft-ietf-curdle-pkix-04, it WILL accept a parameter value * of NULL, as it is required for interoperability with the default Java * keystore. Other implementations MUST NOT copy this behaviour from here * unless they also need to read keys from the default Java keystore. *

* This is really dumb for now. It does not use a general-purpose ASN.1 decoder. * See also getEncoded(). * * @return 32 bytes for Ed25519, throws for other curves */ private static byte[] decode(byte[] d) throws InvalidKeySpecException { try { // // Setup and OID check // int totlen = 48; int idlen = 5; int doid = d[OID_BYTE]; if (doid == OID_OLD) { totlen = 49; idlen = 8; } else if (doid == OID_ED25519) { // Detect parameter value of NULL if (d[IDLEN_BYTE] == 7) { totlen = 50; idlen = 7; } } else { throw new InvalidKeySpecException("unsupported key spec"); } // // Pre-decoding check // if (d.length != totlen) { throw new InvalidKeySpecException("invalid key spec length"); } // // Decoding // int idx = 0; if (d[idx++] != 0x30 || d[idx++] != (totlen - 2) || d[idx++] != 0x02 || d[idx++] != 1 || d[idx++] != 0 || d[idx++] != 0x30 || d[idx++] != idlen || d[idx++] != 0x06 || d[idx++] != 3 || d[idx++] != (1 * 40) + 3 || d[idx++] != 101) { throw new InvalidKeySpecException("unsupported key spec"); } idx++; // OID, checked above // parameters only with old OID if (doid == OID_OLD) { if (d[idx++] != 0x0a || d[idx++] != 1 || d[idx++] != 1) { throw new InvalidKeySpecException("unsupported key spec"); } } else { // Handle parameter value of NULL // // Quote https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 : // For all of the OIDs, the parameters MUST be absent. // Regardless of the defect in the original 1997 syntax, // implementations MUST NOT accept a parameters value of NULL. // // But Java's default keystore puts it in (when decoding as // PKCS8 and then re-encoding to pass on), so we must accept it. if (idlen == 7) { if (d[idx++] != 0x05 || d[idx++] != 0) { throw new InvalidKeySpecException("unsupported key spec"); } } // PrivateKey wrapping the CurvePrivateKey if (d[idx++] != 0x04 || d[idx++] != 34) { throw new InvalidKeySpecException("unsupported key spec"); } } if (d[idx++] != 0x04 || d[idx++] != 32) { throw new InvalidKeySpecException("unsupported key spec"); } byte[] rv = new byte[32]; System.arraycopy(d, idx, rv, 0, 32); return rv; } catch (IndexOutOfBoundsException ioobe) { throw new InvalidKeySpecException(ioobe); } } @Override public EdDSAParameterSpec getParams() { return edDsaSpec; } /** * @return will be null if constructed from a spec which was * directly constructed from H */ public byte[] getSeed() { return seed; } /** * @return the hash of the seed */ public byte[] getH() { return h; } /** * @return the private key */ public byte[] geta() { return a; } /** * @return the public key */ public GroupElement getA() { return A; } /** * @return the public key */ public byte[] getAbyte() { return Abyte; } @Override public int hashCode() { return Arrays.hashCode(seed); } @Override public boolean equals(Object o) { if (o == this) return true; if (!(o instanceof EdDSAPrivateKey)) return false; EdDSAPrivateKey pk = (EdDSAPrivateKey) o; return Arrays.equals(seed, pk.getSeed()) && edDsaSpec.equals(pk.getParams()); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/EdDSAPublicKey.java000066400000000000000000000217571327341674300250520ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.security.PublicKey; import java.security.spec.InvalidKeySpecException; import java.security.spec.X509EncodedKeySpec; import java.util.Arrays; import net.i2p.crypto.eddsa.math.GroupElement; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import net.i2p.crypto.eddsa.spec.EdDSAParameterSpec; import net.i2p.crypto.eddsa.spec.EdDSAPublicKeySpec; /** * An EdDSA public key. *

* Warning: Public key encoding is is based on the current curdle WG draft, * and is subject to change. See getEncoded(). *

* For compatibility with older releases, decoding supports both the old and new * draft specifications. See decode(). *

* Ref: https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 *

* Old Ref: https://tools.ietf.org/html/draft-josefsson-pkix-eddsa-04 *

* @author str4d * */ public class EdDSAPublicKey implements EdDSAKey, PublicKey { private static final long serialVersionUID = 9837459837498475L; private final GroupElement A; private GroupElement Aneg = null; private final byte[] Abyte; private final EdDSAParameterSpec edDsaSpec; // OID 1.3.101.xxx private static final int OID_OLD = 100; private static final int OID_ED25519 = 112; private static final int OID_BYTE = 8; private static final int IDLEN_BYTE = 3; public EdDSAPublicKey(EdDSAPublicKeySpec spec) { this.A = spec.getA(); this.Abyte = this.A.toByteArray(); this.edDsaSpec = spec.getParams(); } public EdDSAPublicKey(X509EncodedKeySpec spec) throws InvalidKeySpecException { this(new EdDSAPublicKeySpec(decode(spec.getEncoded()), EdDSANamedCurveTable.ED_25519_CURVE_SPEC)); } @Override public String getAlgorithm() { return KEY_ALGORITHM; } @Override public String getFormat() { return "X.509"; } /** * Returns the public key in its canonical encoding. *

* This implements the following specs: *

  • * General encoding: https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 *
  • * Key encoding: https://tools.ietf.org/html/rfc8032 *
*

* For keys in older formats, decoding and then re-encoding is sufficient to * migrate them to the canonical encoding. *

* Relevant spec quotes: *
     *  In the X.509 certificate, the subjectPublicKeyInfo field has the
     *  SubjectPublicKeyInfo type, which has the following ASN.1 syntax:
     *
     *  SubjectPublicKeyInfo  ::=  SEQUENCE  {
     *    algorithm         AlgorithmIdentifier,
     *    subjectPublicKey  BIT STRING
     *  }
     *
* *
     *  AlgorithmIdentifier  ::=  SEQUENCE  {
     *    algorithm   OBJECT IDENTIFIER,
     *    parameters  ANY DEFINED BY algorithm OPTIONAL
     *  }
     *
     *  For all of the OIDs, the parameters MUST be absent.
     *
* *
     *  id-Ed25519   OBJECT IDENTIFIER ::= { 1 3 101 112 }
     *
* * @return 44 bytes for Ed25519, null for other curves */ @Override public byte[] getEncoded() { if (!edDsaSpec.equals(EdDSANamedCurveTable.ED_25519_CURVE_SPEC)) return null; int totlen = 12 + Abyte.length; byte[] rv = new byte[totlen]; int idx = 0; // sequence rv[idx++] = 0x30; rv[idx++] = (byte) (totlen - 2); // Algorithm Identifier // sequence rv[idx++] = 0x30; rv[idx++] = 5; // OID // https://msdn.microsoft.com/en-us/library/windows/desktop/bb540809%28v=vs.85%29.aspx rv[idx++] = 0x06; rv[idx++] = 3; rv[idx++] = (1 * 40) + 3; rv[idx++] = 101; rv[idx++] = (byte) OID_ED25519; // params - absent // the key rv[idx++] = 0x03; // bit string rv[idx++] = (byte) (1 + Abyte.length); rv[idx++] = 0; // number of trailing unused bits System.arraycopy(Abyte, 0, rv, idx, Abyte.length); return rv; } /** * Extracts the public key bytes from the provided encoding. *

* This will decode data conforming to the current spec at * https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 * or the old spec at * https://tools.ietf.org/html/draft-josefsson-pkix-eddsa-04. *

* Contrary to draft-ietf-curdle-pkix-04, it WILL accept a parameter value * of NULL, as it is required for interoperability with the default Java * keystore. Other implementations MUST NOT copy this behaviour from here * unless they also need to read keys from the default Java keystore. *

* This is really dumb for now. It does not use a general-purpose ASN.1 decoder. * See also getEncoded(). *

* * @return 32 bytes for Ed25519, throws for other curves */ private static byte[] decode(byte[] d) throws InvalidKeySpecException { try { // // Setup and OID check // int totlen = 44; int idlen = 5; int doid = d[OID_BYTE]; if (doid == OID_OLD) { totlen = 47; idlen = 8; } else if (doid == OID_ED25519) { // Detect parameter value of NULL if (d[IDLEN_BYTE] == 7) { totlen = 46; idlen = 7; } } else { throw new InvalidKeySpecException("unsupported key spec"); } // // Pre-decoding check // if (d.length != totlen) { throw new InvalidKeySpecException("invalid key spec length"); } // // Decoding // int idx = 0; if (d[idx++] != 0x30 || d[idx++] != (totlen - 2) || d[idx++] != 0x30 || d[idx++] != idlen || d[idx++] != 0x06 || d[idx++] != 3 || d[idx++] != (1 * 40) + 3 || d[idx++] != 101) { throw new InvalidKeySpecException("unsupported key spec"); } idx++; // OID, checked above // parameters only with old OID if (doid == OID_OLD) { if (d[idx++] != 0x0a || d[idx++] != 1 || d[idx++] != 1) { throw new InvalidKeySpecException("unsupported key spec"); } } else { // Handle parameter value of NULL // // Quote https://tools.ietf.org/html/draft-ietf-curdle-pkix-04 : // For all of the OIDs, the parameters MUST be absent. // Regardless of the defect in the original 1997 syntax, // implementations MUST NOT accept a parameters value of NULL. // // But Java's default keystore puts it in (when decoding as // PKCS8 and then re-encoding to pass on), so we must accept it. if (idlen == 7) { if (d[idx++] != 0x05 || d[idx++] != 0) { throw new InvalidKeySpecException("unsupported key spec"); } } } if (d[idx++] != 0x03 || d[idx++] != 33 || d[idx++] != 0) { throw new InvalidKeySpecException("unsupported key spec"); } byte[] rv = new byte[32]; System.arraycopy(d, idx, rv, 0, 32); return rv; } catch (IndexOutOfBoundsException ioobe) { throw new InvalidKeySpecException(ioobe); } } @Override public EdDSAParameterSpec getParams() { return edDsaSpec; } public GroupElement getA() { return A; } public GroupElement getNegativeA() { // Only read Aneg once, otherwise read re-ordering might occur between here and return. Requires all GroupElement's fields to be final. GroupElement ourAneg = Aneg; if(ourAneg == null) { ourAneg = A.negate(); Aneg = ourAneg; } return ourAneg; } public byte[] getAbyte() { return Abyte; } @Override public int hashCode() { return Arrays.hashCode(Abyte); } @Override public boolean equals(Object o) { if (o == this) return true; if (!(o instanceof EdDSAPublicKey)) return false; EdDSAPublicKey pk = (EdDSAPublicKey) o; return Arrays.equals(Abyte, pk.getAbyte()) && edDsaSpec.equals(pk.getParams()); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/EdDSASecurityProvider.java000066400000000000000000000045551327341674300265020ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.security.AccessController; import java.security.PrivilegedAction; import java.security.Provider; import java.security.Security; /** * A security {@link Provider} that can be registered via {@link Security#addProvider(Provider)} * * @author str4d */ public class EdDSASecurityProvider extends Provider { private static final long serialVersionUID = 1210027906682292307L; public static final String PROVIDER_NAME = "EdDSA"; public EdDSASecurityProvider() { super(PROVIDER_NAME, 0.3 /* should match POM major.minor version */, "str4d " + PROVIDER_NAME + " security provider wrapper"); AccessController.doPrivileged(new PrivilegedAction() { @Override public Object run() { setup(); return null; } }); } protected void setup() { // See https://docs.oracle.com/javase/8/docs/technotes/guides/security/crypto/HowToImplAProvider.html put("KeyFactory." + EdDSAKey.KEY_ALGORITHM, "net.i2p.crypto.eddsa.KeyFactory"); put("KeyPairGenerator." + EdDSAKey.KEY_ALGORITHM, "net.i2p.crypto.eddsa.KeyPairGenerator"); put("Signature." + EdDSAEngine.SIGNATURE_ALGORITHM, "net.i2p.crypto.eddsa.EdDSAEngine"); // OID Mappings // See section "Mapping from OID to name". // The Key* -> OID mappings correspond to the default algorithm in KeyPairGenerator. // // From draft-ieft-curdle-pkix-04: // id-Ed25519 OBJECT IDENTIFIER ::= { 1 3 101 112 } put("Alg.Alias.KeyFactory.1.3.101.112", EdDSAKey.KEY_ALGORITHM); put("Alg.Alias.KeyFactory.OID.1.3.101.112", EdDSAKey.KEY_ALGORITHM); put("Alg.Alias.KeyPairGenerator.1.3.101.112", EdDSAKey.KEY_ALGORITHM); put("Alg.Alias.KeyPairGenerator.OID.1.3.101.112", EdDSAKey.KEY_ALGORITHM); put("Alg.Alias.Signature.1.3.101.112", EdDSAEngine.SIGNATURE_ALGORITHM); put("Alg.Alias.Signature.OID.1.3.101.112", EdDSAEngine.SIGNATURE_ALGORITHM); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/KeyFactory.java000066400000000000000000000055341327341674300244350ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.security.InvalidKeyException; import java.security.Key; import java.security.KeyFactorySpi; import java.security.PrivateKey; import java.security.PublicKey; import java.security.spec.InvalidKeySpecException; import java.security.spec.KeySpec; import java.security.spec.PKCS8EncodedKeySpec; import java.security.spec.X509EncodedKeySpec; import net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec; import net.i2p.crypto.eddsa.spec.EdDSAPublicKeySpec; /** * @author str4d * */ public final class KeyFactory extends KeyFactorySpi { protected PrivateKey engineGeneratePrivate(KeySpec keySpec) throws InvalidKeySpecException { if (keySpec instanceof EdDSAPrivateKeySpec) { return new EdDSAPrivateKey((EdDSAPrivateKeySpec) keySpec); } if (keySpec instanceof PKCS8EncodedKeySpec) { return new EdDSAPrivateKey((PKCS8EncodedKeySpec) keySpec); } throw new InvalidKeySpecException("key spec not recognised: " + keySpec.getClass()); } protected PublicKey engineGeneratePublic(KeySpec keySpec) throws InvalidKeySpecException { if (keySpec instanceof EdDSAPublicKeySpec) { return new EdDSAPublicKey((EdDSAPublicKeySpec) keySpec); } if (keySpec instanceof X509EncodedKeySpec) { return new EdDSAPublicKey((X509EncodedKeySpec) keySpec); } throw new InvalidKeySpecException("key spec not recognised: " + keySpec.getClass()); } @SuppressWarnings("unchecked") protected T engineGetKeySpec(Key key, Class keySpec) throws InvalidKeySpecException { if (keySpec.isAssignableFrom(EdDSAPublicKeySpec.class) && key instanceof EdDSAPublicKey) { EdDSAPublicKey k = (EdDSAPublicKey) key; if (k.getParams() != null) { return (T) new EdDSAPublicKeySpec(k.getA(), k.getParams()); } } else if (keySpec.isAssignableFrom(EdDSAPrivateKeySpec.class) && key instanceof EdDSAPrivateKey) { EdDSAPrivateKey k = (EdDSAPrivateKey) key; if (k.getParams() != null) { return (T) new EdDSAPrivateKeySpec(k.getSeed(), k.getH(), k.geta(), k.getA(), k.getParams()); } } throw new InvalidKeySpecException("not implemented yet " + key + " " + keySpec); } protected Key engineTranslateKey(Key key) throws InvalidKeyException { throw new InvalidKeyException("No other EdDSA key providers known"); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/KeyPairGenerator.java000066400000000000000000000073061327341674300255670ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.security.InvalidAlgorithmParameterException; import java.security.InvalidParameterException; import java.security.KeyPair; import java.security.KeyPairGeneratorSpi; import java.security.SecureRandom; import java.security.spec.AlgorithmParameterSpec; import java.util.Hashtable; import net.i2p.crypto.eddsa.spec.EdDSAGenParameterSpec; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveSpec; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import net.i2p.crypto.eddsa.spec.EdDSAParameterSpec; import net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec; import net.i2p.crypto.eddsa.spec.EdDSAPublicKeySpec; /** * Default keysize is 256 (Ed25519) */ public final class KeyPairGenerator extends KeyPairGeneratorSpi { private static final int DEFAULT_KEYSIZE = 256; private EdDSAParameterSpec edParams; private SecureRandom random; private boolean initialized; private static final Hashtable edParameters; static { edParameters = new Hashtable(); edParameters.put(Integer.valueOf(256), new EdDSAGenParameterSpec(EdDSANamedCurveTable.ED_25519)); } public void initialize(int keysize, SecureRandom random) { AlgorithmParameterSpec edParams = edParameters.get(Integer.valueOf(keysize)); if (edParams == null) throw new InvalidParameterException("unknown key type."); try { initialize(edParams, random); } catch (InvalidAlgorithmParameterException e) { throw new InvalidParameterException("key type not configurable."); } } @Override public void initialize(AlgorithmParameterSpec params, SecureRandom random) throws InvalidAlgorithmParameterException { if (params instanceof EdDSAParameterSpec) { edParams = (EdDSAParameterSpec) params; } else if (params instanceof EdDSAGenParameterSpec) { edParams = createNamedCurveSpec(((EdDSAGenParameterSpec) params).getName()); } else throw new InvalidAlgorithmParameterException("parameter object not a EdDSAParameterSpec"); this.random = random; initialized = true; } public KeyPair generateKeyPair() { if (!initialized) initialize(DEFAULT_KEYSIZE, new SecureRandom()); byte[] seed = new byte[edParams.getCurve().getField().getb()/8]; random.nextBytes(seed); EdDSAPrivateKeySpec privKey = new EdDSAPrivateKeySpec(seed, edParams); EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(privKey.getA(), edParams); return new KeyPair(new EdDSAPublicKey(pubKey), new EdDSAPrivateKey(privKey)); } /** * Create an EdDSANamedCurveSpec from the provided curve name. The current * implementation fetches the pre-created curve spec from a table. * @param curveName the EdDSA named curve. * @return the specification for the named curve. * @throws InvalidAlgorithmParameterException if the named curve is unknown. */ protected EdDSANamedCurveSpec createNamedCurveSpec(String curveName) throws InvalidAlgorithmParameterException { EdDSANamedCurveSpec spec = EdDSANamedCurveTable.getByName(curveName); if (spec == null) { throw new InvalidAlgorithmParameterException("unknown curve name: " + curveName); } return spec; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/Utils.java000066400000000000000000000053021327341674300234460ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; /** * Basic utilities for EdDSA. * Not for external use, not maintained as a public API. * * @author str4d * */ public class Utils { /** * Constant-time byte comparison. * @param b a byte * @param c a byte * @return 1 if b and c are equal, 0 otherwise. */ public static int equal(int b, int c) { int result = 0; int xor = b ^ c; for (int i = 0; i < 8; i++) { result |= xor >> i; } return (result ^ 0x01) & 0x01; } /** * Constant-time byte[] comparison. * @param b a byte[] * @param c a byte[] * @return 1 if b and c are equal, 0 otherwise. */ public static int equal(byte[] b, byte[] c) { int result = 0; for (int i = 0; i < 32; i++) { result |= b[i] ^ c[i]; } return equal(result, 0); } /** * Constant-time determine if byte is negative. * @param b the byte to check. * @return 1 if the byte is negative, 0 otherwise. */ public static int negative(int b) { return (b >> 8) & 1; } /** * Get the i'th bit of a byte array. * @param h the byte array. * @param i the bit index. * @return 0 or 1, the value of the i'th bit in h */ public static int bit(byte[] h, int i) { return (h[i >> 3] >> (i & 7)) & 1; } /** * Converts a hex string to bytes. * @param s the hex string to be converted. * @return the byte[] */ public static byte[] hexToBytes(String s) { int len = s.length(); byte[] data = new byte[len / 2]; for (int i = 0; i < len; i += 2) { data[i / 2] = (byte) ((Character.digit(s.charAt(i), 16) << 4) + Character.digit(s.charAt(i+1), 16)); } return data; } /** * Converts bytes to a hex string. * @param raw the byte[] to be converted. * @return the hex representation as a string. */ public static String bytesToHex(byte[] raw) { if ( raw == null ) { return null; } final StringBuilder hex = new StringBuilder(2 * raw.length); for (final byte b : raw) { hex.append(Character.forDigit((b & 0xF0) >> 4, 16)) .append(Character.forDigit((b & 0x0F), 16)); } return hex.toString(); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/000077500000000000000000000000001327341674300224345ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/Constants.java000066400000000000000000000022471327341674300252600ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import net.i2p.crypto.eddsa.Utils; final class Constants { public static final byte[] ZERO = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); public static final byte[] ONE = Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000"); public static final byte[] TWO = Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000"); public static final byte[] FOUR = Utils.hexToBytes("0400000000000000000000000000000000000000000000000000000000000000"); public static final byte[] FIVE = Utils.hexToBytes("0500000000000000000000000000000000000000000000000000000000000000"); public static final byte[] EIGHT = Utils.hexToBytes("0800000000000000000000000000000000000000000000000000000000000000"); } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/Curve.java000066400000000000000000000051771327341674300243750ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import java.io.Serializable; /** * A twisted Edwards curve. * Points on the curve satisfy $-x^2 + y^2 = 1 + d x^2y^2$ * @author str4d * */ public class Curve implements Serializable { private static final long serialVersionUID = 4578920872509827L; private final Field f; private final FieldElement d; private final FieldElement d2; private final FieldElement I; private final GroupElement zeroP2; private final GroupElement zeroP3; private final GroupElement zeroP3PrecomputedDouble; private final GroupElement zeroPrecomp; public Curve(Field f, byte[] d, FieldElement I) { this.f = f; this.d = f.fromByteArray(d); this.d2 = this.d.add(this.d); this.I = I; FieldElement zero = f.ZERO; FieldElement one = f.ONE; zeroP2 = GroupElement.p2(this, zero, one, one); zeroP3 = GroupElement.p3(this, zero, one, one, zero, false); zeroP3PrecomputedDouble = GroupElement.p3(this, zero, one, one, zero, true); zeroPrecomp = GroupElement.precomp(this, one, one, zero); } public Field getField() { return f; } public FieldElement getD() { return d; } public FieldElement get2D() { return d2; } public FieldElement getI() { return I; } public GroupElement getZero(GroupElement.Representation repr) { switch (repr) { case P2: return zeroP2; case P3: return zeroP3; case P3PrecomputedDouble: return zeroP3PrecomputedDouble; case PRECOMP: return zeroPrecomp; default: return null; } } public GroupElement createPoint(byte[] P, boolean precompute) { GroupElement ge = new GroupElement(this, P, precompute); return ge; } @Override public int hashCode() { return f.hashCode() ^ d.hashCode() ^ I.hashCode(); } @Override public boolean equals(Object o) { if (o == this) return true; if (!(o instanceof Curve)) return false; Curve c = (Curve) o; return f.equals(c.getField()) && d.equals(c.getD()) && I.equals(c.getI()); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/Encoding.java000066400000000000000000000033031327341674300250240ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; /** * Common interface for all $(b-1)$-bit encodings of elements * of EdDSA finite fields. * @author str4d * */ public abstract class Encoding { protected Field f; public synchronized void setField(Field f) { if (this.f != null) throw new IllegalStateException("already set"); this.f = f; } /** * Encode a FieldElement in its $(b-1)$-bit encoding. * @param x the FieldElement to encode * @return the $(b-1)$-bit encoding of this FieldElement. */ public abstract byte[] encode(FieldElement x); /** * Decode a FieldElement from its $(b-1)$-bit encoding. * The highest bit is masked out. * @param in the $(b-1)$-bit encoding of a FieldElement. * @return the FieldElement represented by 'val'. */ public abstract FieldElement decode(byte[] in); /** * From the Ed25519 paper:
* $x$ is negative if the $(b-1)$-bit encoding of $x$ is lexicographically larger * than the $(b-1)$-bit encoding of -x. If $q$ is an odd prime and the encoding * is the little-endian representation of $\{0, 1,\dots, q-1\}$ then the negative * elements of $F_q$ are $\{1, 3, 5,\dots, q-2\}$. * @param x the FieldElement to check * @return true if negative */ public abstract boolean isNegative(FieldElement x); } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/Field.java000066400000000000000000000044141327341674300243250ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import java.io.Serializable; /** * An EdDSA finite field. Includes several pre-computed values. * @author str4d * */ public class Field implements Serializable { private static final long serialVersionUID = 8746587465875676L; public final FieldElement ZERO; public final FieldElement ONE; public final FieldElement TWO; public final FieldElement FOUR; public final FieldElement FIVE; public final FieldElement EIGHT; private final int b; private final FieldElement q; /** * q-2 */ private final FieldElement qm2; /** * (q-5) / 8 */ private final FieldElement qm5d8; private final Encoding enc; public Field(int b, byte[] q, Encoding enc) { this.b = b; this.enc = enc; this.enc.setField(this); this.q = fromByteArray(q); // Set up constants ZERO = fromByteArray(Constants.ZERO); ONE = fromByteArray(Constants.ONE); TWO = fromByteArray(Constants.TWO); FOUR = fromByteArray(Constants.FOUR); FIVE = fromByteArray(Constants.FIVE); EIGHT = fromByteArray(Constants.EIGHT); // Precompute values qm2 = this.q.subtract(TWO); qm5d8 = this.q.subtract(FIVE).divide(EIGHT); } public FieldElement fromByteArray(byte[] x) { return enc.decode(x); } public int getb() { return b; } public FieldElement getQ() { return q; } public FieldElement getQm2() { return qm2; } public FieldElement getQm5d8() { return qm5d8; } public Encoding getEncoding(){ return enc; } @Override public int hashCode() { return q.hashCode(); } @Override public boolean equals(Object obj) { if (!(obj instanceof Field)) return false; Field f = (Field) obj; return b == f.b && q.equals(f.q); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/FieldElement.java000066400000000000000000000036711327341674300256430ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import java.io.Serializable; /** * Note: concrete subclasses must implement hashCode() and equals() */ public abstract class FieldElement implements Serializable { private static final long serialVersionUID = 1239527465875676L; protected final Field f; public FieldElement(Field f) { if (null == f) { throw new IllegalArgumentException("field cannot be null"); } this.f = f; } /** * Encode a FieldElement in its $(b-1)$-bit encoding. * @return the $(b-1)$-bit encoding of this FieldElement. */ public byte[] toByteArray() { return f.getEncoding().encode(this); } public abstract boolean isNonZero(); public boolean isNegative() { return f.getEncoding().isNegative(this); } public abstract FieldElement add(FieldElement val); public FieldElement addOne() { return add(f.ONE); } public abstract FieldElement subtract(FieldElement val); public FieldElement subtractOne() { return subtract(f.ONE); } public abstract FieldElement negate(); public FieldElement divide(FieldElement val) { return multiply(val.invert()); } public abstract FieldElement multiply(FieldElement val); public abstract FieldElement square(); public abstract FieldElement squareAndDouble(); public abstract FieldElement invert(); public abstract FieldElement pow22523(); public abstract FieldElement cmov(FieldElement val, final int b); // Note: concrete subclasses must implement hashCode() and equals() } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/GroupElement.java000066400000000000000000001142501327341674300257100ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import net.i2p.crypto.eddsa.Utils; import java.io.Serializable; import java.util.Arrays; /** * A point $(x,y)$ on an EdDSA curve. *

* Reviewed/commented by Bloody Rookie (nemproject@gmx.de) *

* Literature:
* [1] Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe and Bo-Yin Yang : High-speed high-security signatures
* [2] Huseyin Hisil, Kenneth Koon-Ho Wong, Gary Carter, Ed Dawson: Twisted Edwards Curves Revisited
* [3] Daniel J. Bernsteina, Tanja Lange: A complete set of addition laws for incomplete Edwards curves
* [4] Daniel J. Bernstein, Peter Birkner, Marc Joye, Tanja Lange and Christiane Peters: Twisted Edwards Curves
* [5] Christiane Pascale Peters: Curves, Codes, and Cryptography (PhD thesis)
* [6] Daniel J. Bernstein, Peter Birkner, Tanja Lange and Christiane Peters: Optimizing double-base elliptic-curve single-scalar multiplication
* * @author str4d */ public class GroupElement implements Serializable { private static final long serialVersionUID = 2395879087349587L; /** * Available representations for a group element. *

    *
  • P2: Projective representation $(X:Y:Z)$ satisfying $x=X/Z, y=Y/Z$. *
  • P3: Extended projective representation $(X:Y:Z:T)$ satisfying $x=X/Z, y=Y/Z, XY=ZT$. *
  • P3PrecomputedDouble: P3 but with dblPrecmp populated. *
  • P1P1: Completed representation $((X:Z), (Y:T))$ satisfying $x=X/Z, y=Y/T$. *
  • PRECOMP: Precomputed representation $(y+x, y-x, 2dxy)$. *
  • CACHED: Cached representation $(Y+X, Y-X, Z, 2dT)$ *
*/ public enum Representation { /** Projective ($P^2$): $(X:Y:Z)$ satisfying $x=X/Z, y=Y/Z$ */ P2, /** Extended ($P^3$): $(X:Y:Z:T)$ satisfying $x=X/Z, y=Y/Z, XY=ZT$ */ P3, /** Can only be requested. Results in P3 representation but also populates dblPrecmp. */ P3PrecomputedDouble, /** Completed ($P \times P$): $((X:Z),(Y:T))$ satisfying $x=X/Z, y=Y/T$ */ P1P1, /** Precomputed (Duif): $(y+x,y-x,2dxy)$ */ PRECOMP, /** Cached: $(Y+X,Y-X,Z,2dT)$ */ CACHED } /** * Creates a new group element in P2 representation. * * @param curve The curve. * @param X The $X$ coordinate. * @param Y The $Y$ coordinate. * @param Z The $Z$ coordinate. * @return The group element in P2 representation. */ public static GroupElement p2( final Curve curve, final FieldElement X, final FieldElement Y, final FieldElement Z) { return new GroupElement(curve, Representation.P2, X, Y, Z, null); } /** * Creates a new group element in P3 representation, without pre-computation. * * @param curve The curve. * @param X The $X$ coordinate. * @param Y The $Y$ coordinate. * @param Z The $Z$ coordinate. * @param T The $T$ coordinate. * @return The group element in P3 representation. */ public static GroupElement p3( final Curve curve, final FieldElement X, final FieldElement Y, final FieldElement Z, final FieldElement T) { return p3(curve, X, Y, Z, T, false); } /** * Creates a new group element in P3 representation, potentially with pre-computation. * * @param curve The curve. * @param X The $X$ coordinate. * @param Y The $Y$ coordinate. * @param Z The $Z$ coordinate. * @param T The $T$ coordinate. * @param precomputeDoubleOnly If true, populate dblPrecmp, else set to null. * @return The group element in P3 representation. */ public static GroupElement p3( final Curve curve, final FieldElement X, final FieldElement Y, final FieldElement Z, final FieldElement T, final boolean precomputeDoubleOnly) { return new GroupElement(curve, Representation.P3, X, Y, Z, T, precomputeDoubleOnly); } /** * Creates a new group element in P1P1 representation. * * @param curve The curve. * @param X The $X$ coordinate. * @param Y The $Y$ coordinate. * @param Z The $Z$ coordinate. * @param T The $T$ coordinate. * @return The group element in P1P1 representation. */ public static GroupElement p1p1( final Curve curve, final FieldElement X, final FieldElement Y, final FieldElement Z, final FieldElement T) { return new GroupElement(curve, Representation.P1P1, X, Y, Z, T); } /** * Creates a new group element in PRECOMP representation. * * @param curve The curve. * @param ypx The $y + x$ value. * @param ymx The $y - x$ value. * @param xy2d The $2 * d * x * y$ value. * @return The group element in PRECOMP representation. */ public static GroupElement precomp( final Curve curve, final FieldElement ypx, final FieldElement ymx, final FieldElement xy2d) { return new GroupElement(curve, Representation.PRECOMP, ypx, ymx, xy2d, null); } /** * Creates a new group element in CACHED representation. * * @param curve The curve. * @param YpX The $Y + X$ value. * @param YmX The $Y - X$ value. * @param Z The $Z$ coordinate. * @param T2d The $2 * d * T$ value. * @return The group element in CACHED representation. */ public static GroupElement cached( final Curve curve, final FieldElement YpX, final FieldElement YmX, final FieldElement Z, final FieldElement T2d) { return new GroupElement(curve, Representation.CACHED, YpX, YmX, Z, T2d); } /** * Variable is package private only so that tests run. */ final Curve curve; /** * Variable is package private only so that tests run. */ final Representation repr; /** * Variable is package private only so that tests run. */ final FieldElement X; /** * Variable is package private only so that tests run. */ final FieldElement Y; /** * Variable is package private only so that tests run. */ final FieldElement Z; /** * Variable is package private only so that tests run. */ final FieldElement T; /** * Precomputed table for {@link #scalarMultiply(byte[])}, * filled if necessary. *

* Variable is package private only so that tests run. */ final GroupElement[][] precmp; /** * Precomputed table for {@link #doubleScalarMultiplyVariableTime(GroupElement, byte[], byte[])}, * filled if necessary. *

* Variable is package private only so that tests run. */ final GroupElement[] dblPrecmp; /** * Creates a group element for a curve, without any pre-computation. * * @param curve The curve. * @param repr The representation used to represent the group element. * @param X The $X$ coordinate. * @param Y The $Y$ coordinate. * @param Z The $Z$ coordinate. * @param T The $T$ coordinate. */ public GroupElement( final Curve curve, final Representation repr, final FieldElement X, final FieldElement Y, final FieldElement Z, final FieldElement T) { this(curve, repr, X, Y, Z, T, false); } /** * Creates a group element for a curve, with optional pre-computation. * * @param curve The curve. * @param repr The representation used to represent the group element. * @param X The $X$ coordinate. * @param Y The $Y$ coordinate. * @param Z The $Z$ coordinate. * @param T The $T$ coordinate. * @param precomputeDouble If true, populate dblPrecmp, else set to null. */ public GroupElement( final Curve curve, final Representation repr, final FieldElement X, final FieldElement Y, final FieldElement Z, final FieldElement T, final boolean precomputeDouble) { this.curve = curve; this.repr = repr; this.X = X; this.Y = Y; this.Z = Z; this.T = T; this.precmp = null; this.dblPrecmp = precomputeDouble ? precomputeDouble() : null; } /** * Creates a group element for a curve from a given encoded point. No pre-computation. *

* A point $(x,y)$ is encoded by storing $y$ in bit 0 to bit 254 and the sign of $x$ in bit 255. * $x$ is recovered in the following way: *

    *
  • $x = sign(x) * \sqrt{(y^2 - 1) / (d * y^2 + 1)} = sign(x) * \sqrt{u / v}$ with $u = y^2 - 1$ and $v = d * y^2 + 1$. *
  • Setting $β = (u * v^3) * (u * v^7)^{((q - 5) / 8)}$ one has $β^2 = \pm(u / v)$. *
  • If $v * β = -u$ multiply $β$ with $i=\sqrt{-1}$. *
  • Set $x := β$. *
  • If $sign(x) \ne$ bit 255 of $s$ then negate $x$. *
* * @param curve The curve. * @param s The encoded point. */ public GroupElement(final Curve curve, final byte[] s) { this(curve, s, false); } /** * Creates a group element for a curve from a given encoded point. With optional pre-computation. *

* A point $(x,y)$ is encoded by storing $y$ in bit 0 to bit 254 and the sign of $x$ in bit 255. * $x$ is recovered in the following way: *

    *
  • $x = sign(x) * \sqrt{(y^2 - 1) / (d * y^2 + 1)} = sign(x) * \sqrt{u / v}$ with $u = y^2 - 1$ and $v = d * y^2 + 1$. *
  • Setting $β = (u * v^3) * (u * v^7)^{((q - 5) / 8)}$ one has $β^2 = \pm(u / v)$. *
  • If $v * β = -u$ multiply $β$ with $i=\sqrt{-1}$. *
  • Set $x := β$. *
  • If $sign(x) \ne$ bit 255 of $s$ then negate $x$. *
* * @param curve The curve. * @param s The encoded point. * @param precomputeSingleAndDouble If true, populate both precmp and dblPrecmp, else set both to null. */ public GroupElement(final Curve curve, final byte[] s, boolean precomputeSingleAndDouble) { FieldElement x, y, yy, u, v, v3, vxx, check; y = curve.getField().fromByteArray(s); yy = y.square(); // u = y^2-1 u = yy.subtractOne(); // v = dy^2+1 v = yy.multiply(curve.getD()).addOne(); // v3 = v^3 v3 = v.square().multiply(v); // x = (v3^2)vu, aka x = uv^7 x = v3.square().multiply(v).multiply(u); // x = (uv^7)^((q-5)/8) x = x.pow22523(); // x = uv^3(uv^7)^((q-5)/8) x = v3.multiply(u).multiply(x); vxx = x.square().multiply(v); check = vxx.subtract(u); // vx^2-u if (check.isNonZero()) { check = vxx.add(u); // vx^2+u if (check.isNonZero()) throw new IllegalArgumentException("not a valid GroupElement"); x = x.multiply(curve.getI()); } if ((x.isNegative() ? 1 : 0) != Utils.bit(s, curve.getField().getb()-1)) { x = x.negate(); } this.curve = curve; this.repr = Representation.P3; this.X = x; this.Y = y; this.Z = curve.getField().ONE; this.T = this.X.multiply(this.Y); if(precomputeSingleAndDouble) { precmp = precomputeSingle(); dblPrecmp = precomputeDouble(); } else { precmp = null; dblPrecmp = null; } } /** * Gets the curve of the group element. * * @return The curve. */ public Curve getCurve() { return this.curve; } /** * Gets the representation of the group element. * * @return The representation. */ public Representation getRepresentation() { return this.repr; } /** * Gets the $X$ value of the group element. * This is for most representation the projective $X$ coordinate. * * @return The $X$ value. */ public FieldElement getX() { return this.X; } /** * Gets the $Y$ value of the group element. * This is for most representation the projective $Y$ coordinate. * * @return The $Y$ value. */ public FieldElement getY() { return this.Y; } /** * Gets the $Z$ value of the group element. * This is for most representation the projective $Z$ coordinate. * * @return The $Z$ value. */ public FieldElement getZ() { return this.Z; } /** * Gets the $T$ value of the group element. * This is for most representation the projective $T$ coordinate. * * @return The $T$ value. */ public FieldElement getT() { return this.T; } /** * Converts the group element to an encoded point on the curve. * * @return The encoded point as byte array. */ public byte[] toByteArray() { switch (this.repr) { case P2: case P3: FieldElement recip = Z.invert(); FieldElement x = X.multiply(recip); FieldElement y = Y.multiply(recip); byte[] s = y.toByteArray(); s[s.length-1] |= (x.isNegative() ? (byte) 0x80 : 0); return s; default: return toP2().toByteArray(); } } /** * Converts the group element to the P2 representation. * * @return The group element in the P2 representation. */ public GroupElement toP2() { return toRep(Representation.P2); } /** * Converts the group element to the P3 representation. * * @return The group element in the P3 representation. */ public GroupElement toP3() { return toRep(Representation.P3); } /** * Converts the group element to the P3 representation, with dblPrecmp populated. * * @return The group element in the P3 representation. */ public GroupElement toP3PrecomputeDouble() { return toRep(Representation.P3PrecomputedDouble); } /** * Converts the group element to the CACHED representation. * * @return The group element in the CACHED representation. */ public GroupElement toCached() { return toRep(Representation.CACHED); } /** * Convert a GroupElement from one Representation to another. * TODO-CR: Add additional conversion? * $r = p$ *

* Supported conversions: *

    *
  • P3 $\rightarrow$ P2 *
  • P3 $\rightarrow$ CACHED (1 multiply, 1 add, 1 subtract) *
  • P1P1 $\rightarrow$ P2 (3 multiply) *
  • P1P1 $\rightarrow$ P3 (4 multiply) * * @param repr The representation to convert to. * @return A new group element in the given representation. */ private GroupElement toRep(final Representation repr) { switch (this.repr) { case P2: switch (repr) { case P2: return p2(this.curve, this.X, this.Y, this.Z); default: throw new IllegalArgumentException(); } case P3: switch (repr) { case P2: return p2(this.curve, this.X, this.Y, this.Z); case P3: return p3(this.curve, this.X, this.Y, this.Z, this.T); case CACHED: return cached(this.curve, this.Y.add(this.X), this.Y.subtract(this.X), this.Z, this.T.multiply(this.curve.get2D())); default: throw new IllegalArgumentException(); } case P1P1: switch (repr) { case P2: return p2(this.curve, this.X.multiply(this.T), Y.multiply(this.Z), this.Z.multiply(this.T)); case P3: return p3(this.curve, this.X.multiply(this.T), Y.multiply(this.Z), this.Z.multiply(this.T), this.X.multiply(this.Y), false); case P3PrecomputedDouble: return p3(this.curve, this.X.multiply(this.T), Y.multiply(this.Z), this.Z.multiply(this.T), this.X.multiply(this.Y), true); case P1P1: return p1p1(this.curve, this.X, this.Y, this.Z, this.T); default: throw new IllegalArgumentException(); } case PRECOMP: switch (repr) { case PRECOMP: return precomp(this.curve, this.X, this.Y, this.Z); default: throw new IllegalArgumentException(); } case CACHED: switch (repr) { case CACHED: return cached(this.curve, this.X, this.Y, this.Z, this.T); default: throw new IllegalArgumentException(); } default: throw new UnsupportedOperationException(); } } /** * Precomputes table for {@link #scalarMultiply(byte[])}. */ private GroupElement[][] precomputeSingle() { // Precomputation for single scalar multiplication. GroupElement[][] precmp = new GroupElement[32][8]; // TODO-CR BR: check that this == base point when the method is called. GroupElement Bi = this; for (int i = 0; i < 32; i++) { GroupElement Bij = Bi; for (int j = 0; j < 8; j++) { final FieldElement recip = Bij.Z.invert(); final FieldElement x = Bij.X.multiply(recip); final FieldElement y = Bij.Y.multiply(recip); precmp[i][j] = precomp(this.curve, y.add(x), y.subtract(x), x.multiply(y).multiply(this.curve.get2D())); Bij = Bij.add(Bi.toCached()).toP3(); } // Only every second summand is precomputed (16^2 = 256) for (int k = 0; k < 8; k++) { Bi = Bi.add(Bi.toCached()).toP3(); } } return precmp; } /** * Precomputes table for {@link #doubleScalarMultiplyVariableTime(GroupElement, byte[], byte[])}. */ private GroupElement[] precomputeDouble() { // Precomputation for double scalar multiplication. // P,3P,5P,7P,9P,11P,13P,15P GroupElement[] dblPrecmp = new GroupElement[8]; GroupElement Bi = this; for (int i = 0; i < 8; i++) { final FieldElement recip = Bi.Z.invert(); final FieldElement x = Bi.X.multiply(recip); final FieldElement y = Bi.Y.multiply(recip); dblPrecmp[i] = precomp(this.curve, y.add(x), y.subtract(x), x.multiply(y).multiply(this.curve.get2D())); // Bi = edwards(B,edwards(B,Bi)) Bi = this.add(this.add(Bi.toCached()).toP3().toCached()).toP3(); } return dblPrecmp; } /** * Doubles a given group element $p$ in $P^2$ or $P^3$ representation and returns the result in $P \times P$ representation. * $r = 2 * p$ where $p = (X : Y : Z)$ or $p = (X : Y : Z : T)$ *

    * $r$ in $P \times P$ representation: *

    * $r = ((X' : Z'), (Y' : T'))$ where *

      *
    • $X' = (X + Y)^2 - (Y^2 + X^2)$ *
    • $Y' = Y^2 + X^2$ *
    • $Z' = y^2 - X^2$ *
    • $T' = 2 * Z^2 - (y^2 - X^2)$ *

    * $r$ converted from $P \times P$ to $P^2$ representation: *

    * $r = (X'' : Y'' : Z'')$ where *

      *
    • $X'' = X' * Z' = ((X + Y)^2 - Y^2 - X^2) * (2 * Z^2 - (y^2 - X^2))$ *
    • $Y'' = Y' * T' = (Y^2 + X^2) * (2 * Z^2 - (y^2 - X^2))$ *
    • $Z'' = Z' * T' = (y^2 - X^2) * (2 * Z^2 - (y^2 - X^2))$ *

    * Formula for the $P^2$ representation is in agreement with the formula given in [4] page 12 (with $a = -1$) * up to a common factor -1 which does not matter: *

    * $$ * B = (X + Y)^2; C = X^2; D = Y^2; E = -C = -X^2; F := E + D = Y^2 - X^2; H = Z^2; J = F − 2 * H; \\ * X3 = (B − C − D) · J = X' * (-T'); \\ * Y3 = F · (E − D) = Z' * (-Y'); \\ * Z3 = F · J = Z' * (-T'). * $$ * * @return The P1P1 representation */ public GroupElement dbl() { switch (this.repr) { case P2: case P3: // Ignore T for P3 representation FieldElement XX, YY, B, A, AA, Yn, Zn; XX = this.X.square(); YY = this.Y.square(); B = this.Z.squareAndDouble(); A = this.X.add(this.Y); AA = A.square(); Yn = YY.add(XX); Zn = YY.subtract(XX); return p1p1(this.curve, AA.subtract(Yn), Yn, Zn, B.subtract(Zn)); default: throw new UnsupportedOperationException(); } } /** * GroupElement addition using the twisted Edwards addition law with * extended coordinates (Hisil2008). *

    * this must be in $P^3$ representation and $q$ in PRECOMP representation. * $r = p + q$ where $p = this = (X1 : Y1 : Z1 : T1), q = (q.X, q.Y, q.Z) = (Y2/Z2 + X2/Z2, Y2/Z2 - X2/Z2, 2 * d * X2/Z2 * Y2/Z2)$ *

    * $r$ in $P \times P$ representation: *

    * $r = ((X' : Z'), (Y' : T'))$ where *

      *
    • $X' = (Y1 + X1) * q.X - (Y1 - X1) * q.Y = ((Y1 + X1) * (Y2 + X2) - (Y1 - X1) * (Y2 - X2)) * 1/Z2$ *
    • $Y' = (Y1 + X1) * q.X + (Y1 - X1) * q.Y = ((Y1 + X1) * (Y2 + X2) + (Y1 - X1) * (Y2 - X2)) * 1/Z2$ *
    • $Z' = 2 * Z1 + T1 * q.Z = 2 * Z1 + T1 * 2 * d * X2 * Y2 * 1/Z2^2 = (2 * Z1 * Z2 + 2 * d * T1 * T2) * 1/Z2$ *
    • $T' = 2 * Z1 - T1 * q.Z = 2 * Z1 - T1 * 2 * d * X2 * Y2 * 1/Z2^2 = (2 * Z1 * Z2 - 2 * d * T1 * T2) * 1/Z2$ *

    * Setting $A = (Y1 - X1) * (Y2 - X2), B = (Y1 + X1) * (Y2 + X2), C = 2 * d * T1 * T2, D = 2 * Z1 * Z2$ we get *

      *
    • $X' = (B - A) * 1/Z2$ *
    • $Y' = (B + A) * 1/Z2$ *
    • $Z' = (D + C) * 1/Z2$ *
    • $T' = (D - C) * 1/Z2$ *

    * $r$ converted from $P \times P$ to $P^2$ representation: *

    * $r = (X'' : Y'' : Z'' : T'')$ where *

      *
    • $X'' = X' * Z' = (B - A) * (D + C) * 1/Z2^2$ *
    • $Y'' = Y' * T' = (B + A) * (D - C) * 1/Z2^2$ *
    • $Z'' = Z' * T' = (D + C) * (D - C) * 1/Z2^2$ *
    • $T'' = X' * Y' = (B - A) * (B + A) * 1/Z2^2$ *

    * TODO-CR BR: Formula for the $P^2$ representation is not in agreement with the formula given in [2] page 6
    * TODO-CR BR: (the common factor $1/Z2^2$ does not matter):
    * $$ * E = B - A, F = D - C, G = D + C, H = B + A \\ * X3 = E * F = (B - A) * (D - C); \\ * Y3 = G * H = (D + C) * (B + A); \\ * Z3 = F * G = (D - C) * (D + C); \\ * T3 = E * H = (B - A) * (B + A); * $$ * * @param q the PRECOMP representation of the GroupElement to add. * @return the P1P1 representation of the result. */ private GroupElement madd(GroupElement q) { if (this.repr != Representation.P3) throw new UnsupportedOperationException(); if (q.repr != Representation.PRECOMP) throw new IllegalArgumentException(); FieldElement YpX, YmX, A, B, C, D; YpX = this.Y.add(this.X); YmX = this.Y.subtract(this.X); A = YpX.multiply(q.X); // q->y+x B = YmX.multiply(q.Y); // q->y-x C = q.Z.multiply(this.T); // q->2dxy D = this.Z.add(this.Z); return p1p1(this.curve, A.subtract(B), A.add(B), D.add(C), D.subtract(C)); } /** * GroupElement subtraction using the twisted Edwards addition law with * extended coordinates (Hisil2008). *

    * this must be in $P^3$ representation and $q$ in PRECOMP representation. * $r = p - q$ where $p = this = (X1 : Y1 : Z1 : T1), q = (q.X, q.Y, q.Z) = (Y2/Z2 + X2/Z2, Y2/Z2 - X2/Z2, 2 * d * X2/Z2 * Y2/Z2)$ *

    * Negating $q$ means negating the value of $X2$ and $T2$ (the latter is irrelevant here). * The formula is in accordance to {@link #madd the above addition}. * * @param q the PRECOMP representation of the GroupElement to subtract. * @return the P1P1 representation of the result. */ private GroupElement msub(GroupElement q) { if (this.repr != Representation.P3) throw new UnsupportedOperationException(); if (q.repr != Representation.PRECOMP) throw new IllegalArgumentException(); FieldElement YpX, YmX, A, B, C, D; YpX = this.Y.add(this.X); YmX = this.Y.subtract(this.X); A = YpX.multiply(q.Y); // q->y-x B = YmX.multiply(q.X); // q->y+x C = q.Z.multiply(this.T); // q->2dxy D = this.Z.add(this.Z); return p1p1(this.curve, A.subtract(B), A.add(B), D.subtract(C), D.add(C)); } /** * GroupElement addition using the twisted Edwards addition law with * extended coordinates (Hisil2008). *

    * this must be in $P^3$ representation and $q$ in CACHED representation. * $r = p + q$ where $p = this = (X1 : Y1 : Z1 : T1), q = (q.X, q.Y, q.Z, q.T) = (Y2 + X2, Y2 - X2, Z2, 2 * d * T2)$ *

    * $r$ in $P \times P$ representation: *

      *
    • $X' = (Y1 + X1) * (Y2 + X2) - (Y1 - X1) * (Y2 - X2)$ *
    • $Y' = (Y1 + X1) * (Y2 + X2) + (Y1 - X1) * (Y2 - X2)$ *
    • $Z' = 2 * Z1 * Z2 + 2 * d * T1 * T2$ *
    • $T' = 2 * Z1 * T2 - 2 * d * T1 * T2$ *

    * Setting $A = (Y1 - X1) * (Y2 - X2), B = (Y1 + X1) * (Y2 + X2), C = 2 * d * T1 * T2, D = 2 * Z1 * Z2$ we get *

      *
    • $X' = (B - A)$ *
    • $Y' = (B + A)$ *
    • $Z' = (D + C)$ *
    • $T' = (D - C)$ *

    * Same result as in {@link #madd} (up to a common factor which does not matter). * * @param q the CACHED representation of the GroupElement to add. * @return the P1P1 representation of the result. */ public GroupElement add(GroupElement q) { if (this.repr != Representation.P3) throw new UnsupportedOperationException(); if (q.repr != Representation.CACHED) throw new IllegalArgumentException(); FieldElement YpX, YmX, A, B, C, ZZ, D; YpX = this.Y.add(this.X); YmX = this.Y.subtract(this.X); A = YpX.multiply(q.X); // q->Y+X B = YmX.multiply(q.Y); // q->Y-X C = q.T.multiply(this.T); // q->2dT ZZ = this.Z.multiply(q.Z); D = ZZ.add(ZZ); return p1p1(this.curve, A.subtract(B), A.add(B), D.add(C), D.subtract(C)); } /** * GroupElement subtraction using the twisted Edwards addition law with * extended coordinates (Hisil2008). *

    * $r = p - q$ *

    * Negating $q$ means negating the value of the coordinate $X2$ and $T2$. * The formula is in accordance to {@link #add the above addition}. * * @param q the PRECOMP representation of the GroupElement to subtract. * @return the P1P1 representation of the result. */ public GroupElement sub(GroupElement q) { if (this.repr != Representation.P3) throw new UnsupportedOperationException(); if (q.repr != Representation.CACHED) throw new IllegalArgumentException(); FieldElement YpX, YmX, A, B, C, ZZ, D; YpX = Y.add(X); YmX = Y.subtract(X); A = YpX.multiply(q.Y); // q->Y-X B = YmX.multiply(q.X); // q->Y+X C = q.T.multiply(T); // q->2dT ZZ = Z.multiply(q.Z); D = ZZ.add(ZZ); return p1p1(curve, A.subtract(B), A.add(B), D.subtract(C), D.add(C)); } /** * Negates this group element by subtracting it from the neutral group element. *

    * TODO-CR BR: why not simply negate the coordinates $X$ and $T$? * * @return The negative of this group element. */ public GroupElement negate() { if (this.repr != Representation.P3) throw new UnsupportedOperationException(); return this.curve.getZero(Representation.P3).sub(toCached()).toP3PrecomputeDouble(); } @Override public int hashCode() { return Arrays.hashCode(this.toByteArray()); } @Override public boolean equals(Object obj) { if (obj == this) return true; if (!(obj instanceof GroupElement)) return false; GroupElement ge = (GroupElement) obj; if (!this.repr.equals(ge.repr)) { try { ge = ge.toRep(this.repr); } catch (RuntimeException e) { return false; } } switch (this.repr) { case P2: case P3: // Try easy way first if (this.Z.equals(ge.Z)) return this.X.equals(ge.X) && this.Y.equals(ge.Y); // X1/Z1 = X2/Z2 --> X1*Z2 = X2*Z1 final FieldElement x1 = this.X.multiply(ge.Z); final FieldElement y1 = this.Y.multiply(ge.Z); final FieldElement x2 = ge.X.multiply(this.Z); final FieldElement y2 = ge.Y.multiply(this.Z); return x1.equals(x2) && y1.equals(y2); case P1P1: return toP2().equals(ge); case PRECOMP: // Compare directly, PRECOMP is derived directly from x and y return this.X.equals(ge.X) && this.Y.equals(ge.Y) && this.Z.equals(ge.Z); case CACHED: // Try easy way first if (this.Z.equals(ge.Z)) return this.X.equals(ge.X) && this.Y.equals(ge.Y) && this.T.equals(ge.T); // (Y+X)/Z = y+x etc. final FieldElement x3 = this.X.multiply(ge.Z); final FieldElement y3 = this.Y.multiply(ge.Z); final FieldElement t3 = this.T.multiply(ge.Z); final FieldElement x4 = ge.X.multiply(this.Z); final FieldElement y4 = ge.Y.multiply(this.Z); final FieldElement t4 = ge.T.multiply(this.Z); return x3.equals(x4) && y3.equals(y4) && t3.equals(t4); default: return false; } } /** * Convert a to radix 16. *

    * Method is package private only so that tests run. * * @param a $= a[0]+256*a[1]+...+256^{31} a[31]$ * @return 64 bytes, each between -8 and 7 */ static byte[] toRadix16(final byte[] a) { final byte[] e = new byte[64]; int i; // Radix 16 notation for (i = 0; i < 32; i++) { e[2*i+0] = (byte) (a[i] & 15); e[2*i+1] = (byte) ((a[i] >> 4) & 15); } /* each e[i] is between 0 and 15 */ /* e[63] is between 0 and 7 */ int carry = 0; for (i = 0; i < 63; i++) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry << 4; } e[63] += carry; /* each e[i] is between -8 and 7 */ return e; } /** * Constant-time conditional move. *

    * Replaces this with $u$ if $b == 1$.
    * Replaces this with this if $b == 0$. *

    * Method is package private only so that tests run. * * @param u The group element to return if $b == 1$. * @param b in $\{0, 1\}$ * @return $u$ if $b == 1$; this if $b == 0$. Results undefined if $b$ is not in $\{0, 1\}$. */ GroupElement cmov(final GroupElement u, final int b) { return precomp(curve, X.cmov(u.X, b), Y.cmov(u.Y, b), Z.cmov(u.Z, b)); } /** * Look up $16^i r_i B$ in the precomputed table. *

    * No secret array indices, no secret branching. * Constant time. *

    * Must have previously precomputed. *

    * Method is package private only so that tests run. * * @param pos $= i/2$ for $i$ in $\{0, 2, 4,..., 62\}$ * @param b $= r_i$ * @return the GroupElement */ GroupElement select(final int pos, final int b) { // Is r_i negative? final int bnegative = Utils.negative(b); // |r_i| final int babs = b - (((-bnegative) & b) << 1); // 16^i |r_i| B final GroupElement t = this.curve.getZero(Representation.PRECOMP) .cmov(this.precmp[pos][0], Utils.equal(babs, 1)) .cmov(this.precmp[pos][1], Utils.equal(babs, 2)) .cmov(this.precmp[pos][2], Utils.equal(babs, 3)) .cmov(this.precmp[pos][3], Utils.equal(babs, 4)) .cmov(this.precmp[pos][4], Utils.equal(babs, 5)) .cmov(this.precmp[pos][5], Utils.equal(babs, 6)) .cmov(this.precmp[pos][6], Utils.equal(babs, 7)) .cmov(this.precmp[pos][7], Utils.equal(babs, 8)); // -16^i |r_i| B final GroupElement tminus = precomp(curve, t.Y, t.X, t.Z.negate()); // 16^i r_i B return t.cmov(tminus, bnegative); } /** * $h = a * B$ where $a = a[0]+256*a[1]+\dots+256^{31} a[31]$ and * $B$ is this point. If its lookup table has not been precomputed, it * will be at the start of the method (and cached for later calls). * Constant time. *

    * Preconditions: (TODO: Check this applies here) * $a[31] \le 127$ * @param a $= a[0]+256*a[1]+\dots+256^{31} a[31]$ * @return the GroupElement */ public GroupElement scalarMultiply(final byte[] a) { GroupElement t; int i; final byte[] e = toRadix16(a); GroupElement h = this.curve.getZero(Representation.P3); for (i = 1; i < 64; i += 2) { t = select(i/2, e[i]); h = h.madd(t).toP3(); } h = h.dbl().toP2().dbl().toP2().dbl().toP2().dbl().toP3(); for (i = 0; i < 64; i += 2) { t = select(i/2, e[i]); h = h.madd(t).toP3(); } return h; } /** * Calculates a sliding-windows base 2 representation for a given value $a$. * To learn more about it see [6] page 8. *

    * Output: $r$ which satisfies * $a = r0 * 2^0 + r1 * 2^1 + \dots + r255 * 2^{255}$ with $ri$ in $\{-15, -13, -11, -9, -7, -5, -3, -1, 0, 1, 3, 5, 7, 9, 11, 13, 15\}$ *

    * Method is package private only so that tests run. * * @param a $= a[0]+256*a[1]+\dots+256^{31} a[31]$. * @return The byte array $r$ in the above described form. */ static byte[] slide(final byte[] a) { byte[] r = new byte[256]; // Put each bit of 'a' into a separate byte, 0 or 1 for (int i = 0; i < 256; ++i) { r[i] = (byte) (1 & (a[i >> 3] >> (i & 7))); } // Note: r[i] will always be odd. for (int i = 0; i < 256; ++i) { if (r[i] != 0) { for (int b = 1; b <= 6 && i + b < 256; ++b) { // Accumulate bits if possible if (r[i + b] != 0) { if (r[i] + (r[i + b] << b) <= 15) { r[i] += r[i + b] << b; r[i + b] = 0; } else if (r[i] - (r[i + b] << b) >= -15) { r[i] -= r[i + b] << b; for (int k = i + b; k < 256; ++k) { if (r[k] == 0) { r[k] = 1; break; } r[k] = 0; } } else break; } } } } return r; } /** * $r = a * A + b * B$ where $a = a[0]+256*a[1]+\dots+256^{31} a[31]$, * $b = b[0]+256*b[1]+\dots+256^{31} b[31]$ and $B$ is this point. *

    * $A$ must have been previously precomputed. * * @param A in P3 representation. * @param a $= a[0]+256*a[1]+\dots+256^{31} a[31]$ * @param b $= b[0]+256*b[1]+\dots+256^{31} b[31]$ * @return the GroupElement */ public GroupElement doubleScalarMultiplyVariableTime(final GroupElement A, final byte[] a, final byte[] b) { // TODO-CR BR: A check that this is the base point is needed. final byte[] aslide = slide(a); final byte[] bslide = slide(b); GroupElement r = this.curve.getZero(Representation.P2); int i; for (i = 255; i >= 0; --i) { if (aslide[i] != 0 || bslide[i] != 0) break; } for (; i >= 0; --i) { GroupElement t = r.dbl(); if (aslide[i] > 0) { t = t.toP3().madd(A.dblPrecmp[aslide[i]/2]); } else if(aslide[i] < 0) { t = t.toP3().msub(A.dblPrecmp[(-aslide[i])/2]); } if (bslide[i] > 0) { t = t.toP3().madd(this.dblPrecmp[bslide[i]/2]); } else if(bslide[i] < 0) { t = t.toP3().msub(this.dblPrecmp[(-bslide[i])/2]); } r = t.toP2(); } return r; } /** * Verify that a point is on its curve. * @return true if the point lies on its curve. */ public boolean isOnCurve() { return isOnCurve(curve); } /** * Verify that a point is on the curve. * @param curve The curve to check. * @return true if the point lies on the curve. */ public boolean isOnCurve(Curve curve) { switch (repr) { case P2: case P3: FieldElement recip = Z.invert(); FieldElement x = X.multiply(recip); FieldElement y = Y.multiply(recip); FieldElement xx = x.square(); FieldElement yy = y.square(); FieldElement dxxyy = curve.getD().multiply(xx).multiply(yy); return curve.getField().ONE.add(dxxyy).add(xx).equals(yy); default: return toP2().isOnCurve(curve); } } @Override public String toString() { return "[GroupElement\nX="+X+"\nY="+Y+"\nZ="+Z+"\nT="+T+"\n]"; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/ScalarOps.java000066400000000000000000000016751327341674300251770ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; public interface ScalarOps { /** * Reduce the given scalar mod $l$. *

    * From the Ed25519 paper:
    * Here we interpret $2b$-bit strings in little-endian form as integers in * $\{0, 1,..., 2^{(2b)}-1\}$. * @param s the scalar to reduce * @return $s \bmod l$ */ public byte[] reduce(byte[] s); /** * $r = (a * b + c) \bmod l$ * @param a a scalar * @param b a scalar * @param c a scalar * @return $(a*b + c) \bmod l$ */ public byte[] multiplyAndAdd(byte[] a, byte[] b, byte[] c); } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/bigint/000077500000000000000000000000001327341674300237105ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/bigint/BigIntegerFieldElement.java000066400000000000000000000073311327341674300310540ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.bigint; import java.io.Serializable; import java.math.BigInteger; import net.i2p.crypto.eddsa.math.Field; import net.i2p.crypto.eddsa.math.FieldElement; /** * A particular element of the field \Z/(2^255-19). * @author str4d * */ public class BigIntegerFieldElement extends FieldElement implements Serializable { private static final long serialVersionUID = 4890398908392808L; /** * Variable is package private for encoding. */ final BigInteger bi; public BigIntegerFieldElement(Field f, BigInteger bi) { super(f); this.bi = bi; } public boolean isNonZero() { return !bi.equals(BigInteger.ZERO); } public FieldElement add(FieldElement val) { return new BigIntegerFieldElement(f, bi.add(((BigIntegerFieldElement)val).bi)).mod(f.getQ()); } @Override public FieldElement addOne() { return new BigIntegerFieldElement(f, bi.add(BigInteger.ONE)).mod(f.getQ()); } public FieldElement subtract(FieldElement val) { return new BigIntegerFieldElement(f, bi.subtract(((BigIntegerFieldElement)val).bi)).mod(f.getQ()); } @Override public FieldElement subtractOne() { return new BigIntegerFieldElement(f, bi.subtract(BigInteger.ONE)).mod(f.getQ()); } public FieldElement negate() { return f.getQ().subtract(this); } @Override public FieldElement divide(FieldElement val) { return divide(((BigIntegerFieldElement)val).bi); } public FieldElement divide(BigInteger val) { return new BigIntegerFieldElement(f, bi.divide(val)).mod(f.getQ()); } public FieldElement multiply(FieldElement val) { return new BigIntegerFieldElement(f, bi.multiply(((BigIntegerFieldElement)val).bi)).mod(f.getQ()); } public FieldElement square() { return multiply(this); } public FieldElement squareAndDouble() { FieldElement sq = square(); return sq.add(sq); } public FieldElement invert() { // Euler's theorem //return modPow(f.getQm2(), f.getQ()); return new BigIntegerFieldElement(f, bi.modInverse(((BigIntegerFieldElement)f.getQ()).bi)); } public FieldElement mod(FieldElement m) { return new BigIntegerFieldElement(f, bi.mod(((BigIntegerFieldElement)m).bi)); } public FieldElement modPow(FieldElement e, FieldElement m) { return new BigIntegerFieldElement(f, bi.modPow(((BigIntegerFieldElement)e).bi, ((BigIntegerFieldElement)m).bi)); } public FieldElement pow(FieldElement e){ return modPow(e, f.getQ()); } public FieldElement pow22523(){ return pow(f.getQm5d8()); } @Override public FieldElement cmov(FieldElement val, int b) { // Not constant-time, but it doesn't really matter because none of the underlying BigInteger operations // are either, so there's not much point in trying hard here ... return b == 0 ? this : val; } @Override public int hashCode() { return bi.hashCode(); } @Override public boolean equals(Object obj) { if (!(obj instanceof BigIntegerFieldElement)) return false; BigIntegerFieldElement fe = (BigIntegerFieldElement) obj; return bi.equals(fe.bi); } @Override public String toString() { return "[BigIntegerFieldElement val="+bi+"]"; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/bigint/BigIntegerLittleEndianEncoding.java000066400000000000000000000064341327341674300325450ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.bigint; import java.io.Serializable; import java.math.BigInteger; import net.i2p.crypto.eddsa.math.Encoding; import net.i2p.crypto.eddsa.math.Field; import net.i2p.crypto.eddsa.math.FieldElement; public class BigIntegerLittleEndianEncoding extends Encoding implements Serializable { private static final long serialVersionUID = 3984579843759837L; /** * Mask where only the first b-1 bits are set. */ private BigInteger mask; @Override public synchronized void setField(Field f) { super.setField(f); mask = BigInteger.ONE.shiftLeft(f.getb()-1).subtract(BigInteger.ONE); } public byte[] encode(FieldElement x) { return encode(((BigIntegerFieldElement)x).bi.and(mask)); } /** * Convert $x$ to little endian. * Constant time. * * @param x the BigInteger value to encode * @return array of length $b/8$ * @throws IllegalStateException if field not set */ public byte[] encode(BigInteger x) { if (f == null) throw new IllegalStateException("field not set"); byte[] in = x.toByteArray(); byte[] out = new byte[f.getb()/8]; for (int i = 0; i < in.length; i++) { out[i] = in[in.length-1-i]; } for (int i = in.length; i < out.length; i++) { out[i] = 0; } return out; } /** * Decode a FieldElement from its $(b-1)$-bit encoding. * The highest bit is masked out. * * @param in the $(b-1)$-bit encoding of a FieldElement. * @return the FieldElement represented by 'val'. * @throws IllegalStateException if field not set * @throws IllegalArgumentException if encoding is invalid */ public FieldElement decode(byte[] in) { if (f == null) throw new IllegalStateException("field not set"); if (in.length != f.getb()/8) throw new IllegalArgumentException("Not a valid encoding"); return new BigIntegerFieldElement(f, toBigInteger(in).and(mask)); } /** * Convert in to big endian * * @param in the $(b-1)$-bit encoding of a FieldElement. * @return the decoded value as a BigInteger */ public BigInteger toBigInteger(byte[] in) { byte[] out = new byte[in.length]; for (int i = 0; i < in.length; i++) { out[i] = in[in.length-1-i]; } return new BigInteger(1, out); } /** * From the Ed25519 paper:
    * $x$ is negative if the $(b-1)$-bit encoding of $x$ is lexicographically larger * than the $(b-1)$-bit encoding of $-x$. If $q$ is an odd prime and the encoding * is the little-endian representation of $\{0, 1,\dots, q-1\}$ then the negative * elements of $F_q$ are $\{1, 3, 5,\dots, q-2\}$. * @return true if negative */ public boolean isNegative(FieldElement x) { return ((BigIntegerFieldElement)x).bi.testBit(0); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/bigint/BigIntegerScalarOps.java000066400000000000000000000021061327341674300304010ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.bigint; import java.math.BigInteger; import net.i2p.crypto.eddsa.math.Field; import net.i2p.crypto.eddsa.math.ScalarOps; public class BigIntegerScalarOps implements ScalarOps { private final BigInteger l; private final BigIntegerLittleEndianEncoding enc; public BigIntegerScalarOps(Field f, BigInteger l) { this.l = l; enc = new BigIntegerLittleEndianEncoding(); enc.setField(f); } public byte[] reduce(byte[] s) { return enc.encode(enc.toBigInteger(s).mod(l)); } public byte[] multiplyAndAdd(byte[] a, byte[] b, byte[] c) { return enc.encode(enc.toBigInteger(a).multiply(enc.toBigInteger(b)).add(enc.toBigInteger(c)).mod(l)); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/bigint/package.html000066400000000000000000000003221327341674300261660ustar00rootroot00000000000000

    Low-level, non-optimized implementation using BigIntegers for any curve. See the ed25519 implementation for Curve 25519.

    str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/ed25519/000077500000000000000000000000001327341674300234325ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/ed25519/Ed25519FieldElement.java000066400000000000000000001010651327341674300275140ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.ed25519; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.math.*; import java.util.Arrays; /** * Class to represent a field element of the finite field $p = 2^{255} - 19$ elements. *

    * An element $t$, entries $t[0] \dots t[9]$, represents the integer * $t[0]+2^{26} t[1]+2^{51} t[2]+2^{77} t[3]+2^{102} t[4]+\dots+2^{230} t[9]$. * Bounds on each $t[i]$ vary depending on context. *

    * Reviewed/commented by Bloody Rookie (nemproject@gmx.de) */ public class Ed25519FieldElement extends FieldElement { /** * Variable is package private for encoding. */ final int[] t; /** * Creates a field element. * * @param f The underlying field, must be the finite field with $p = 2^{255} - 19$ elements * @param t The $2^{25.5}$ bit representation of the field element. */ public Ed25519FieldElement(Field f, int[] t) { super(f); if (t.length != 10) throw new IllegalArgumentException("Invalid radix-2^51 representation"); this.t = t; } private static final byte[] ZERO = new byte[32]; /** * Gets a value indicating whether or not the field element is non-zero. * * @return 1 if it is non-zero, 0 otherwise. */ public boolean isNonZero() { final byte[] s = toByteArray(); return Utils.equal(s, ZERO) == 0; } /** * $h = f + g$ *

    * TODO-CR BR: $h$ is allocated via new, probably not a good idea. Do we need the copying into temp variables if we do that? *

    * Preconditions: *

      *
    • $|f|$ bounded by $1.1*2^{25},1.1*2^{24},1.1*2^{25},1.1*2^{24},$ etc. *
    • $|g|$ bounded by $1.1*2^{25},1.1*2^{24},1.1*2^{25},1.1*2^{24},$ etc. *

    * Postconditions: *

      *
    • $|h|$ bounded by $1.1*2^{26},1.1*2^{25},1.1*2^{26},1.1*2^{25},$ etc. *
    * * @param val The field element to add. * @return The field element this + val. */ public FieldElement add(FieldElement val) { int[] g = ((Ed25519FieldElement)val).t; int[] h = new int[10]; for (int i = 0; i < 10; i++) { h[i] = t[i] + g[i]; } return new Ed25519FieldElement(f, h); } /** * $h = f - g$ *

    * Can overlap $h$ with $f$ or $g$. *

    * TODO-CR BR: See above. *

    * Preconditions: *

      *
    • $|f|$ bounded by $1.1*2^{25},1.1*2^{24},1.1*2^{25},1.1*2^{24},$ etc. *
    • $|g|$ bounded by $1.1*2^{25},1.1*2^{24},1.1*2^{25},1.1*2^{24},$ etc. *

    * Postconditions: *

      *
    • $|h|$ bounded by $1.1*2^{26},1.1*2^{25},1.1*2^{26},1.1*2^{25},$ etc. *
    * * @param val The field element to subtract. * @return The field element this - val. **/ public FieldElement subtract(FieldElement val) { int[] g = ((Ed25519FieldElement)val).t; int[] h = new int[10]; for (int i = 0; i < 10; i++) { h[i] = t[i] - g[i]; } return new Ed25519FieldElement(f, h); } /** * $h = -f$ *

    * TODO-CR BR: see above. *

    * Preconditions: *

      *
    • $|f|$ bounded by $1.1*2^{25},1.1*2^{24},1.1*2^{25},1.1*2^{24},$ etc. *

    * Postconditions: *

      *
    • $|h|$ bounded by $1.1*2^{25},1.1*2^{24},1.1*2^{25},1.1*2^{24},$ etc. *
    * * @return The field element (-1) * this. */ public FieldElement negate() { int[] h = new int[10]; for (int i = 0; i < 10; i++) { h[i] = - t[i]; } return new Ed25519FieldElement(f, h); } /** * $h = f * g$ *

    * Can overlap $h$ with $f$ or $g$. *

    * Preconditions: *

      *
    • $|f|$ bounded by * $1.65*2^{26},1.65*2^{25},1.65*2^{26},1.65*2^{25},$ etc. *
    • $|g|$ bounded by * $1.65*2^{26},1.65*2^{25},1.65*2^{26},1.65*2^{25},$ etc. *

    * Postconditions: *

      *
    • $|h|$ bounded by * $1.01*2^{25},1.01*2^{24},1.01*2^{25},1.01*2^{24},$ etc. *

    * Notes on implementation strategy: *

    * Using schoolbook multiplication. Karatsuba would save a little in some * cost models. *

    * Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than * 64-bit postcomputations. *

    * There is one remaining multiplication by 19 in the carry chain; one *19 * precomputation can be merged into this, but the resulting data flow is * considerably less clean. *

    * There are 12 carries below. 10 of them are 2-way parallelizable and * vectorizable. Can get away with 11 carries, but then data flow is much * deeper. *

    * With tighter constraints on inputs can squeeze carries into int32. * * @param val The field element to multiply. * @return The (reasonably reduced) field element this * val. */ public FieldElement multiply(FieldElement val) { int[] g = ((Ed25519FieldElement)val).t; int g1_19 = 19 * g[1]; /* 1.959375*2^29 */ int g2_19 = 19 * g[2]; /* 1.959375*2^30; still ok */ int g3_19 = 19 * g[3]; int g4_19 = 19 * g[4]; int g5_19 = 19 * g[5]; int g6_19 = 19 * g[6]; int g7_19 = 19 * g[7]; int g8_19 = 19 * g[8]; int g9_19 = 19 * g[9]; int f1_2 = 2 * t[1]; int f3_2 = 2 * t[3]; int f5_2 = 2 * t[5]; int f7_2 = 2 * t[7]; int f9_2 = 2 * t[9]; long f0g0 = t[0] * (long) g[0]; long f0g1 = t[0] * (long) g[1]; long f0g2 = t[0] * (long) g[2]; long f0g3 = t[0] * (long) g[3]; long f0g4 = t[0] * (long) g[4]; long f0g5 = t[0] * (long) g[5]; long f0g6 = t[0] * (long) g[6]; long f0g7 = t[0] * (long) g[7]; long f0g8 = t[0] * (long) g[8]; long f0g9 = t[0] * (long) g[9]; long f1g0 = t[1] * (long) g[0]; long f1g1_2 = f1_2 * (long) g[1]; long f1g2 = t[1] * (long) g[2]; long f1g3_2 = f1_2 * (long) g[3]; long f1g4 = t[1] * (long) g[4]; long f1g5_2 = f1_2 * (long) g[5]; long f1g6 = t[1] * (long) g[6]; long f1g7_2 = f1_2 * (long) g[7]; long f1g8 = t[1] * (long) g[8]; long f1g9_38 = f1_2 * (long) g9_19; long f2g0 = t[2] * (long) g[0]; long f2g1 = t[2] * (long) g[1]; long f2g2 = t[2] * (long) g[2]; long f2g3 = t[2] * (long) g[3]; long f2g4 = t[2] * (long) g[4]; long f2g5 = t[2] * (long) g[5]; long f2g6 = t[2] * (long) g[6]; long f2g7 = t[2] * (long) g[7]; long f2g8_19 = t[2] * (long) g8_19; long f2g9_19 = t[2] * (long) g9_19; long f3g0 = t[3] * (long) g[0]; long f3g1_2 = f3_2 * (long) g[1]; long f3g2 = t[3] * (long) g[2]; long f3g3_2 = f3_2 * (long) g[3]; long f3g4 = t[3] * (long) g[4]; long f3g5_2 = f3_2 * (long) g[5]; long f3g6 = t[3] * (long) g[6]; long f3g7_38 = f3_2 * (long) g7_19; long f3g8_19 = t[3] * (long) g8_19; long f3g9_38 = f3_2 * (long) g9_19; long f4g0 = t[4] * (long) g[0]; long f4g1 = t[4] * (long) g[1]; long f4g2 = t[4] * (long) g[2]; long f4g3 = t[4] * (long) g[3]; long f4g4 = t[4] * (long) g[4]; long f4g5 = t[4] * (long) g[5]; long f4g6_19 = t[4] * (long) g6_19; long f4g7_19 = t[4] * (long) g7_19; long f4g8_19 = t[4] * (long) g8_19; long f4g9_19 = t[4] * (long) g9_19; long f5g0 = t[5] * (long) g[0]; long f5g1_2 = f5_2 * (long) g[1]; long f5g2 = t[5] * (long) g[2]; long f5g3_2 = f5_2 * (long) g[3]; long f5g4 = t[5] * (long) g[4]; long f5g5_38 = f5_2 * (long) g5_19; long f5g6_19 = t[5] * (long) g6_19; long f5g7_38 = f5_2 * (long) g7_19; long f5g8_19 = t[5] * (long) g8_19; long f5g9_38 = f5_2 * (long) g9_19; long f6g0 = t[6] * (long) g[0]; long f6g1 = t[6] * (long) g[1]; long f6g2 = t[6] * (long) g[2]; long f6g3 = t[6] * (long) g[3]; long f6g4_19 = t[6] * (long) g4_19; long f6g5_19 = t[6] * (long) g5_19; long f6g6_19 = t[6] * (long) g6_19; long f6g7_19 = t[6] * (long) g7_19; long f6g8_19 = t[6] * (long) g8_19; long f6g9_19 = t[6] * (long) g9_19; long f7g0 = t[7] * (long) g[0]; long f7g1_2 = f7_2 * (long) g[1]; long f7g2 = t[7] * (long) g[2]; long f7g3_38 = f7_2 * (long) g3_19; long f7g4_19 = t[7] * (long) g4_19; long f7g5_38 = f7_2 * (long) g5_19; long f7g6_19 = t[7] * (long) g6_19; long f7g7_38 = f7_2 * (long) g7_19; long f7g8_19 = t[7] * (long) g8_19; long f7g9_38 = f7_2 * (long) g9_19; long f8g0 = t[8] * (long) g[0]; long f8g1 = t[8] * (long) g[1]; long f8g2_19 = t[8] * (long) g2_19; long f8g3_19 = t[8] * (long) g3_19; long f8g4_19 = t[8] * (long) g4_19; long f8g5_19 = t[8] * (long) g5_19; long f8g6_19 = t[8] * (long) g6_19; long f8g7_19 = t[8] * (long) g7_19; long f8g8_19 = t[8] * (long) g8_19; long f8g9_19 = t[8] * (long) g9_19; long f9g0 = t[9] * (long) g[0]; long f9g1_38 = f9_2 * (long) g1_19; long f9g2_19 = t[9] * (long) g2_19; long f9g3_38 = f9_2 * (long) g3_19; long f9g4_19 = t[9] * (long) g4_19; long f9g5_38 = f9_2 * (long) g5_19; long f9g6_19 = t[9] * (long) g6_19; long f9g7_38 = f9_2 * (long) g7_19; long f9g8_19 = t[9] * (long) g8_19; long f9g9_38 = f9_2 * (long) g9_19; /** * Remember: 2^255 congruent 19 modulo p. * h = h0 * 2^0 + h1 * 2^26 + h2 * 2^(26+25) + h3 * 2^(26+25+26) + ... + h9 * 2^(5*26+5*25). * So to get the real number we would have to multiply the coefficients with the corresponding powers of 2. * To get an idea what is going on below, look at the calculation of h0: * h0 is the coefficient to the power 2^0 so it collects (sums) all products that have the power 2^0. * f0 * g0 really is f0 * 2^0 * g0 * 2^0 = (f0 * g0) * 2^0. * f1 * g9 really is f1 * 2^26 * g9 * 2^230 = f1 * g9 * 2^256 = 2 * f1 * g9 * 2^255 congruent 2 * 19 * f1 * g9 * 2^0 modulo p. * f2 * g8 really is f2 * 2^51 * g8 * 2^204 = f2 * g8 * 2^255 congruent 19 * f2 * g8 * 2^0 modulo p. * and so on... */ long h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; long h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; long h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; long h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; long h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; long h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; long h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; long h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; long h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; long h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0; long carry0; long carry1; long carry2; long carry3; long carry4; long carry5; long carry6; long carry7; long carry8; long carry9; /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; /* |h0| <= 2^25 */ /* |h4| <= 2^25 */ /* |h1| <= 1.71*2^59 */ /* |h5| <= 1.71*2^59 */ carry1 = (h1 + (long) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (long) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; /* |h1| <= 2^24; from now on fits into int32 */ /* |h5| <= 2^24; from now on fits into int32 */ /* |h2| <= 1.41*2^60 */ /* |h6| <= 1.41*2^60 */ carry2 = (h2 + (long) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (long) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; /* |h2| <= 2^25; from now on fits into int32 unchanged */ /* |h6| <= 2^25; from now on fits into int32 unchanged */ /* |h3| <= 1.71*2^59 */ /* |h7| <= 1.71*2^59 */ carry3 = (h3 + (long) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (long) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; /* |h3| <= 2^24; from now on fits into int32 unchanged */ /* |h7| <= 2^24; from now on fits into int32 unchanged */ /* |h4| <= 1.72*2^34 */ /* |h8| <= 1.41*2^60 */ carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (long) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; /* |h4| <= 2^25; from now on fits into int32 unchanged */ /* |h8| <= 2^25; from now on fits into int32 unchanged */ /* |h5| <= 1.01*2^24 */ /* |h9| <= 1.71*2^59 */ carry9 = (h9 + (long) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; /* |h9| <= 2^24; from now on fits into int32 unchanged */ /* |h0| <= 1.1*2^39 */ carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; /* |h0| <= 2^25; from now on fits into int32 unchanged */ /* |h1| <= 1.01*2^24 */ int[] h = new int[10]; h[0] = (int) h0; h[1] = (int) h1; h[2] = (int) h2; h[3] = (int) h3; h[4] = (int) h4; h[5] = (int) h5; h[6] = (int) h6; h[7] = (int) h7; h[8] = (int) h8; h[9] = (int) h9; return new Ed25519FieldElement(f, h); } /** * $h = f * f$ *

    * Can overlap $h$ with $f$. *

    * Preconditions: *

      *
    • $|f|$ bounded by $1.65*2^{26},1.65*2^{25},1.65*2^{26},1.65*2^{25},$ etc. *

    * Postconditions: *

      *
    • $|h|$ bounded by $1.01*2^{25},1.01*2^{24},1.01*2^{25},1.01*2^{24},$ etc. *

    * See {@link #multiply(FieldElement)} for discussion * of implementation strategy. * * @return The (reasonably reduced) square of this field element. */ public FieldElement square() { int f0 = t[0]; int f1 = t[1]; int f2 = t[2]; int f3 = t[3]; int f4 = t[4]; int f5 = t[5]; int f6 = t[6]; int f7 = t[7]; int f8 = t[8]; int f9 = t[9]; int f0_2 = 2 * f0; int f1_2 = 2 * f1; int f2_2 = 2 * f2; int f3_2 = 2 * f3; int f4_2 = 2 * f4; int f5_2 = 2 * f5; int f6_2 = 2 * f6; int f7_2 = 2 * f7; int f5_38 = 38 * f5; /* 1.959375*2^30 */ int f6_19 = 19 * f6; /* 1.959375*2^30 */ int f7_38 = 38 * f7; /* 1.959375*2^30 */ int f8_19 = 19 * f8; /* 1.959375*2^30 */ int f9_38 = 38 * f9; /* 1.959375*2^30 */ long f0f0 = f0 * (long) f0; long f0f1_2 = f0_2 * (long) f1; long f0f2_2 = f0_2 * (long) f2; long f0f3_2 = f0_2 * (long) f3; long f0f4_2 = f0_2 * (long) f4; long f0f5_2 = f0_2 * (long) f5; long f0f6_2 = f0_2 * (long) f6; long f0f7_2 = f0_2 * (long) f7; long f0f8_2 = f0_2 * (long) f8; long f0f9_2 = f0_2 * (long) f9; long f1f1_2 = f1_2 * (long) f1; long f1f2_2 = f1_2 * (long) f2; long f1f3_4 = f1_2 * (long) f3_2; long f1f4_2 = f1_2 * (long) f4; long f1f5_4 = f1_2 * (long) f5_2; long f1f6_2 = f1_2 * (long) f6; long f1f7_4 = f1_2 * (long) f7_2; long f1f8_2 = f1_2 * (long) f8; long f1f9_76 = f1_2 * (long) f9_38; long f2f2 = f2 * (long) f2; long f2f3_2 = f2_2 * (long) f3; long f2f4_2 = f2_2 * (long) f4; long f2f5_2 = f2_2 * (long) f5; long f2f6_2 = f2_2 * (long) f6; long f2f7_2 = f2_2 * (long) f7; long f2f8_38 = f2_2 * (long) f8_19; long f2f9_38 = f2 * (long) f9_38; long f3f3_2 = f3_2 * (long) f3; long f3f4_2 = f3_2 * (long) f4; long f3f5_4 = f3_2 * (long) f5_2; long f3f6_2 = f3_2 * (long) f6; long f3f7_76 = f3_2 * (long) f7_38; long f3f8_38 = f3_2 * (long) f8_19; long f3f9_76 = f3_2 * (long) f9_38; long f4f4 = f4 * (long) f4; long f4f5_2 = f4_2 * (long) f5; long f4f6_38 = f4_2 * (long) f6_19; long f4f7_38 = f4 * (long) f7_38; long f4f8_38 = f4_2 * (long) f8_19; long f4f9_38 = f4 * (long) f9_38; long f5f5_38 = f5 * (long) f5_38; long f5f6_38 = f5_2 * (long) f6_19; long f5f7_76 = f5_2 * (long) f7_38; long f5f8_38 = f5_2 * (long) f8_19; long f5f9_76 = f5_2 * (long) f9_38; long f6f6_19 = f6 * (long) f6_19; long f6f7_38 = f6 * (long) f7_38; long f6f8_38 = f6_2 * (long) f8_19; long f6f9_38 = f6 * (long) f9_38; long f7f7_38 = f7 * (long) f7_38; long f7f8_38 = f7_2 * (long) f8_19; long f7f9_76 = f7_2 * (long) f9_38; long f8f8_19 = f8 * (long) f8_19; long f8f9_38 = f8 * (long) f9_38; long f9f9_38 = f9 * (long) f9_38; /** * Same procedure as in multiply, but this time we have a higher symmetry leading to less summands. * e.g. f1f9_76 really stands for f1 * 2^26 * f9 * 2^230 + f9 * 2^230 + f1 * 2^26 congruent 2 * 2 * 19 * f1 * f9 2^0 modulo p. */ long h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; long h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; long h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; long h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; long h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; long h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; long h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; long h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; long h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; long h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; long carry0; long carry1; long carry2; long carry3; long carry4; long carry5; long carry6; long carry7; long carry8; long carry9; carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (long) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (long) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (long) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (long) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (long) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (long) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (long) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (long) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; int[] h = new int[10]; h[0] = (int) h0; h[1] = (int) h1; h[2] = (int) h2; h[3] = (int) h3; h[4] = (int) h4; h[5] = (int) h5; h[6] = (int) h6; h[7] = (int) h7; h[8] = (int) h8; h[9] = (int) h9; return new Ed25519FieldElement(f, h); } /** * $h = 2 * f * f$ *

    * Can overlap $h$ with $f$. *

    * Preconditions: *

      *
    • $|f|$ bounded by $1.65*2^{26},1.65*2^{25},1.65*2^{26},1.65*2^{25},$ etc. *

    * Postconditions: *

      *
    • $|h|$ bounded by $1.01*2^{25},1.01*2^{24},1.01*2^{25},1.01*2^{24},$ etc. *

    * See {@link #multiply(FieldElement)} for discussion * of implementation strategy. * * @return The (reasonably reduced) square of this field element times 2. */ public FieldElement squareAndDouble() { int f0 = t[0]; int f1 = t[1]; int f2 = t[2]; int f3 = t[3]; int f4 = t[4]; int f5 = t[5]; int f6 = t[6]; int f7 = t[7]; int f8 = t[8]; int f9 = t[9]; int f0_2 = 2 * f0; int f1_2 = 2 * f1; int f2_2 = 2 * f2; int f3_2 = 2 * f3; int f4_2 = 2 * f4; int f5_2 = 2 * f5; int f6_2 = 2 * f6; int f7_2 = 2 * f7; int f5_38 = 38 * f5; /* 1.959375*2^30 */ int f6_19 = 19 * f6; /* 1.959375*2^30 */ int f7_38 = 38 * f7; /* 1.959375*2^30 */ int f8_19 = 19 * f8; /* 1.959375*2^30 */ int f9_38 = 38 * f9; /* 1.959375*2^30 */ long f0f0 = f0 * (long) f0; long f0f1_2 = f0_2 * (long) f1; long f0f2_2 = f0_2 * (long) f2; long f0f3_2 = f0_2 * (long) f3; long f0f4_2 = f0_2 * (long) f4; long f0f5_2 = f0_2 * (long) f5; long f0f6_2 = f0_2 * (long) f6; long f0f7_2 = f0_2 * (long) f7; long f0f8_2 = f0_2 * (long) f8; long f0f9_2 = f0_2 * (long) f9; long f1f1_2 = f1_2 * (long) f1; long f1f2_2 = f1_2 * (long) f2; long f1f3_4 = f1_2 * (long) f3_2; long f1f4_2 = f1_2 * (long) f4; long f1f5_4 = f1_2 * (long) f5_2; long f1f6_2 = f1_2 * (long) f6; long f1f7_4 = f1_2 * (long) f7_2; long f1f8_2 = f1_2 * (long) f8; long f1f9_76 = f1_2 * (long) f9_38; long f2f2 = f2 * (long) f2; long f2f3_2 = f2_2 * (long) f3; long f2f4_2 = f2_2 * (long) f4; long f2f5_2 = f2_2 * (long) f5; long f2f6_2 = f2_2 * (long) f6; long f2f7_2 = f2_2 * (long) f7; long f2f8_38 = f2_2 * (long) f8_19; long f2f9_38 = f2 * (long) f9_38; long f3f3_2 = f3_2 * (long) f3; long f3f4_2 = f3_2 * (long) f4; long f3f5_4 = f3_2 * (long) f5_2; long f3f6_2 = f3_2 * (long) f6; long f3f7_76 = f3_2 * (long) f7_38; long f3f8_38 = f3_2 * (long) f8_19; long f3f9_76 = f3_2 * (long) f9_38; long f4f4 = f4 * (long) f4; long f4f5_2 = f4_2 * (long) f5; long f4f6_38 = f4_2 * (long) f6_19; long f4f7_38 = f4 * (long) f7_38; long f4f8_38 = f4_2 * (long) f8_19; long f4f9_38 = f4 * (long) f9_38; long f5f5_38 = f5 * (long) f5_38; long f5f6_38 = f5_2 * (long) f6_19; long f5f7_76 = f5_2 * (long) f7_38; long f5f8_38 = f5_2 * (long) f8_19; long f5f9_76 = f5_2 * (long) f9_38; long f6f6_19 = f6 * (long) f6_19; long f6f7_38 = f6 * (long) f7_38; long f6f8_38 = f6_2 * (long) f8_19; long f6f9_38 = f6 * (long) f9_38; long f7f7_38 = f7 * (long) f7_38; long f7f8_38 = f7_2 * (long) f8_19; long f7f9_76 = f7_2 * (long) f9_38; long f8f8_19 = f8 * (long) f8_19; long f8f9_38 = f8 * (long) f9_38; long f9f9_38 = f9 * (long) f9_38; long h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; long h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; long h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; long h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; long h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; long h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; long h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; long h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; long h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; long h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; long carry0; long carry1; long carry2; long carry3; long carry4; long carry5; long carry6; long carry7; long carry8; long carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (long) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (long) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (long) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (long) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (long) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (long) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (long) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (long) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; int[] h = new int[10]; h[0] = (int) h0; h[1] = (int) h1; h[2] = (int) h2; h[3] = (int) h3; h[4] = (int) h4; h[5] = (int) h5; h[6] = (int) h6; h[7] = (int) h7; h[8] = (int) h8; h[9] = (int) h9; return new Ed25519FieldElement(f, h); } /** * Invert this field element. *

    * The inverse is found via Fermat's little theorem:
    * $a^p \cong a \mod p$ and therefore $a^{(p-2)} \cong a^{-1} \mod p$ * * @return The inverse of this field element. */ public FieldElement invert() { FieldElement t0, t1, t2, t3; // 2 == 2 * 1 t0 = square(); // 4 == 2 * 2 t1 = t0.square(); // 8 == 2 * 4 t1 = t1.square(); // 9 == 8 + 1 t1 = multiply(t1); // 11 == 9 + 2 t0 = t0.multiply(t1); // 22 == 2 * 11 t2 = t0.square(); // 31 == 22 + 9 t1 = t1.multiply(t2); // 2^6 - 2^1 t2 = t1.square(); // 2^10 - 2^5 for (int i = 1; i < 5; ++i) { t2 = t2.square(); } // 2^10 - 2^0 t1 = t2.multiply(t1); // 2^11 - 2^1 t2 = t1.square(); // 2^20 - 2^10 for (int i = 1; i < 10; ++i) { t2 = t2.square(); } // 2^20 - 2^0 t2 = t2.multiply(t1); // 2^21 - 2^1 t3 = t2.square(); // 2^40 - 2^20 for (int i = 1; i < 20; ++i) { t3 = t3.square(); } // 2^40 - 2^0 t2 = t3.multiply(t2); // 2^41 - 2^1 t2 = t2.square(); // 2^50 - 2^10 for (int i = 1; i < 10; ++i) { t2 = t2.square(); } // 2^50 - 2^0 t1 = t2.multiply(t1); // 2^51 - 2^1 t2 = t1.square(); // 2^100 - 2^50 for (int i = 1; i < 50; ++i) { t2 = t2.square(); } // 2^100 - 2^0 t2 = t2.multiply(t1); // 2^101 - 2^1 t3 = t2.square(); // 2^200 - 2^100 for (int i = 1; i < 100; ++i) { t3 = t3.square(); } // 2^200 - 2^0 t2 = t3.multiply(t2); // 2^201 - 2^1 t2 = t2.square(); // 2^250 - 2^50 for (int i = 1; i < 50; ++i) { t2 = t2.square(); } // 2^250 - 2^0 t1 = t2.multiply(t1); // 2^251 - 2^1 t1 = t1.square(); // 2^255 - 2^5 for (int i = 1; i < 5; ++i) { t1 = t1.square(); } // 2^255 - 21 return t1.multiply(t0); } /** * Gets this field element to the power of $(2^{252} - 3)$. * This is a helper function for calculating the square root. *

    * TODO-CR BR: I think it makes sense to have a sqrt function. * * @return This field element to the power of $(2^{252} - 3)$. */ public FieldElement pow22523() { FieldElement t0, t1, t2; // 2 == 2 * 1 t0 = square(); // 4 == 2 * 2 t1 = t0.square(); // 8 == 2 * 4 t1 = t1.square(); // z9 = z1*z8 t1 = multiply(t1); // 11 == 9 + 2 t0 = t0.multiply(t1); // 22 == 2 * 11 t0 = t0.square(); // 31 == 22 + 9 t0 = t1.multiply(t0); // 2^6 - 2^1 t1 = t0.square(); // 2^10 - 2^5 for (int i = 1; i < 5; ++i) { t1 = t1.square(); } // 2^10 - 2^0 t0 = t1.multiply(t0); // 2^11 - 2^1 t1 = t0.square(); // 2^20 - 2^10 for (int i = 1; i < 10; ++i) { t1 = t1.square(); } // 2^20 - 2^0 t1 = t1.multiply(t0); // 2^21 - 2^1 t2 = t1.square(); // 2^40 - 2^20 for (int i = 1; i < 20; ++i) { t2 = t2.square(); } // 2^40 - 2^0 t1 = t2.multiply(t1); // 2^41 - 2^1 t1 = t1.square(); // 2^50 - 2^10 for (int i = 1; i < 10; ++i) { t1 = t1.square(); } // 2^50 - 2^0 t0 = t1.multiply(t0); // 2^51 - 2^1 t1 = t0.square(); // 2^100 - 2^50 for (int i = 1; i < 50; ++i) { t1 = t1.square(); } // 2^100 - 2^0 t1 = t1.multiply(t0); // 2^101 - 2^1 t2 = t1.square(); // 2^200 - 2^100 for (int i = 1; i < 100; ++i) { t2 = t2.square(); } // 2^200 - 2^0 t1 = t2.multiply(t1); // 2^201 - 2^1 t1 = t1.square(); // 2^250 - 2^50 for (int i = 1; i < 50; ++i) { t1 = t1.square(); } // 2^250 - 2^0 t0 = t1.multiply(t0); // 2^251 - 2^1 t0 = t0.square(); // 2^252 - 2^2 t0 = t0.square(); // 2^252 - 3 return multiply(t0); } /** * Constant-time conditional move. Well, actually it is a conditional copy. * Logic is inspired by the SUPERCOP implementation at: * https://github.com/floodyberry/supercop/blob/master/crypto_sign/ed25519/ref10/fe_cmov.c * * @param val the other field element. * @param b must be 0 or 1, otherwise results are undefined. * @return a copy of this if $b == 0$, or a copy of val if $b == 1$. */ @Override public FieldElement cmov(FieldElement val, int b) { Ed25519FieldElement that = (Ed25519FieldElement) val; b = -b; int[] result = new int[10]; for (int i = 0; i < 10; i++) { result[i] = this.t[i]; int x = this.t[i] ^ that.t[i]; x &= b; result[i] ^= x; } return new Ed25519FieldElement(this.f, result); } @Override public int hashCode() { return Arrays.hashCode(t); } @Override public boolean equals(Object obj) { if (!(obj instanceof Ed25519FieldElement)) return false; Ed25519FieldElement fe = (Ed25519FieldElement) obj; return 1==Utils.equal(toByteArray(), fe.toByteArray()); } @Override public String toString() { return "[Ed25519FieldElement val="+Utils.bytesToHex(toByteArray())+"]"; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/ed25519/Ed25519LittleEndianEncoding.java000066400000000000000000000213311327341674300311770ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.ed25519; import net.i2p.crypto.eddsa.math.*; /** * Helper class for encoding/decoding from/to the 32 byte representation. *

    * Reviewed/commented by Bloody Rookie (nemproject@gmx.de) */ public class Ed25519LittleEndianEncoding extends Encoding { /** * Encodes a given field element in its 32 byte representation. This is done in two steps: *

      *
    1. Reduce the value of the field element modulo $p$. *
    2. Convert the field element to the 32 byte representation. *

    * The idea for the modulo $p$ reduction algorithm is as follows: *

    *

    Assumption:

    *
      *
    • $p = 2^{255} - 19$ *
    • $h = h_0 + 2^{25} * h_1 + 2^{(26+25)} * h_2 + \dots + 2^{230} * h_9$ where $0 \le |h_i| \lt 2^{27}$ for all $i=0,\dots,9$. *
    • $h \cong r \mod p$, i.e. $h = r + q * p$ for some suitable $0 \le r \lt p$ and an integer $q$. *

    * Then $q = [2^{-255} * (h + 19 * 2^{-25} * h_9 + 1/2)]$ where $[x] = floor(x)$. *

    *

    Proof:

    *

    * We begin with some very raw estimation for the bounds of some expressions: *

    * $$ * \begin{equation} * |h| \lt 2^{230} * 2^{30} = 2^{260} \Rightarrow |r + q * p| \lt 2^{260} \Rightarrow |q| \lt 2^{10}. \\ * \Rightarrow -1/4 \le a := 19^2 * 2^{-255} * q \lt 1/4. \\ * |h - 2^{230} * h_9| = |h_0 + \dots + 2^{204} * h_8| \lt 2^{204} * 2^{30} = 2^{234}. \\ * \Rightarrow -1/4 \le b := 19 * 2^{-255} * (h - 2^{230} * h_9) \lt 1/4 * \end{equation} * $$ *

    * Therefore $0 \lt 1/2 - a - b \lt 1$. *

    * Set $x := r + 19 * 2^{-255} * r + 1/2 - a - b$. Then: *

    * $$ * 0 \le x \lt 255 - 20 + 19 + 1 = 2^{255} \\ * \Rightarrow 0 \le 2^{-255} * x \lt 1. * $$ *

    * Since $q$ is an integer we have *

    * $$ * [q + 2^{-255} * x] = q \quad (1) * $$ *

    * Have a closer look at $x$: *

    * $$ * \begin{align} * x &= h - q * (2^{255} - 19) + 19 * 2^{-255} * (h - q * (2^{255} - 19)) + 1/2 - 19^2 * 2^{-255} * q - 19 * 2^{-255} * (h - 2^{230} * h_9) \\ * &= h - q * 2^{255} + 19 * q + 19 * 2^{-255} * h - 19 * q + 19^2 * 2^{-255} * q + 1/2 - 19^2 * 2^{-255} * q - 19 * 2^{-255} * h + 19 * 2^{-25} * h_9 \\ * &= h + 19 * 2^{-25} * h_9 + 1/2 - q^{255}. * \end{align} * $$ *

    * Inserting the expression for $x$ into $(1)$ we get the desired expression for $q$. */ public byte[] encode(FieldElement x) { int[] h = ((Ed25519FieldElement)x).t; int h0 = h[0]; int h1 = h[1]; int h2 = h[2]; int h3 = h[3]; int h4 = h[4]; int h5 = h[5]; int h6 = h[6]; int h7 = h[7]; int h8 = h[8]; int h9 = h[9]; int q; int carry0; int carry1; int carry2; int carry3; int carry4; int carry5; int carry6; int carry7; int carry8; int carry9; // Step 1: // Calculate q q = (19 * h9 + (1 << 24)) >> 25; q = (h0 + q) >> 26; q = (h1 + q) >> 25; q = (h2 + q) >> 26; q = (h3 + q) >> 25; q = (h4 + q) >> 26; q = (h5 + q) >> 25; q = (h6 + q) >> 26; q = (h7 + q) >> 25; q = (h8 + q) >> 26; q = (h9 + q) >> 25; // r = h - q * p = h - 2^255 * q + 19 * q // First add 19 * q then discard the bit 255 h0 += 19 * q; carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = h9 >> 25; h9 -= carry9 << 25; // Step 2 (straight forward conversion): byte[] s = new byte[32]; s[0] = (byte) h0; s[1] = (byte) (h0 >> 8); s[2] = (byte) (h0 >> 16); s[3] = (byte) ((h0 >> 24) | (h1 << 2)); s[4] = (byte) (h1 >> 6); s[5] = (byte) (h1 >> 14); s[6] = (byte) ((h1 >> 22) | (h2 << 3)); s[7] = (byte) (h2 >> 5); s[8] = (byte) (h2 >> 13); s[9] = (byte) ((h2 >> 21) | (h3 << 5)); s[10] = (byte) (h3 >> 3); s[11] = (byte) (h3 >> 11); s[12] = (byte) ((h3 >> 19) | (h4 << 6)); s[13] = (byte) (h4 >> 2); s[14] = (byte) (h4 >> 10); s[15] = (byte) (h4 >> 18); s[16] = (byte) h5; s[17] = (byte) (h5 >> 8); s[18] = (byte) (h5 >> 16); s[19] = (byte) ((h5 >> 24) | (h6 << 1)); s[20] = (byte) (h6 >> 7); s[21] = (byte) (h6 >> 15); s[22] = (byte) ((h6 >> 23) | (h7 << 3)); s[23] = (byte) (h7 >> 5); s[24] = (byte) (h7 >> 13); s[25] = (byte) ((h7 >> 21) | (h8 << 4)); s[26] = (byte) (h8 >> 4); s[27] = (byte) (h8 >> 12); s[28] = (byte) ((h8 >> 20) | (h9 << 6)); s[29] = (byte) (h9 >> 2); s[30] = (byte) (h9 >> 10); s[31] = (byte) (h9 >> 18); return s; } static int load_3(byte[] in, int offset) { int result = in[offset++] & 0xff; result |= (in[offset++] & 0xff) << 8; result |= (in[offset] & 0xff) << 16; return result; } static long load_4(byte[] in, int offset) { int result = in[offset++] & 0xff; result |= (in[offset++] & 0xff) << 8; result |= (in[offset++] & 0xff) << 16; result |= in[offset] << 24; return ((long)result) & 0xffffffffL; } /** * Decodes a given field element in its 10 byte $2^{25.5}$ representation. * * @param in The 32 byte representation. * @return The field element in its $2^{25.5}$ bit representation. */ public FieldElement decode(byte[] in) { long h0 = load_4(in, 0); long h1 = load_3(in, 4) << 6; long h2 = load_3(in, 7) << 5; long h3 = load_3(in, 10) << 3; long h4 = load_3(in, 13) << 2; long h5 = load_4(in, 16); long h6 = load_3(in, 20) << 7; long h7 = load_3(in, 23) << 5; long h8 = load_3(in, 26) << 4; long h9 = (load_3(in, 29) & 0x7FFFFF) << 2; long carry0; long carry1; long carry2; long carry3; long carry4; long carry5; long carry6; long carry7; long carry8; long carry9; // Remember: 2^255 congruent 19 modulo p carry9 = (h9 + (long) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (long) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (long) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (long) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (long) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (long) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (long) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (long) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (long) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (long) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; int[] h = new int[10]; h[0] = (int) h0; h[1] = (int) h1; h[2] = (int) h2; h[3] = (int) h3; h[4] = (int) h4; h[5] = (int) h5; h[6] = (int) h6; h[7] = (int) h7; h[8] = (int) h8; h[9] = (int) h9; return new Ed25519FieldElement(f, h); } /** * Is the FieldElement negative in this encoding? *

    * Return true if $x$ is in $\{1,3,5,\dots,q-2\}$
    * Return false if $x$ is in $\{0,2,4,\dots,q-1\}$ *

    * Preconditions: *

      *
    • $|x|$ bounded by $1.1*2^{26},1.1*2^{25},1.1*2^{26},1.1*2^{25}$, etc. *
    * * @return true if $x$ is in $\{1,3,5,\dots,q-2\}$, false otherwise. */ public boolean isNegative(FieldElement x) { byte[] s = encode(x); return (s[0] & 1) != 0; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/ed25519/Ed25519ScalarOps.java000066400000000000000000000635661327341674300270630ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.ed25519; import net.i2p.crypto.eddsa.math.ScalarOps; import static net.i2p.crypto.eddsa.math.ed25519.Ed25519LittleEndianEncoding.load_3; import static net.i2p.crypto.eddsa.math.ed25519.Ed25519LittleEndianEncoding.load_4; /** * Class for reducing a huge integer modulo the group order q and * doing a combined multiply plus add plus reduce operation. *

    * $q = 2^{252} + 27742317777372353535851937790883648493$. *

    * Reviewed/commented by Bloody Rookie (nemproject@gmx.de) */ public class Ed25519ScalarOps implements ScalarOps { /** * Reduction modulo the group order $q$. *

    * Input: * $s[0]+256*s[1]+\dots+256^{63}*s[63] = s$ *

    * Output: * $s[0]+256*s[1]+\dots+256^{31}*s[31] = s \bmod q$ * where $q = 2^{252} + 27742317777372353535851937790883648493$. */ public byte[] reduce(byte[] s) { // s0,..., s22 have 21 bits, s23 has 29 bits long s0 = 0x1FFFFF & load_3(s, 0); long s1 = 0x1FFFFF & (load_4(s, 2) >> 5); long s2 = 0x1FFFFF & (load_3(s, 5) >> 2); long s3 = 0x1FFFFF & (load_4(s, 7) >> 7); long s4 = 0x1FFFFF & (load_4(s, 10) >> 4); long s5 = 0x1FFFFF & (load_3(s, 13) >> 1); long s6 = 0x1FFFFF & (load_4(s, 15) >> 6); long s7 = 0x1FFFFF & (load_3(s, 18) >> 3); long s8 = 0x1FFFFF & load_3(s, 21); long s9 = 0x1FFFFF & (load_4(s, 23) >> 5); long s10 = 0x1FFFFF & (load_3(s, 26) >> 2); long s11 = 0x1FFFFF & (load_4(s, 28) >> 7); long s12 = 0x1FFFFF & (load_4(s, 31) >> 4); long s13 = 0x1FFFFF & (load_3(s, 34) >> 1); long s14 = 0x1FFFFF & (load_4(s, 36) >> 6); long s15 = 0x1FFFFF & (load_3(s, 39) >> 3); long s16 = 0x1FFFFF & load_3(s, 42); long s17 = 0x1FFFFF & (load_4(s, 44) >> 5); long s18 = 0x1FFFFF & (load_3(s, 47) >> 2); long s19 = 0x1FFFFF & (load_4(s, 49) >> 7); long s20 = 0x1FFFFF & (load_4(s, 52) >> 4); long s21 = 0x1FFFFF & (load_3(s, 55) >> 1); long s22 = 0x1FFFFF & (load_4(s, 57) >> 6); long s23 = (load_4(s, 60) >> 3); long carry0; long carry1; long carry2; long carry3; long carry4; long carry5; long carry6; long carry7; long carry8; long carry9; long carry10; long carry11; long carry12; long carry13; long carry14; long carry15; long carry16; /** * Lots of magic numbers :) * To understand what's going on below, note that * * (1) q = 2^252 + q0 where q0 = 27742317777372353535851937790883648493. * (2) s11 is the coefficient of 2^(11*21), s23 is the coefficient of 2^(^23*21) and 2^252 = 2^((23-11) * 21)). * (3) 2^252 congruent -q0 modulo q. * (4) -q0 = 666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21) - 997805 * 2^(3*21) + 136657 * 2^(4*21) - 683901 * 2^(5*21) * * Thus * s23 * 2^(23*11) = s23 * 2^(12*21) * 2^(11*21) = s3 * 2^252 * 2^(11*21) congruent * s23 * (666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21) - 997805 * 2^(3*21) + 136657 * 2^(4*21) - 683901 * 2^(5*21)) * 2^(11*21) modulo q = * s23 * (666643 * 2^(11*21) + 470296 * 2^(12*21) + 654183 * 2^(13*21) - 997805 * 2^(14*21) + 136657 * 2^(15*21) - 683901 * 2^(16*21)). * * The same procedure is then applied for s22,...,s18. */ s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; // not used again //s23 = 0; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; // not used again //s22 = 0; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; // not used again //s21 = 0; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; // not used again //s20 = 0; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; // not used again //s19 = 0; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; // not used again //s18 = 0; /** * Time to reduce the coefficient in order not to get an overflow. */ carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; /** * Continue with above procedure. */ s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; // not used again //s17 = 0; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; // not used again //s16 = 0; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; // not used again //s15 = 0; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; // not used again //s14 = 0; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; // not used again //s13 = 0; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; // set below //s12 = 0; /** * Reduce coefficients again. */ carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; //carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 = carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; // set below //s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; //carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; carry11 = s11 >> 21; s12 = carry11; s11 -= carry11 << 21; // TODO-CR BR: Is it really needed to do it TWO times? (it doesn't hurt, just a question). s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; // not used again //s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; // s0, ..., s11 got 21 bits each. byte[] result = new byte[32]; result[0] = (byte) s0; result[1] = (byte) (s0 >> 8); result[2] = (byte) ((s0 >> 16) | (s1 << 5)); result[3] = (byte) (s1 >> 3); result[4] = (byte) (s1 >> 11); result[5] = (byte) ((s1 >> 19) | (s2 << 2)); result[6] = (byte) (s2 >> 6); result[7] = (byte) ((s2 >> 14) | (s3 << 7)); result[8] = (byte) (s3 >> 1); result[9] = (byte) (s3 >> 9); result[10] = (byte) ((s3 >> 17) | (s4 << 4)); result[11] = (byte) (s4 >> 4); result[12] = (byte) (s4 >> 12); result[13] = (byte) ((s4 >> 20) | (s5 << 1)); result[14] = (byte) (s5 >> 7); result[15] = (byte) ((s5 >> 15) | (s6 << 6)); result[16] = (byte) (s6 >> 2); result[17] = (byte) (s6 >> 10); result[18] = (byte) ((s6 >> 18) | (s7 << 3)); result[19] = (byte) (s7 >> 5); result[20] = (byte) (s7 >> 13); result[21] = (byte) s8; result[22] = (byte) (s8 >> 8); result[23] = (byte) ((s8 >> 16) | (s9 << 5)); result[24] = (byte) (s9 >> 3); result[25] = (byte) (s9 >> 11); result[26] = (byte) ((s9 >> 19) | (s10 << 2)); result[27] = (byte) (s10 >> 6); result[28] = (byte) ((s10 >> 14) | (s11 << 7)); result[29] = (byte) (s11 >> 1); result[30] = (byte) (s11 >> 9); result[31] = (byte) (s11 >> 17); return result; } /** * $(ab+c) \bmod q$ *

    * Input: *

      *
    • $a[0]+256*a[1]+\dots+256^{31}*a[31] = a$ *
    • $b[0]+256*b[1]+\dots+256^{31}*b[31] = b$ *
    • $c[0]+256*c[1]+\dots+256^{31}*c[31] = c$ *

    * Output: * $result[0]+256*result[1]+\dots+256^{31}*result[31] = (ab+c) \bmod q$ * where $q = 2^{252} + 27742317777372353535851937790883648493$. *

    * See the comments in {@link #reduce(byte[])} for an explanation of the algorithm. */ public byte[] multiplyAndAdd(byte[] a, byte[] b, byte[] c) { long a0 = 0x1FFFFF & load_3(a, 0); long a1 = 0x1FFFFF & (load_4(a, 2) >> 5); long a2 = 0x1FFFFF & (load_3(a, 5) >> 2); long a3 = 0x1FFFFF & (load_4(a, 7) >> 7); long a4 = 0x1FFFFF & (load_4(a, 10) >> 4); long a5 = 0x1FFFFF & (load_3(a, 13) >> 1); long a6 = 0x1FFFFF & (load_4(a, 15) >> 6); long a7 = 0x1FFFFF & (load_3(a, 18) >> 3); long a8 = 0x1FFFFF & load_3(a, 21); long a9 = 0x1FFFFF & (load_4(a, 23) >> 5); long a10 = 0x1FFFFF & (load_3(a, 26) >> 2); long a11 = (load_4(a, 28) >> 7); long b0 = 0x1FFFFF & load_3(b, 0); long b1 = 0x1FFFFF & (load_4(b, 2) >> 5); long b2 = 0x1FFFFF & (load_3(b, 5) >> 2); long b3 = 0x1FFFFF & (load_4(b, 7) >> 7); long b4 = 0x1FFFFF & (load_4(b, 10) >> 4); long b5 = 0x1FFFFF & (load_3(b, 13) >> 1); long b6 = 0x1FFFFF & (load_4(b, 15) >> 6); long b7 = 0x1FFFFF & (load_3(b, 18) >> 3); long b8 = 0x1FFFFF & load_3(b, 21); long b9 = 0x1FFFFF & (load_4(b, 23) >> 5); long b10 = 0x1FFFFF & (load_3(b, 26) >> 2); long b11 = (load_4(b, 28) >> 7); long c0 = 0x1FFFFF & load_3(c, 0); long c1 = 0x1FFFFF & (load_4(c, 2) >> 5); long c2 = 0x1FFFFF & (load_3(c, 5) >> 2); long c3 = 0x1FFFFF & (load_4(c, 7) >> 7); long c4 = 0x1FFFFF & (load_4(c, 10) >> 4); long c5 = 0x1FFFFF & (load_3(c, 13) >> 1); long c6 = 0x1FFFFF & (load_4(c, 15) >> 6); long c7 = 0x1FFFFF & (load_3(c, 18) >> 3); long c8 = 0x1FFFFF & load_3(c, 21); long c9 = 0x1FFFFF & (load_4(c, 23) >> 5); long c10 = 0x1FFFFF & (load_3(c, 26) >> 2); long c11 = (load_4(c, 28) >> 7); long s0; long s1; long s2; long s3; long s4; long s5; long s6; long s7; long s8; long s9; long s10; long s11; long s12; long s13; long s14; long s15; long s16; long s17; long s18; long s19; long s20; long s21; long s22; long s23; long carry0; long carry1; long carry2; long carry3; long carry4; long carry5; long carry6; long carry7; long carry8; long carry9; long carry10; long carry11; long carry12; long carry13; long carry14; long carry15; long carry16; long carry17; long carry18; long carry19; long carry20; long carry21; long carry22; s0 = c0 + a0*b0; s1 = c1 + a0*b1 + a1*b0; s2 = c2 + a0*b2 + a1*b1 + a2*b0; s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0; s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0; s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0; s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0; s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0; s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0; s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0; s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0; s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0; s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1; s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2; s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3; s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4; s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5; s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6; s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7; s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8; s20 = a9*b11 + a10*b10 + a11*b9; s21 = a10*b11 + a11*b10; s22 = a11*b11; // set below //s23 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; //carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; carry22 = (s22 + (1<<20)) >> 21; s23 = carry22; s22 -= carry22 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; // not used again //s23 = 0; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; // not used again //s22 = 0; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; // not used again //s21 = 0; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; // not used again //s20 = 0; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; // not used again //s19 = 0; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; // not used again //s18 = 0; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; // not used again //s17 = 0; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; // not used again //s16 = 0; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; // not used again //s15 = 0; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; // not used again //s14 = 0; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; // not used again //s13 = 0; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; // set below //s12 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; //carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 = carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; // set below //s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; //carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; carry11 = s11 >> 21; s12 = carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; // not used again //s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; byte[] result = new byte[32]; result[0] = (byte) s0; result[1] = (byte) (s0 >> 8); result[2] = (byte) ((s0 >> 16) | (s1 << 5)); result[3] = (byte) (s1 >> 3); result[4] = (byte) (s1 >> 11); result[5] = (byte) ((s1 >> 19) | (s2 << 2)); result[6] = (byte) (s2 >> 6); result[7] = (byte) ((s2 >> 14) | (s3 << 7)); result[8] = (byte) (s3 >> 1); result[9] = (byte) (s3 >> 9); result[10] = (byte) ((s3 >> 17) | (s4 << 4)); result[11] = (byte) (s4 >> 4); result[12] = (byte) (s4 >> 12); result[13] = (byte) ((s4 >> 20) | (s5 << 1)); result[14] = (byte) (s5 >> 7); result[15] = (byte) ((s5 >> 15) | (s6 << 6)); result[16] = (byte) (s6 >> 2); result[17] = (byte) (s6 >> 10); result[18] = (byte) ((s6 >> 18) | (s7 << 3)); result[19] = (byte) (s7 >> 5); result[20] = (byte) (s7 >> 13); result[21] = (byte) s8; result[22] = (byte) (s8 >> 8); result[23] = (byte) ((s8 >> 16) | (s9 << 5)); result[24] = (byte) (s9 >> 3); result[25] = (byte) (s9 >> 11); result[26] = (byte) ((s9 >> 19) | (s10 << 2)); result[27] = (byte) (s10 >> 6); result[28] = (byte) ((s10 >> 14) | (s11 << 7)); result[29] = (byte) (s11 >> 1); result[30] = (byte) (s11 >> 9); result[31] = (byte) (s11 >> 17); return result; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/ed25519/package.html000066400000000000000000000003221327341674300257100ustar00rootroot00000000000000

    Low-level, optimized implementation using Radix $2^{51}$ for Curve 25519. See the bigint implementation for other curves.

    str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/math/package.html000066400000000000000000000005421327341674300247160ustar00rootroot00000000000000

    Data structures that definie curves and fields, and the mathematical operaions on them.

    Low-level implementation is in bigint for any curve using BigIntegers, and in ed25519 for Curve 25519 using Radix $2^{51}$.

    str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/package.html000066400000000000000000000005071327341674300237660ustar00rootroot00000000000000

    Java implementation of EdDSA, a digital signature scheme using a variant of elliptic curve cryptography based on Twisted Edwards curves.

    Contains a generic implementation for any curve using BigIntegers, and an optimized implementation for Curve 25519 using Radix 2^51.

    str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/000077500000000000000000000000001327341674300224355ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/EdDSAGenParameterSpec.java000066400000000000000000000014561327341674300272740ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import java.security.spec.AlgorithmParameterSpec; /** * Implementation of AlgorithmParameterSpec that holds the name of a named * EdDSA curve specification. * @author str4d * */ public class EdDSAGenParameterSpec implements AlgorithmParameterSpec { private final String name; public EdDSAGenParameterSpec(String stdName) { name = stdName; } public String getName() { return name; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/EdDSANamedCurveSpec.java000066400000000000000000000016741327341674300267550ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import net.i2p.crypto.eddsa.math.Curve; import net.i2p.crypto.eddsa.math.GroupElement; import net.i2p.crypto.eddsa.math.ScalarOps; /** * EdDSA Curve specification that can also be referred to by name. * @author str4d * */ public class EdDSANamedCurveSpec extends EdDSAParameterSpec { private final String name; public EdDSANamedCurveSpec(String name, Curve curve, String hashAlgo, ScalarOps sc, GroupElement B) { super(curve, hashAlgo, sc, B); this.name = name; } public String getName() { return name; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/EdDSANamedCurveTable.java000066400000000000000000000054271327341674300271120ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import java.util.HashMap; import java.util.Locale; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.math.Curve; import net.i2p.crypto.eddsa.math.Field; import net.i2p.crypto.eddsa.math.ed25519.Ed25519LittleEndianEncoding; import net.i2p.crypto.eddsa.math.ed25519.Ed25519ScalarOps; /** * The named EdDSA curves. * @author str4d * */ public class EdDSANamedCurveTable { public static final String ED_25519 = "Ed25519"; private static final Field ed25519field = new Field( 256, // b Utils.hexToBytes("edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f"), // q new Ed25519LittleEndianEncoding()); private static final Curve ed25519curve = new Curve(ed25519field, Utils.hexToBytes("a3785913ca4deb75abd841414d0a700098e879777940c78c73fe6f2bee6c0352"), // d ed25519field.fromByteArray(Utils.hexToBytes("b0a00e4a271beec478e42fad0618432fa7d7fb3d99004d2b0bdfc14f8024832b"))); // I public static final EdDSANamedCurveSpec ED_25519_CURVE_SPEC = new EdDSANamedCurveSpec( ED_25519, ed25519curve, "SHA-512", // H new Ed25519ScalarOps(), // l ed25519curve.createPoint( // B Utils.hexToBytes("5866666666666666666666666666666666666666666666666666666666666666"), true)); // Precompute tables for B private static volatile HashMap curves = new HashMap(); private static synchronized void putCurve(String name, EdDSANamedCurveSpec curve) { HashMap newCurves = new HashMap(curves); newCurves.put(name, curve); curves = newCurves; } public static void defineCurve(EdDSANamedCurveSpec curve) { putCurve(curve.getName().toLowerCase(Locale.ENGLISH), curve); } static void defineCurveAlias(String name, String alias) { EdDSANamedCurveSpec curve = curves.get(name.toLowerCase(Locale.ENGLISH)); if (curve == null) { throw new IllegalStateException(); } putCurve(alias.toLowerCase(Locale.ENGLISH), curve); } static { // RFC 8032 defineCurve(ED_25519_CURVE_SPEC); } public static EdDSANamedCurveSpec getByName(String name) { return curves.get(name.toLowerCase(Locale.ENGLISH)); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/EdDSAParameterSpec.java000066400000000000000000000053671327341674300266470ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import java.security.MessageDigest; import java.security.NoSuchAlgorithmException; import java.security.spec.AlgorithmParameterSpec; import net.i2p.crypto.eddsa.math.Curve; import net.i2p.crypto.eddsa.math.GroupElement; import net.i2p.crypto.eddsa.math.ScalarOps; import java.io.Serializable; /** * Parameter specification for an EdDSA algorithm. * @author str4d * */ public class EdDSAParameterSpec implements AlgorithmParameterSpec, Serializable { private static final long serialVersionUID = 8274987108472012L; private final Curve curve; private final String hashAlgo; private final ScalarOps sc; private final GroupElement B; /** * @param curve the curve * @param hashAlgo the JCA string for the hash algorithm * @param sc the parameter L represented as ScalarOps * @param B the parameter B * @throws IllegalArgumentException if hash algorithm is unsupported or length is wrong */ public EdDSAParameterSpec(Curve curve, String hashAlgo, ScalarOps sc, GroupElement B) { try { MessageDigest hash = MessageDigest.getInstance(hashAlgo); // EdDSA hash function must produce 2b-bit output if (curve.getField().getb()/4 != hash.getDigestLength()) throw new IllegalArgumentException("Hash output is not 2b-bit"); } catch (NoSuchAlgorithmException e) { throw new IllegalArgumentException("Unsupported hash algorithm"); } this.curve = curve; this.hashAlgo = hashAlgo; this.sc = sc; this.B = B; } public Curve getCurve() { return curve; } public String getHashAlgorithm() { return hashAlgo; } public ScalarOps getScalarOps() { return sc; } /** * @return the base (generator) */ public GroupElement getB() { return B; } @Override public int hashCode() { return hashAlgo.hashCode() ^ curve.hashCode() ^ B.hashCode(); } @Override public boolean equals(Object o) { if (o == this) return true; if (!(o instanceof EdDSAParameterSpec)) return false; EdDSAParameterSpec s = (EdDSAParameterSpec) o; return hashAlgo.equals(s.getHashAlgorithm()) && curve.equals(s.getCurve()) && B.equals(s.getB()); } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/EdDSAPrivateKeySpec.java000066400000000000000000000071561327341674300270100ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import java.security.MessageDigest; import java.security.NoSuchAlgorithmException; import java.security.spec.KeySpec; import java.util.Arrays; import net.i2p.crypto.eddsa.math.GroupElement; /** * @author str4d * */ public class EdDSAPrivateKeySpec implements KeySpec { private final byte[] seed; private final byte[] h; private final byte[] a; private final GroupElement A; private final EdDSAParameterSpec spec; /** * @param seed the private key * @param spec the parameter specification for this key * @throws IllegalArgumentException if seed length is wrong or hash algorithm is unsupported */ public EdDSAPrivateKeySpec(byte[] seed, EdDSAParameterSpec spec) { if (seed.length != spec.getCurve().getField().getb()/8) throw new IllegalArgumentException("seed length is wrong"); this.spec = spec; this.seed = seed; try { MessageDigest hash = MessageDigest.getInstance(spec.getHashAlgorithm()); int b = spec.getCurve().getField().getb(); // H(k) h = hash.digest(seed); /*a = BigInteger.valueOf(2).pow(b-2); for (int i=3;i<(b-2);i++) { a = a.add(BigInteger.valueOf(2).pow(i).multiply(BigInteger.valueOf(Utils.bit(h,i)))); }*/ // Saves ~0.4ms per key when running signing tests. // TODO: are these bitflips the same for any hash function? h[0] &= 248; h[(b/8)-1] &= 63; h[(b/8)-1] |= 64; a = Arrays.copyOfRange(h, 0, b/8); A = spec.getB().scalarMultiply(a); } catch (NoSuchAlgorithmException e) { throw new IllegalArgumentException("Unsupported hash algorithm"); } } /** * Initialize directly from the hash. * getSeed() will return null if this constructor is used. * * @param spec the parameter specification for this key * @param h the private key * @throws IllegalArgumentException if hash length is wrong * @since 0.1.1 */ public EdDSAPrivateKeySpec(EdDSAParameterSpec spec, byte[] h) { if (h.length != spec.getCurve().getField().getb()/4) throw new IllegalArgumentException("hash length is wrong"); this.seed = null; this.h = h; this.spec = spec; int b = spec.getCurve().getField().getb(); h[0] &= 248; h[(b/8)-1] &= 63; h[(b/8)-1] |= 64; a = Arrays.copyOfRange(h, 0, b/8); A = spec.getB().scalarMultiply(a); } public EdDSAPrivateKeySpec(byte[] seed, byte[] h, byte[] a, GroupElement A, EdDSAParameterSpec spec) { this.seed = seed; this.h = h; this.a = a; this.A = A; this.spec = spec; } /** * @return will be null if constructed directly from the private key */ public byte[] getSeed() { return seed; } /** * @return the hash */ public byte[] getH() { return h; } /** * @return the private key */ public byte[] geta() { return a; } /** * @return the public key */ public GroupElement getA() { return A; } public EdDSAParameterSpec getParams() { return spec; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/EdDSAPublicKeySpec.java000066400000000000000000000033241327341674300266050ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import java.security.spec.KeySpec; import net.i2p.crypto.eddsa.math.GroupElement; /** * @author str4d * */ public class EdDSAPublicKeySpec implements KeySpec { private final GroupElement A; private GroupElement Aneg = null; private final EdDSAParameterSpec spec; /** * @param pk the public key * @param spec the parameter specification for this key * @throws IllegalArgumentException if key length is wrong */ public EdDSAPublicKeySpec(byte[] pk, EdDSAParameterSpec spec) { if (pk.length != spec.getCurve().getField().getb()/8) throw new IllegalArgumentException("public-key length is wrong"); this.A = new GroupElement(spec.getCurve(), pk); this.spec = spec; } public EdDSAPublicKeySpec(GroupElement A, EdDSAParameterSpec spec) { this.A = A; this.spec = spec; } public GroupElement getA() { return A; } public GroupElement getNegativeA() { // Only read Aneg once, otherwise read re-ordering might occur between here and return. Requires all GroupElement's fields to be final. GroupElement ourAneg = Aneg; if(ourAneg == null) { ourAneg = A.negate(); Aneg = ourAneg; } return ourAneg; } public EdDSAParameterSpec getParams() { return spec; } } str4d-ed25519-java-7c26a63/src/net/i2p/crypto/eddsa/spec/package.html000066400000000000000000000002551327341674300247200ustar00rootroot00000000000000

    Specifications for curves and keys, and a table for named curves. Contains the following curves:

    • "Ed25519"
    str4d-ed25519-java-7c26a63/test/000077500000000000000000000000001327341674300160135ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/000077500000000000000000000000001327341674300166015ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/000077500000000000000000000000001327341674300172735ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/000077500000000000000000000000001327341674300206135ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/000077500000000000000000000000001327341674300216735ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/Ed25519TestVectors.java000066400000000000000000000037711327341674300257120ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.io.BufferedReader; import java.io.IOException; import java.io.InputStream; import java.io.InputStreamReader; import java.util.ArrayList; import java.util.Collection; import java.util.List; public class Ed25519TestVectors { public static class TestTuple { public static int numCases; public int caseNum; public byte[] seed; public byte[] pk; public byte[] message; public byte[] sig; public TestTuple(String line) { caseNum = ++numCases; String[] x = line.split(":"); seed = Utils.hexToBytes(x[0].substring(0, 64)); pk = Utils.hexToBytes(x[1]); message = Utils.hexToBytes(x[2]); sig = Utils.hexToBytes(x[3].substring(0, 128)); } } public static Collection testCases = getTestData("test.data"); public static Collection getTestData(String fileName) { List testCases = new ArrayList(); BufferedReader file = null; try { InputStream is = Ed25519TestVectors.class.getResourceAsStream(fileName); if (is == null) throw new IOException("Resource not found: " + fileName); file = new BufferedReader(new InputStreamReader(is)); String line; while ((line = file.readLine()) != null) { testCases.add(new TestTuple(line)); } } catch (IOException e) { e.printStackTrace(); } finally { if (file != null) try { file.close(); } catch (IOException e) {} } return testCases; } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/EdDSAEngineTest.java000066400000000000000000000230041327341674300254030ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import static org.hamcrest.Matchers.equalTo; import static org.hamcrest.Matchers.is; import static org.junit.Assert.assertThat; import java.nio.charset.Charset; import java.security.MessageDigest; import java.security.PrivateKey; import java.security.PublicKey; import java.security.Signature; import java.security.SignatureException; import java.security.cert.X509Certificate; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import net.i2p.crypto.eddsa.spec.EdDSAParameterSpec; import net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec; import net.i2p.crypto.eddsa.spec.EdDSAPublicKeySpec; import org.junit.Rule; import org.junit.Test; import org.junit.rules.ExpectedException; import sun.security.util.DerValue; import sun.security.x509.X509Key; /** * @author str4d * */ public class EdDSAEngineTest { static final byte[] TEST_SEED = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); static final byte[] TEST_PK = Utils.hexToBytes("3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29"); static final byte[] TEST_MSG = "This is a secret message".getBytes(Charset.forName("UTF-8")); static final byte[] TEST_MSG_SIG = Utils.hexToBytes("94825896c7075c31bcb81f06dba2bdcd9dcf16e79288d4b9f87c248215c8468d475f429f3de3b4a2cf67fe17077ae19686020364d6d4fa7a0174bab4a123ba0f"); @Rule public ExpectedException exception = ExpectedException.none(); @Test public void testSign() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); //Signature sgr = Signature.getInstance("EdDSA", "I2P"); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); for (Ed25519TestVectors.TestTuple testCase : Ed25519TestVectors.testCases) { EdDSAPrivateKeySpec privKey = new EdDSAPrivateKeySpec(testCase.seed, spec); PrivateKey sKey = new EdDSAPrivateKey(privKey); sgr.initSign(sKey); sgr.update(testCase.message); assertThat("Test case " + testCase.caseNum + " failed", sgr.sign(), is(equalTo(testCase.sig))); } } @Test public void testVerify() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); //Signature sgr = Signature.getInstance("EdDSA", "I2P"); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); for (Ed25519TestVectors.TestTuple testCase : Ed25519TestVectors.testCases) { EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(testCase.pk, spec); PublicKey vKey = new EdDSAPublicKey(pubKey); sgr.initVerify(vKey); sgr.update(testCase.message); assertThat("Test case " + testCase.caseNum + " failed", sgr.verify(testCase.sig), is(true)); } } /** * Checks that a wrong-length signature throws an IAE. */ @Test public void testVerifyWrongSigLength() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); //Signature sgr = Signature.getInstance("EdDSA", "I2P"); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(TEST_PK, spec); PublicKey vKey = new EdDSAPublicKey(pubKey); sgr.initVerify(vKey); sgr.update(TEST_MSG); exception.expect(SignatureException.class); exception.expectMessage("signature length is wrong"); sgr.verify(new byte[] {0}); } @Test public void testSignResetsForReuse() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); EdDSAPrivateKeySpec privKey = new EdDSAPrivateKeySpec(TEST_SEED, spec); PrivateKey sKey = new EdDSAPrivateKey(privKey); sgr.initSign(sKey); // First usage sgr.update(new byte[] {0}); sgr.sign(); // Second usage sgr.update(TEST_MSG); assertThat("Second sign failed", sgr.sign(), is(equalTo(TEST_MSG_SIG))); } @Test public void testVerifyResetsForReuse() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(TEST_PK, spec); PublicKey vKey = new EdDSAPublicKey(pubKey); sgr.initVerify(vKey); // First usage sgr.update(new byte[] {0}); sgr.verify(TEST_MSG_SIG); // Second usage sgr.update(TEST_MSG); assertThat("Second verify failed", sgr.verify(TEST_MSG_SIG), is(true)); } @Test public void testSignOneShotMode() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); EdDSAPrivateKeySpec privKey = new EdDSAPrivateKeySpec(TEST_SEED, spec); PrivateKey sKey = new EdDSAPrivateKey(privKey); sgr.initSign(sKey); sgr.setParameter(EdDSAEngine.ONE_SHOT_MODE); sgr.update(TEST_MSG); assertThat("One-shot mode sign failed", sgr.sign(), is(equalTo(TEST_MSG_SIG))); } @Test public void testVerifyOneShotMode() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(TEST_PK, spec); PublicKey vKey = new EdDSAPublicKey(pubKey); sgr.initVerify(vKey); sgr.setParameter(EdDSAEngine.ONE_SHOT_MODE); sgr.update(TEST_MSG); assertThat("One-shot mode verify failed", sgr.verify(TEST_MSG_SIG), is(true)); } @Test public void testSignOneShotModeMultipleUpdates() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); EdDSAPrivateKeySpec privKey = new EdDSAPrivateKeySpec(TEST_SEED, spec); PrivateKey sKey = new EdDSAPrivateKey(privKey); sgr.initSign(sKey); sgr.setParameter(EdDSAEngine.ONE_SHOT_MODE); sgr.update(TEST_MSG); exception.expect(SignatureException.class); exception.expectMessage("update() already called"); sgr.update(TEST_MSG); } @Test public void testVerifyOneShotModeMultipleUpdates() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(TEST_PK, spec); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); PublicKey vKey = new EdDSAPublicKey(pubKey); sgr.initVerify(vKey); sgr.setParameter(EdDSAEngine.ONE_SHOT_MODE); sgr.update(TEST_MSG); exception.expect(SignatureException.class); exception.expectMessage("update() already called"); sgr.update(TEST_MSG); } @Test public void testSignOneShot() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); EdDSAPrivateKeySpec privKey = new EdDSAPrivateKeySpec(TEST_SEED, spec); EdDSAEngine sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); PrivateKey sKey = new EdDSAPrivateKey(privKey); sgr.initSign(sKey); assertThat("signOneShot() failed", sgr.signOneShot(TEST_MSG), is(equalTo(TEST_MSG_SIG))); } @Test public void testVerifyOneShot() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(TEST_PK, spec); EdDSAEngine sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); PublicKey vKey = new EdDSAPublicKey(pubKey); sgr.initVerify(vKey); assertThat("verifyOneShot() failed", sgr.verifyOneShot(TEST_MSG, TEST_MSG_SIG), is(true)); } @Test public void testVerifyX509PublicKeyInfo() throws Exception { EdDSAParameterSpec spec = EdDSANamedCurveTable.getByName("Ed25519"); Signature sgr = new EdDSAEngine(MessageDigest.getInstance(spec.getHashAlgorithm())); for (Ed25519TestVectors.TestTuple testCase : Ed25519TestVectors.testCases) { EdDSAPublicKeySpec pubKey = new EdDSAPublicKeySpec(testCase.pk, spec); PublicKey vKey = new EdDSAPublicKey(pubKey); PublicKey x509Key = X509Key.parse(new DerValue(vKey.getEncoded())); sgr.initVerify(x509Key); sgr.update(testCase.message); assertThat("Test case " + testCase.caseNum + " failed", sgr.verify(testCase.sig), is(true)); } } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/EdDSAPrivateKeyTest.java000066400000000000000000000062721327341674300262710ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import static org.hamcrest.Matchers.*; import static org.junit.Assert.*; import java.security.spec.PKCS8EncodedKeySpec; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec; import org.junit.Test; /** * @author str4d * */ public class EdDSAPrivateKeyTest { /** * The example private key MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC * from https://tools.ietf.org/html/draft-ietf-curdle-pkix-04#section-10.3 */ static final byte[] TEST_PRIVKEY = Utils.hexToBytes("302e020100300506032b657004220420d4ee72dbf913584ad5b6d8f1f769f8ad3afe7c28cbf1d4fbe097a88f44755842"); static final byte[] TEST_PRIVKEY_NULL_PARAMS = Utils.hexToBytes("3030020100300706032b6570050004220420d4ee72dbf913584ad5b6d8f1f769f8ad3afe7c28cbf1d4fbe097a88f44755842"); static final byte[] TEST_PRIVKEY_OLD = Utils.hexToBytes("302f020100300806032b65640a01010420d4ee72dbf913584ad5b6d8f1f769f8ad3afe7c28cbf1d4fbe097a88f44755842"); @Test public void testDecodeAndEncode() throws Exception { // Decode PKCS8EncodedKeySpec encoded = new PKCS8EncodedKeySpec(TEST_PRIVKEY); EdDSAPrivateKey keyIn = new EdDSAPrivateKey(encoded); // Encode EdDSAPrivateKeySpec decoded = new EdDSAPrivateKeySpec( keyIn.getSeed(), keyIn.getH(), keyIn.geta(), keyIn.getA(), keyIn.getParams()); EdDSAPrivateKey keyOut = new EdDSAPrivateKey(decoded); // Check assertThat(keyOut.getEncoded(), is(equalTo(TEST_PRIVKEY))); } @Test public void testDecodeWithNullAndEncode() throws Exception { // Decode PKCS8EncodedKeySpec encoded = new PKCS8EncodedKeySpec(TEST_PRIVKEY_NULL_PARAMS); EdDSAPrivateKey keyIn = new EdDSAPrivateKey(encoded); // Encode EdDSAPrivateKeySpec decoded = new EdDSAPrivateKeySpec( keyIn.getSeed(), keyIn.getH(), keyIn.geta(), keyIn.getA(), keyIn.getParams()); EdDSAPrivateKey keyOut = new EdDSAPrivateKey(decoded); // Check assertThat(keyOut.getEncoded(), is(equalTo(TEST_PRIVKEY))); } @Test public void testReEncodeOldEncoding() throws Exception { // Decode PKCS8EncodedKeySpec encoded = new PKCS8EncodedKeySpec(TEST_PRIVKEY_OLD); EdDSAPrivateKey keyIn = new EdDSAPrivateKey(encoded); // Encode EdDSAPrivateKeySpec decoded = new EdDSAPrivateKeySpec( keyIn.getSeed(), keyIn.getH(), keyIn.geta(), keyIn.getA(), keyIn.getParams()); EdDSAPrivateKey keyOut = new EdDSAPrivateKey(decoded); // Check assertThat(keyOut.getEncoded(), is(equalTo(TEST_PRIVKEY))); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/EdDSAPublicKeyTest.java000066400000000000000000000055461327341674300261000ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import static org.hamcrest.Matchers.*; import static org.junit.Assert.*; import java.security.spec.X509EncodedKeySpec; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.spec.EdDSAPublicKeySpec; import org.junit.Test; /** * @author str4d * */ public class EdDSAPublicKeyTest { /** * The example public key MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE= * from https://tools.ietf.org/html/draft-ietf-curdle-pkix-04#section-10.1 */ static final byte[] TEST_PUBKEY = Utils.hexToBytes("302a300506032b657003210019bf44096984cdfe8541bac167dc3b96c85086aa30b6b6cb0c5c38ad703166e1"); static final byte[] TEST_PUBKEY_NULL_PARAMS = Utils.hexToBytes("302c300706032b6570050003210019bf44096984cdfe8541bac167dc3b96c85086aa30b6b6cb0c5c38ad703166e1"); static final byte[] TEST_PUBKEY_OLD = Utils.hexToBytes("302d300806032b65640a010103210019bf44096984cdfe8541bac167dc3b96c85086aa30b6b6cb0c5c38ad703166e1"); @Test public void testDecodeAndEncode() throws Exception { // Decode X509EncodedKeySpec encoded = new X509EncodedKeySpec(TEST_PUBKEY); EdDSAPublicKey keyIn = new EdDSAPublicKey(encoded); // Encode EdDSAPublicKeySpec decoded = new EdDSAPublicKeySpec( keyIn.getA(), keyIn.getParams()); EdDSAPublicKey keyOut = new EdDSAPublicKey(decoded); // Check assertThat(keyOut.getEncoded(), is(equalTo(TEST_PUBKEY))); } @Test public void testDecodeWithNullAndEncode() throws Exception { // Decode X509EncodedKeySpec encoded = new X509EncodedKeySpec(TEST_PUBKEY_NULL_PARAMS); EdDSAPublicKey keyIn = new EdDSAPublicKey(encoded); // Encode EdDSAPublicKeySpec decoded = new EdDSAPublicKeySpec( keyIn.getA(), keyIn.getParams()); EdDSAPublicKey keyOut = new EdDSAPublicKey(decoded); // Check assertThat(keyOut.getEncoded(), is(equalTo(TEST_PUBKEY))); } @Test public void testReEncodeOldEncoding() throws Exception { // Decode X509EncodedKeySpec encoded = new X509EncodedKeySpec(TEST_PUBKEY_OLD); EdDSAPublicKey keyIn = new EdDSAPublicKey(encoded); // Encode EdDSAPublicKeySpec decoded = new EdDSAPublicKeySpec( keyIn.getA(), keyIn.getParams()); EdDSAPublicKey keyOut = new EdDSAPublicKey(decoded); // Check assertThat(keyOut.getEncoded(), is(equalTo(TEST_PUBKEY))); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/EdDSASecurityProviderTest.java000066400000000000000000000027441327341674300275300ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import java.security.KeyFactory; import java.security.KeyPairGenerator; import java.security.NoSuchProviderException; import java.security.Security; import java.security.Signature; import net.i2p.crypto.eddsa.EdDSASecurityProvider; import org.junit.Rule; import org.junit.Test; import org.junit.rules.ExpectedException; /** * @author str4d * */ public class EdDSASecurityProviderTest { @Rule public ExpectedException exception = ExpectedException.none(); @Test public void canGetInstancesWhenProviderIsPresent() throws Exception { Security.addProvider(new EdDSASecurityProvider()); KeyPairGenerator keyGen = KeyPairGenerator.getInstance("EdDSA", "EdDSA"); KeyFactory keyFac = KeyFactory.getInstance("EdDSA", "EdDSA"); Signature sgr = Signature.getInstance("NONEwithEdDSA", "EdDSA"); Security.removeProvider("EdDSA"); } @Test public void cannotGetInstancesWhenProviderIsNotPresent() throws Exception { exception.expect(NoSuchProviderException.class); KeyPairGenerator keyGen = KeyPairGenerator.getInstance("EdDSA", "EdDSA"); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/UtilsTest.java000066400000000000000000000120271327341674300245000ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa; import org.hamcrest.core.IsEqual; import org.junit.*; import java.security.SecureRandom; import static org.hamcrest.Matchers.is; import static org.junit.Assert.assertThat; /** * @author str4d * additional test by the NEM project team. * */ public class UtilsTest { private static final String hex1 = "3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29"; private static final String hex2 = "47a3f5b71494bcd961f3a4e859a238d6eaf8e648746d2f56a89b5e236f98d45f"; private static final String hex3 = "5fd396e4a2b5dc9078f57e3ab5a87c28fd128e5f78cc4a97f4122dc45f6e4bb9"; private static final byte[] bytes1 = { 59, 106, 39, -68, -50, -74, -92, 45, 98, -93, -88, -48, 42, 111, 13, 115, 101, 50, 21, 119, 29, -30, 67, -90, 58, -64, 72, -95, -117, 89, -38, 41 }; private static final byte[] bytes2 = { 71, -93, -11, -73, 20, -108, -68, -39, 97, -13, -92, -24, 89, -94, 56, -42, -22, -8, -26, 72, 116, 109, 47, 86, -88, -101, 94, 35, 111, -104, -44, 95 }; private static final byte[] bytes3 = { 95, -45, -106, -28, -94, -75, -36, -112, 120, -11, 126, 58, -75, -88, 124, 40, -3, 18, -114, 95, 120, -52, 74, -105, -12, 18, 45, -60, 95, 110, 75, -71 }; /** * Test method for {@link net.i2p.crypto.eddsa.Utils#equal(int, int)}. */ @Test public void testIntEqual() { assertThat(Utils.equal(0, 0), is(1)); assertThat(Utils.equal(1, 1), is(1)); assertThat(Utils.equal(1, 0), is(0)); assertThat(Utils.equal(1, 127), is(0)); assertThat(Utils.equal(-127, 127), is(0)); assertThat(Utils.equal(-42, -42), is(1)); assertThat(Utils.equal(255, 255), is(1)); assertThat(Utils.equal(-255, -256), is(0)); } @Test public void equalsReturnsOneForEqualByteArrays() { final SecureRandom random = new SecureRandom(); final byte[] bytes1 = new byte[32]; final byte[] bytes2 = new byte[32]; for (int i=0; i<100; i++) { random.nextBytes(bytes1); System.arraycopy(bytes1, 0, bytes2, 0, 32); Assert.assertThat(Utils.equal(bytes1, bytes2), IsEqual.equalTo(1)); } } @Test public void equalsReturnsZeroForUnequalByteArrays() { final SecureRandom random = new SecureRandom(); final byte[] bytes1 = new byte[32]; final byte[] bytes2 = new byte[32]; random.nextBytes(bytes1); for (int i=0; i<32; i++) { System.arraycopy(bytes1, 0, bytes2, 0, 32); bytes2[i] = (byte)(bytes2[i] ^ 0xff); Assert.assertThat(Utils.equal(bytes1, bytes2), IsEqual.equalTo(0)); } } /** * Test method for {@link net.i2p.crypto.eddsa.Utils#equal(byte[], byte[])}. */ @Test public void testByteArrayEqual() { byte[] zero = new byte[32]; byte[] one = new byte[32]; one[0] = 1; assertThat(Utils.equal(zero, zero), is(1)); assertThat(Utils.equal(one, one), is(1)); assertThat(Utils.equal(one, zero), is(0)); assertThat(Utils.equal(zero, one), is(0)); } /** * Test method for {@link net.i2p.crypto.eddsa.Utils#negative(int)}. */ @Test public void testNegative() { assertThat(Utils.negative(0), is(0)); assertThat(Utils.negative(1), is(0)); assertThat(Utils.negative(-1), is(1)); assertThat(Utils.negative(32), is(0)); assertThat(Utils.negative(-100), is(1)); assertThat(Utils.negative(127), is(0)); assertThat(Utils.negative(-255), is(1)); } /** * Test method for {@link net.i2p.crypto.eddsa.Utils#bit(byte[], int)}. */ @Test public void testBit() { assertThat(Utils.bit(new byte[] {0}, 0), is(0)); assertThat(Utils.bit(new byte[] {8}, 3), is(1)); assertThat(Utils.bit(new byte[] {1, 2, 3}, 9), is(1)); assertThat(Utils.bit(new byte[] {1, 2, 3}, 15), is(0)); assertThat(Utils.bit(new byte[] {1, 2, 3}, 16), is(1)); } @Test public void hexToBytesReturnsCorrectByteArray() { Assert.assertThat(Utils.hexToBytes(hex1), IsEqual.equalTo(bytes1)); Assert.assertThat(Utils.hexToBytes(hex2), IsEqual.equalTo(bytes2)); Assert.assertThat(Utils.hexToBytes(hex3), IsEqual.equalTo(bytes3)); } @Test public void bytesToHexReturnsCorrectHexString() { Assert.assertThat(Utils.bytesToHex(bytes1), IsEqual.equalTo(hex1)); Assert.assertThat(Utils.bytesToHex(bytes2), IsEqual.equalTo(hex2)); Assert.assertThat(Utils.bytesToHex(bytes3), IsEqual.equalTo(hex3)); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/000077500000000000000000000000001327341674300226245ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/AbstractFieldElementTest.java000066400000000000000000000170531327341674300303560ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import net.i2p.crypto.eddsa.math.*; import org.hamcrest.core.*; import org.junit.*; import java.math.BigInteger; /** * Tests rely on the BigInteger class. */ public abstract class AbstractFieldElementTest { protected abstract FieldElement getRandomFieldElement(); protected abstract BigInteger toBigInteger(FieldElement f); protected abstract BigInteger getQ(); protected abstract Field getField(); // region isNonZero protected abstract FieldElement getZeroFieldElement(); protected abstract FieldElement getNonZeroFieldElement(); @Test public void isNonZeroReturnsFalseIfFieldElementIsZero() { // Act: final FieldElement f = getZeroFieldElement(); // Assert: Assert.assertThat(f.isNonZero(), IsEqual.equalTo(false)); } @Test public void isNonZeroReturnsTrueIfFieldElementIsNonZero() { // Act: final FieldElement f = getNonZeroFieldElement(); // Assert: Assert.assertThat(f.isNonZero(), IsEqual.equalTo(true)); } // endregion // region mod q arithmetic @Test public void addReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final FieldElement f2 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); final BigInteger b2 = toBigInteger(f2); // Act: final FieldElement f3 = f1.add(f2); final BigInteger b3 = toBigInteger(f3).mod(getQ()); // Assert: Assert.assertThat(b3, IsEqual.equalTo(b1.add(b2).mod(getQ()))); } } @Test public void subtractReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final FieldElement f2 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); final BigInteger b2 = toBigInteger(f2); // Act: final FieldElement f3 = f1.subtract(f2); final BigInteger b3 = toBigInteger(f3).mod(getQ()); // Assert: Assert.assertThat(b3, IsEqual.equalTo(b1.subtract(b2).mod(getQ()))); } } @Test public void negateReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); // Act: final FieldElement f2 = f1.negate(); final BigInteger b2 = toBigInteger(f2).mod(getQ()); // Assert: Assert.assertThat(b2, IsEqual.equalTo(b1.negate().mod(getQ()))); } } @Test public void multiplyReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final FieldElement f2 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); final BigInteger b2 = toBigInteger(f2); // Act: final FieldElement f3 = f1.multiply(f2); final BigInteger b3 = toBigInteger(f3).mod(getQ()); // Assert: Assert.assertThat(b3, IsEqual.equalTo(b1.multiply(b2).mod(getQ()))); } } @Test public void squareReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); // Act: final FieldElement f2 = f1.square(); final BigInteger b2 = toBigInteger(f2).mod(getQ()); // Assert: Assert.assertThat(b2, IsEqual.equalTo(b1.multiply(b1).mod(getQ()))); } } @Test public void squareAndDoubleReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); // Act: final FieldElement f2 = f1.squareAndDouble(); final BigInteger b2 = toBigInteger(f2).mod(getQ()); // Assert: Assert.assertThat(b2, IsEqual.equalTo(b1.multiply(b1).multiply(new BigInteger("2")).mod(getQ()))); } } @Test public void invertReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); // Act: final FieldElement f2 = f1.invert(); final BigInteger b2 = toBigInteger(f2).mod(getQ()); // Assert: Assert.assertThat(b2, IsEqual.equalTo(b1.modInverse(getQ()))); } } @Test public void pow22523ReturnsCorrectResult() { for (int i=0; i<1000; i++) { // Arrange: final FieldElement f1 = getRandomFieldElement(); final BigInteger b1 = toBigInteger(f1); // Act: final FieldElement f2 = f1.pow22523(); final BigInteger b2 = toBigInteger(f2).mod(getQ()); // Assert: Assert.assertThat(b2, IsEqual.equalTo(b1.modPow(BigInteger.ONE.shiftLeft(252).subtract(new BigInteger("3")), getQ()))); } } // endregion // region cmov @Test public void cmovReturnsCorrectResult() { final FieldElement zero = getZeroFieldElement(); final FieldElement nz = getNonZeroFieldElement(); final FieldElement f = getRandomFieldElement(); Assert.assertThat(zero.cmov(nz, 0), IsEqual.equalTo(zero)); Assert.assertThat(zero.cmov(nz, 1), IsEqual.equalTo(nz)); Assert.assertThat(f.cmov(nz, 0), IsEqual.equalTo(f)); Assert.assertThat(f.cmov(nz, 1), IsEqual.equalTo(nz)); } // endregion // region hashCode / equals @Test public void equalsOnlyReturnsTrueForEquivalentObjects() { // Arrange: final FieldElement f1 = getRandomFieldElement(); final FieldElement f2 = getField().getEncoding().decode(f1.toByteArray()); final FieldElement f3 = getRandomFieldElement(); final FieldElement f4 = getRandomFieldElement(); // Assert: Assert.assertThat(f1, IsEqual.equalTo(f2)); Assert.assertThat(f1, IsNot.not(IsEqual.equalTo(f3))); Assert.assertThat(f1, IsNot.not(IsEqual.equalTo(f4))); Assert.assertThat(f3, IsNot.not(IsEqual.equalTo(f4))); } @Test public void hashCodesAreEqualForEquivalentObjects() { // Arrange: final FieldElement f1 = getRandomFieldElement(); final FieldElement f2 = getField().getEncoding().decode(f1.toByteArray()); final FieldElement f3 = getRandomFieldElement(); final FieldElement f4 = getRandomFieldElement(); // Assert: Assert.assertThat(f1.hashCode(), IsEqual.equalTo(f2.hashCode())); Assert.assertThat(f1.hashCode(), IsNot.not(IsEqual.equalTo(f3.hashCode()))); Assert.assertThat(f1.hashCode(), IsNot.not(IsEqual.equalTo(f4.hashCode()))); Assert.assertThat(f3.hashCode(), IsNot.not(IsEqual.equalTo(f4.hashCode()))); } // endregion } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/ConstantsTest.java000066400000000000000000000060241327341674300263050ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import static org.hamcrest.Matchers.equalTo; import static org.hamcrest.Matchers.greaterThanOrEqualTo; import static org.hamcrest.Matchers.is; import static org.junit.Assert.assertThat; import static org.junit.Assert.fail; import java.security.MessageDigest; import java.security.NoSuchAlgorithmException; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveSpec; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import org.junit.Test; /** * Based on the tests in checkparams.py from the Python Ed25519 implementation. * @author str4d * */ public class ConstantsTest { static final EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); static final Curve curve = ed25519.getCurve(); static final FieldElement ZERO = curve.getField().ZERO; static final FieldElement ONE = curve.getField().ONE; static final FieldElement TWO = curve.getField().TWO; static final GroupElement P3_ZERO = GroupElement.p3(curve, ZERO, ONE, ONE, ZERO); @Test public void testb() { int b = curve.getField().getb(); assertThat(b, is(greaterThanOrEqualTo(10))); try { MessageDigest h = MessageDigest.getInstance(ed25519.getHashAlgorithm()); assertThat(8 * h.getDigestLength(), is(equalTo(2 * b))); } catch (NoSuchAlgorithmException e) { fail(e.getMessage()); } } /*@Test public void testq() { FieldElement q = curve.getField().getQ(); assertThat(TWO.modPow(q.subtractOne(), q), is(equalTo(ONE))); assertThat(q.mod(curve.getField().FOUR), is(equalTo(ONE))); } @Test public void testl() { int b = curve.getField().getb(); BigInteger l = ed25519.getL(); assertThat(TWO.modPow(l.subtract(BigInteger.ONE), l), is(equalTo(ONE))); assertThat(l, is(greaterThanOrEqualTo(BigInteger.valueOf(2).pow(b-4)))); assertThat(l, is(lessThanOrEqualTo(BigInteger.valueOf(2).pow(b-3)))); } @Test public void testd() { FieldElement q = curve.getField().getQ(); FieldElement qm1 = q.subtractOne(); assertThat(curve.getD().modPow(qm1.divide(curve.getField().TWO), q), is(equalTo(qm1))); } @Test public void testI() { FieldElement q = curve.getField().getQ(); assertThat(curve.getI().modPow(curve.getField().TWO, q), is(equalTo(q.subtractOne()))); }*/ @Test public void testB() { GroupElement B = ed25519.getB(); assertThat(B.isOnCurve(curve), is(true)); //assertThat(B.scalarMultiply(new BigIntegerLittleEndianEncoding().encode(ed25519.getL(), curve.getField().getb()/8)), is(equalTo(P3_ZERO))); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/GroupElementTest.java000066400000000000000000001114121327341674300267350ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import net.i2p.crypto.eddsa.*; import net.i2p.crypto.eddsa.spec.*; import org.hamcrest.core.*; import org.junit.*; import org.junit.rules.ExpectedException; import java.math.BigInteger; import java.util.Arrays; import static org.hamcrest.Matchers.*; import static org.junit.Assert.assertThat; /** * @author str4d * Additional tests by NEM project team. * */ public class GroupElementTest { static final byte[] BYTES_ZEROZERO = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_ONEONE = Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000080"); static final byte[] BYTES_TENZERO = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_ONETEN = Utils.hexToBytes("0a00000000000000000000000000000000000000000000000000000000000080"); static final EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); static final Curve curve = ed25519.getCurve(); static final FieldElement ZERO = curve.getField().ZERO; static final FieldElement ONE = curve.getField().ONE; static final FieldElement TWO = curve.getField().TWO; static final FieldElement TEN = curve.getField().fromByteArray(Utils.hexToBytes("0a00000000000000000000000000000000000000000000000000000000000000")); static final GroupElement P2_ZERO = GroupElement.p2(curve, ZERO, ONE, ONE); static final FieldElement[] PKR = new FieldElement[] { curve.getField().fromByteArray(Utils.hexToBytes("5849722e338aced7b50c7f0e9328f9a10c847b08e40af5c5b0577b0fd8984f15")), curve.getField().fromByteArray(Utils.hexToBytes("3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29")) }; static final byte[] BYTES_PKR = Utils.hexToBytes("3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29"); @Rule public ExpectedException exception = ExpectedException.none(); /** * Test method for {@link GroupElement#p2(Curve, FieldElement, FieldElement, FieldElement)}. */ @Test public void testP2() { final GroupElement t = GroupElement.p2(curve, ZERO, ONE, ONE); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.P2)); assertThat(t.X, is(ZERO)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is((FieldElement) null)); } /** * Test method for {@link GroupElement#p3(Curve, FieldElement, FieldElement, FieldElement, FieldElement)}. */ @Test public void testP3() { final GroupElement t = GroupElement.p3(curve, ZERO, ONE, ONE, ZERO); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.P3)); assertThat(t.X, is(ZERO)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is(ZERO)); } /** * Test method for {@link GroupElement#p3(Curve, FieldElement, FieldElement, FieldElement, FieldElement, boolean)}. */ @Test public void testP3WithExplicitFlag() { final GroupElement t = GroupElement.p3(curve, ZERO, ONE, ONE, ZERO, false); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.P3)); assertThat(t.X, is(ZERO)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is(ZERO)); } /** * Test method for {@link GroupElement#p1p1(Curve, FieldElement, FieldElement, FieldElement, FieldElement)}. */ @Test public void testP1p1() { final GroupElement t = GroupElement.p1p1(curve, ZERO, ONE, ONE, ONE); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.P1P1)); assertThat(t.X, is(ZERO)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is(ONE)); } /** * Test method for {@link GroupElement#precomp(Curve, FieldElement, FieldElement, FieldElement)}. */ @Test public void testPrecomp() { final GroupElement t = GroupElement.precomp(curve, ONE, ONE, ZERO); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.PRECOMP)); assertThat(t.X, is(ONE)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ZERO)); assertThat(t.T, is((FieldElement) null)); } /** * Test method for {@link GroupElement#cached(Curve, FieldElement, FieldElement, FieldElement, FieldElement)}. */ @Test public void testCached() { final GroupElement t = GroupElement.cached(curve, ONE, ONE, ONE, ZERO); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.CACHED)); assertThat(t.X, is(ONE)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is(ZERO)); } /** * Test method for {@link GroupElement#GroupElement(Curve, GroupElement.Representation, FieldElement, FieldElement, FieldElement, FieldElement)}. */ @Test public void testGroupElementCurveRepresentationFieldElementFieldElementFieldElementFieldElement() { final GroupElement t = new GroupElement(curve, GroupElement.Representation.P3, ZERO, ONE, ONE, ZERO); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.P3)); assertThat(t.X, is(ZERO)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is(ZERO)); } /** * Test method for {@link GroupElement#GroupElement(Curve, GroupElement.Representation, FieldElement, FieldElement, FieldElement, FieldElement, boolean)}. */ @Test public void testGroupElementCurveRepresentationFieldElementFieldElementFieldElementFieldElementWithExplicitFlag() { final GroupElement t = new GroupElement(curve, GroupElement.Representation.P3, ZERO, ONE, ONE, ZERO, false); assertThat(t.curve, is(equalTo(curve))); assertThat(t.repr, is(GroupElement.Representation.P3)); assertThat(t.X, is(ZERO)); assertThat(t.Y, is(ONE)); assertThat(t.Z, is(ONE)); assertThat(t.T, is(ZERO)); } /** * Tests {@link GroupElement#GroupElement(Curve, byte[])} and * {@link GroupElement#toByteArray()} against valid public keys. */ @Test public void testToAndFromByteArray() { GroupElement t; for (Ed25519TestVectors.TestTuple testCase : Ed25519TestVectors.testCases) { t = new GroupElement(curve, testCase.pk); assertThat("Test case " + testCase.caseNum + " failed", t.toByteArray(), is(equalTo(testCase.pk))); } } /** * Test method for {@link GroupElement#GroupElement(Curve, byte[])}. */ @Test public void testGroupElementByteArray() { final GroupElement t = new GroupElement(curve, BYTES_PKR); final GroupElement s = GroupElement.p3(curve, PKR[0], PKR[1], ONE, PKR[0].multiply(PKR[1])); assertThat(t, is(equalTo(s))); } @Test public void constructorUsingByteArrayReturnsExpectedResult() { for (int i=0; i<100; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); final byte[] bytes = g.toByteArray(); // Act: final GroupElement h1 = new GroupElement(curve, bytes); final GroupElement h2 = MathUtils.toGroupElement(bytes); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); } } /** * Test method for {@link GroupElement#toByteArray()}. *

    * TODO 20141001 BR: why test with points which are not on the curve? */ @Test public void testToByteArray() { byte[] zerozero = GroupElement.p2(curve, ZERO, ZERO, ONE).toByteArray(); assertThat(zerozero.length, is(equalTo(BYTES_ZEROZERO.length))); assertThat(zerozero, is(equalTo(BYTES_ZEROZERO))); byte[] oneone = GroupElement.p2(curve, ONE, ONE, ONE).toByteArray(); assertThat(oneone.length, is(equalTo(BYTES_ONEONE.length))); assertThat(oneone, is(equalTo(BYTES_ONEONE))); byte[] tenzero = GroupElement.p2(curve, TEN, ZERO, ONE).toByteArray(); assertThat(tenzero.length, is(equalTo(BYTES_TENZERO.length))); assertThat(tenzero, is(equalTo(BYTES_TENZERO))); byte[] oneten = GroupElement.p2(curve, ONE, TEN, ONE).toByteArray(); assertThat(oneten.length, is(equalTo(BYTES_ONETEN.length))); assertThat(oneten, is(equalTo(BYTES_ONETEN))); byte[] pkr = GroupElement.p2(curve, PKR[0], PKR[1], ONE).toByteArray(); assertThat(pkr.length, is(equalTo(BYTES_PKR.length))); assertThat(pkr, is(equalTo(BYTES_PKR))); } @Test public void toByteArrayReturnsExpectedResult() { for (int i=0; i<100; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final byte[] gBytes = g.toByteArray(); final byte[] bytes = MathUtils.toByteArray(MathUtils.toBigInteger(g.getY())); if (MathUtils.toBigInteger(g.getX()).mod(new BigInteger("2")).equals(BigInteger.ONE)) { bytes[31] |= 0x80; } // Assert: Assert.assertThat(Arrays.equals(gBytes, bytes), IsEqual.equalTo(true)); } } // region toX where X is the representation /** * Test method for {@link GroupElement#toP2()}. */ @Test public void testToP2() { GroupElement p3zero = curve.getZero(GroupElement.Representation.P3); GroupElement t = p3zero.toP2(); assertThat(t.repr, is(GroupElement.Representation.P2)); assertThat(t.X, is(p3zero.X)); assertThat(t.Y, is(p3zero.Y)); assertThat(t.Z, is(p3zero.Z)); assertThat(t.T, is((FieldElement) null)); GroupElement B = ed25519.getB(); t = B.toP2(); assertThat(t.repr, is(GroupElement.Representation.P2)); assertThat(t.X, is(B.X)); assertThat(t.Y, is(B.Y)); assertThat(t.Z, is(B.Z)); assertThat(t.T, is((FieldElement) null)); } @Test (expected = IllegalArgumentException.class) public void toP2ThrowsIfGroupElementHasPrecompRepresentation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP); // Assert: g.toP2(); } @Test (expected = IllegalArgumentException.class) public void toP2ThrowsIfGroupElementHasCachedRepresentation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.CACHED); // Assert: g.toP2(); } @Test public void toP2ReturnsExpectedResultIfGroupElementHasP2Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P2); // Act: final GroupElement h = g.toP2(); // Assert: Assert.assertThat(h, IsEqual.equalTo(g)); Assert.assertThat(h.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P2)); Assert.assertThat(h.getX(), IsEqual.equalTo(g.getX())); Assert.assertThat(h.getY(), IsEqual.equalTo(g.getY())); Assert.assertThat(h.getZ(), IsEqual.equalTo(g.getZ())); Assert.assertThat(h.getT(), IsEqual.equalTo(null)); } } @Test public void toP2ReturnsExpectedResultIfGroupElementHasP3Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final GroupElement h1 = g.toP2(); final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P2); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P2)); Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX())); Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY())); Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ())); Assert.assertThat(h1.getT(), IsEqual.equalTo(null)); } } @Test public void toP2ReturnsExpectedResultIfGroupElementHasP1P1Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1); // Act: final GroupElement h1 = g.toP2(); final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P2); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P2)); Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX().multiply(g.getT()))); Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().multiply(g.getZ()))); Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ().multiply(g.getT()))); Assert.assertThat(h1.getT(), IsEqual.equalTo(null)); } } @Test (expected = IllegalArgumentException.class) public void toP3ThrowsIfGroupElementHasP2Representation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P2); // Assert: g.toP3(); } @Test (expected = IllegalArgumentException.class) public void toP3ThrowsIfGroupElementHasPrecompRepresentation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP); // Assert: g.toP3(); } @Test (expected = IllegalArgumentException.class) public void toP3ThrowsIfGroupElementHasCachedRepresentation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.CACHED); // Assert: g.toP3(); } @Test public void toP3ReturnsExpectedResultIfGroupElementHasP1P1Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1); // Act: final GroupElement h1 = g.toP3(); final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P3); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P3)); Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX().multiply(g.getT()))); Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().multiply(g.getZ()))); Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ().multiply(g.getT()))); Assert.assertThat(h1.getT(), IsEqual.equalTo(g.getX().multiply(g.getY()))); } } @Test public void toP3ReturnsExpectedResultIfGroupElementHasP3Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final GroupElement h = g.toP3(); // Assert: Assert.assertThat(h, IsEqual.equalTo(g)); Assert.assertThat(h.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P3)); Assert.assertThat(h, IsEqual.equalTo(g)); Assert.assertThat(h.getX(), IsEqual.equalTo(g.getX())); Assert.assertThat(h.getY(), IsEqual.equalTo(g.getY())); Assert.assertThat(h.getZ(), IsEqual.equalTo(g.getZ())); Assert.assertThat(h.getT(), IsEqual.equalTo(g.getT())); } } @Test public void toP3PrecomputeDoubleReturnsExpectedResultIfGroupElementHasP1P1Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1); // Act: final GroupElement h1 = g.toP3PrecomputeDouble(); final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.P3PrecomputedDouble); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.P3)); Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getX().multiply(g.getT()))); Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().multiply(g.getZ()))); Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ().multiply(g.getT()))); Assert.assertThat(h1.getT(), IsEqual.equalTo(g.getX().multiply(g.getY()))); Assert.assertThat(h1.precmp, IsNull.nullValue()); Assert.assertThat(h1.dblPrecmp, IsNull.notNullValue()); Assert.assertThat(h1.dblPrecmp, IsEqual.equalTo(h2.dblPrecmp)); } } @Test (expected = IllegalArgumentException.class) public void toCachedThrowsIfGroupElementHasP2Representation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P2); // Assert: g.toCached(); } @Test (expected = IllegalArgumentException.class) public void toCachedThrowsIfGroupElementHasPrecompRepresentation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.PRECOMP); // Assert: g.toCached(); } @Test (expected = IllegalArgumentException.class) public void toCachedThrowsIfGroupElementHasP1P1Representation() { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.P1P1); // Assert: g.toCached(); } @Test public void toCachedReturnsExpectedResultIfGroupElementHasCachedRepresentation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.toRepresentation(MathUtils.getRandomGroupElement(), GroupElement.Representation.CACHED); // Act: final GroupElement h = g.toCached(); // Assert: Assert.assertThat(h, IsEqual.equalTo(g)); Assert.assertThat(h.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.CACHED)); Assert.assertThat(h, IsEqual.equalTo(g)); Assert.assertThat(h.getX(), IsEqual.equalTo(g.getX())); Assert.assertThat(h.getY(), IsEqual.equalTo(g.getY())); Assert.assertThat(h.getZ(), IsEqual.equalTo(g.getZ())); Assert.assertThat(h.getT(), IsEqual.equalTo(g.getT())); } } @Test public void toCachedReturnsExpectedResultIfGroupElementHasP3Representation() { for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final GroupElement h1 = g.toCached(); final GroupElement h2 = MathUtils.toRepresentation(g, GroupElement.Representation.CACHED); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); Assert.assertThat(h1.getRepresentation(), IsEqual.equalTo(GroupElement.Representation.CACHED)); Assert.assertThat(h1, IsEqual.equalTo(g)); Assert.assertThat(h1.getX(), IsEqual.equalTo(g.getY().add(g.getX()))); Assert.assertThat(h1.getY(), IsEqual.equalTo(g.getY().subtract(g.getX()))); Assert.assertThat(h1.getZ(), IsEqual.equalTo(g.getZ())); Assert.assertThat(h1.getT(), IsEqual.equalTo(g.getT().multiply(curve.get2D()))); } } // endregion /** * Test method for precomputation. */ @Test public void testPrecompute() { GroupElement B = ed25519.getB(); assertThat(B.precmp, is(equalTo(PrecomputationTestVectors.testPrecmp))); assertThat(B.dblPrecmp, is(equalTo(PrecomputationTestVectors.testDblPrecmp))); } @Test public void precomputedTableContainsExpectedGroupElements() { // Arrange: GroupElement g = ed25519.getB(); // Act + Assert: for (int i = 0; i < 32; i++) { GroupElement h = g; for (int j = 0; j < 8; j++) { Assert.assertThat(MathUtils.toRepresentation(h, GroupElement.Representation.PRECOMP), IsEqual.equalTo(ed25519.getB().precmp[i][j])); h = MathUtils.addGroupElements(h, g); } for (int k = 0; k < 8; k++) { g = MathUtils.addGroupElements(g, g); } } } @Test public void dblPrecomputedTableContainsExpectedGroupElements() { // Arrange: GroupElement g = ed25519.getB(); GroupElement h = MathUtils.addGroupElements(g, g); // Act + Assert: for (int i=0; i<8; i++) { Assert.assertThat(MathUtils.toRepresentation(g, GroupElement.Representation.PRECOMP), IsEqual.equalTo(ed25519.getB().dblPrecmp[i])); g = MathUtils.addGroupElements(g, h); } } /** * Test method for {@link GroupElement#dbl()}. */ @Test public void testDbl() { GroupElement B = ed25519.getB(); // 2 * B = B + B assertThat(B.dbl(), is(equalTo(B.add(B.toCached())))); } @Test public void dblReturnsExpectedResult() { for (int i=0; i<1000; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final GroupElement h1 = g.dbl(); final GroupElement h2 = MathUtils.doubleGroupElement(g); // Assert: Assert.assertThat(h2, IsEqual.equalTo(h1)); } } @Test public void addingNeutralGroupElementDoesNotChangeGroupElement() { final GroupElement neutral = GroupElement.p3(curve, curve.getField().ZERO, curve.getField().ONE, curve.getField().ONE, curve.getField().ZERO); for (int i=0; i<1000; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final GroupElement h1 = g.add(neutral.toCached()); final GroupElement h2 = neutral.add(g.toCached()); // Assert: Assert.assertThat(g, IsEqual.equalTo(h1)); Assert.assertThat(g, IsEqual.equalTo(h2)); } } @Test public void addReturnsExpectedResult() { for (int i=0; i<1000; i++) { // Arrange: final GroupElement g1 = MathUtils.getRandomGroupElement(); final GroupElement g2 = MathUtils.getRandomGroupElement(); // Act: final GroupElement h1 = g1.add(g2.toCached()); final GroupElement h2 = MathUtils.addGroupElements(g1, g2); // Assert: Assert.assertThat(h2, IsEqual.equalTo(h1)); } } @Test public void subReturnsExpectedResult() { for (int i=0; i<1000; i++) { // Arrange: final GroupElement g1 = MathUtils.getRandomGroupElement(); final GroupElement g2 = MathUtils.getRandomGroupElement(); // Act: final GroupElement h1 = g1.sub(g2.toCached()); final GroupElement h2 = MathUtils.addGroupElements(g1, MathUtils.negateGroupElement(g2)); // Assert: Assert.assertThat(h2, IsEqual.equalTo(h1)); } } // region hashCode / equals /** * Test method for {@link GroupElement#equals(java.lang.Object)}. */ @Test public void testEqualsObject() { assertThat(GroupElement.p2(curve, ZERO, ONE, ONE), is(equalTo(P2_ZERO))); } @Test public void equalsOnlyReturnsTrueForEquivalentObjects() { // Arrange: final GroupElement g1 = MathUtils.getRandomGroupElement(); final GroupElement g2 = MathUtils.toRepresentation(g1, GroupElement.Representation.P2); final GroupElement g3 = MathUtils.toRepresentation(g1, GroupElement.Representation.CACHED); final GroupElement g4 = MathUtils.toRepresentation(g1, GroupElement.Representation.P1P1); final GroupElement g5 = MathUtils.getRandomGroupElement(); // Assert Assert.assertThat(g2, IsEqual.equalTo(g1)); Assert.assertThat(g3, IsEqual.equalTo(g1)); Assert.assertThat(g1, IsEqual.equalTo(g4)); Assert.assertThat(g1, IsNot.not(IsEqual.equalTo(g5))); Assert.assertThat(g2, IsNot.not(IsEqual.equalTo(g5))); Assert.assertThat(g3, IsNot.not(IsEqual.equalTo(g5))); Assert.assertThat(g5, IsNot.not(IsEqual.equalTo(g4))); } @Test public void hashCodesAreEqualForEquivalentObjects() { // Arrange: final GroupElement g1 = MathUtils.getRandomGroupElement(); final GroupElement g2 = MathUtils.toRepresentation(g1, GroupElement.Representation.P2); final GroupElement g3 = MathUtils.toRepresentation(g1, GroupElement.Representation.P1P1); final GroupElement g4 = MathUtils.getRandomGroupElement(); // Assert Assert.assertThat(g2.hashCode(), IsEqual.equalTo(g1.hashCode())); Assert.assertThat(g3.hashCode(), IsEqual.equalTo(g1.hashCode())); Assert.assertThat(g1.hashCode(), IsNot.not(IsEqual.equalTo(g4.hashCode()))); Assert.assertThat(g2.hashCode(), IsNot.not(IsEqual.equalTo(g4.hashCode()))); Assert.assertThat(g3.hashCode(), IsNot.not(IsEqual.equalTo(g4.hashCode()))); } // endregion static final byte[] BYTES_ZERO = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_ONE = Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_42 = Utils.hexToBytes("2A00000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_1234567890 = Utils.hexToBytes("D202964900000000000000000000000000000000000000000000000000000000"); static final byte[] RADIX16_ZERO = Utils.hexToBytes("00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"); static final byte[] RADIX16_ONE = Utils.hexToBytes("01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"); static final byte[] RADIX16_42 = Utils.hexToBytes("FA030000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"); /** * Test method for {@link GroupElement#toRadix16(byte[])}. */ @Test public void testToRadix16() { assertThat(GroupElement.toRadix16(BYTES_ZERO), is(RADIX16_ZERO)); assertThat(GroupElement.toRadix16(BYTES_ONE), is(RADIX16_ONE)); assertThat(GroupElement.toRadix16(BYTES_42), is(RADIX16_42)); byte[] from1234567890 = GroupElement.toRadix16(BYTES_1234567890); int total = 0; for (int i = 0; i < from1234567890.length; i++) { assertThat(from1234567890[i], is(greaterThanOrEqualTo((byte)-8))); assertThat(from1234567890[i], is(lessThanOrEqualTo((byte)8))); total += from1234567890[i] * Math.pow(16, i); } assertThat(total, is(1234567890)); byte[] pkrR16 = GroupElement.toRadix16(BYTES_PKR); for (int i = 0; i < pkrR16.length; i++) { assertThat(pkrR16[i], is(greaterThanOrEqualTo((byte)-8))); assertThat(pkrR16[i], is(lessThanOrEqualTo((byte)8))); } } /** * Test method for {@link GroupElement#cmov(GroupElement, int)}. */ @Test public void testCmov() { GroupElement a = curve.getZero(GroupElement.Representation.PRECOMP); GroupElement b = GroupElement.precomp(curve, TWO, ZERO, TEN); assertThat(a.cmov(b, 0), is(equalTo(a))); assertThat(a.cmov(b, 1), is(equalTo(b))); } /** * Test method for {@link GroupElement#select(int, int)}. */ @Test public void testSelect() { GroupElement B = ed25519.getB(); for (int i = 0; i < 32; i++) { // 16^i 0 B assertThat(i + ",0", B.select(i, 0), is(equalTo(GroupElement.precomp(curve, ONE, ONE, ZERO)))); for (int j = 1; j < 8; j++) { // 16^i r_i B GroupElement t = B.select(i, j); assertThat(i + "," + j, t, is(equalTo(B.precmp[i][j-1]))); // -16^i r_i B t = B.select(i, -j); GroupElement neg = GroupElement.precomp(curve, B.precmp[i][j-1].Y, B.precmp[i][j-1].X, B.precmp[i][j-1].Z.negate()); assertThat(i + "," + -j, t, is(equalTo(neg))); } } } // region scalar multiplication /** * Test method for {@link GroupElement#scalarMultiply(byte[])}. * Test values generated with Python Ed25519 implementation. */ @Test public void testScalarMultiplyByteArray() { // Little-endian byte[] zero = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); byte[] one = Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000"); byte[] two = Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000"); byte[] a = Utils.hexToBytes("d072f8dd9c07fa7bc8d22a4b325d26301ee9202f6db89aa7c3731529e37e437c"); GroupElement A = new GroupElement(curve, Utils.hexToBytes("d4cf8595571830644bd14af416954d09ab7159751ad9e0f7a6cbd92379e71a66")); assertThat("scalarMultiply(0) failed", ed25519.getB().scalarMultiply(zero), is(equalTo(curve.getZero(GroupElement.Representation.P3)))); assertThat("scalarMultiply(1) failed", ed25519.getB().scalarMultiply(one), is(equalTo(ed25519.getB()))); assertThat("scalarMultiply(2) failed", ed25519.getB().scalarMultiply(two), is(equalTo(ed25519.getB().dbl()))); assertThat("scalarMultiply(a) failed", ed25519.getB().scalarMultiply(a), is(equalTo(A))); } @Test public void scalarMultiplyBasePointWithZeroReturnsNeutralElement() { // Arrange: final GroupElement basePoint = ed25519.getB(); // Act: final GroupElement g = basePoint.scalarMultiply(curve.getField().ZERO.toByteArray()); // Assert: Assert.assertThat(curve.getZero(GroupElement.Representation.P3), IsEqual.equalTo(g)); } @Test public void scalarMultiplyBasePointWithOneReturnsBasePoint() { // Arrange: final GroupElement basePoint = ed25519.getB(); // Act: final GroupElement g = basePoint.scalarMultiply(curve.getField().ONE.toByteArray()); // Assert: Assert.assertThat(basePoint, IsEqual.equalTo(g)); } // This test is slow (~6s) due to math utils using an inferior algorithm to calculate the result. @Test public void scalarMultiplyBasePointReturnsExpectedResult() { for (int i=0; i<10; i++) { // Arrange: final GroupElement basePoint = ed25519.getB(); final FieldElement f = MathUtils.getRandomFieldElement(); // Act: final GroupElement g = basePoint.scalarMultiply(f.toByteArray()); final GroupElement h = MathUtils.scalarMultiplyGroupElement(basePoint, f); // Assert: Assert.assertThat(g, IsEqual.equalTo(h)); } } @Test public void testDoubleScalarMultiplyVariableTime() { // Little-endian byte[] zero = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); byte[] one = Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000"); byte[] two = Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000"); byte[] a = Utils.hexToBytes("d072f8dd9c07fa7bc8d22a4b325d26301ee9202f6db89aa7c3731529e37e437c"); GroupElement A = new GroupElement(curve, Utils.hexToBytes("d4cf8595571830644bd14af416954d09ab7159751ad9e0f7a6cbd92379e71a66")); GroupElement B = ed25519.getB(); GroupElement geZero = curve.getZero(GroupElement.Representation.P3PrecomputedDouble); // 0 * GE(0) + 0 * GE(0) = GE(0) assertThat(geZero.doubleScalarMultiplyVariableTime(geZero, zero, zero), is(equalTo(geZero))); // 0 * GE(0) + 0 * B = GE(0) assertThat(B.doubleScalarMultiplyVariableTime(geZero, zero, zero), is(equalTo(geZero))); // 1 * GE(0) + 0 * B = GE(0) assertThat(B.doubleScalarMultiplyVariableTime(geZero, one, zero), is(equalTo(geZero))); // 1 * GE(0) + 1 * B = B assertThat(B.doubleScalarMultiplyVariableTime(geZero, one, one), is(equalTo(B))); // 1 * B + 1 * B = 2 * B assertThat(B.doubleScalarMultiplyVariableTime(B, one, one), is(equalTo(B.dbl()))); // 1 * B + 2 * B = 3 * B assertThat(B.doubleScalarMultiplyVariableTime(B, one, two), is(equalTo(B.dbl().toP3().add(B.toCached())))); // 2 * B + 2 * B = 4 * B assertThat(B.doubleScalarMultiplyVariableTime(B, two, two), is(equalTo(B.dbl().toP3().dbl()))); // 0 * B + a * B = A assertThat(B.doubleScalarMultiplyVariableTime(B, zero, a), is(equalTo(A))); // a * B + 0 * B = A assertThat(B.doubleScalarMultiplyVariableTime(B, a, zero), is(equalTo(A))); // a * B + a * B = 2 * A assertThat(B.doubleScalarMultiplyVariableTime(B, a, a), is(equalTo(A.dbl()))); } // This test is slow (~6s) due to math utils using an inferior algorithm to calculate the result. @Test public void doubleScalarMultiplyVariableTimeReturnsExpectedResult() { for (int i=0; i<10; i++) { // Arrange: final GroupElement basePoint = ed25519.getB(); final GroupElement g = MathUtils.getRandomGroupElement(true); final FieldElement f1 = MathUtils.getRandomFieldElement(); final FieldElement f2 = MathUtils.getRandomFieldElement(); // Act: final GroupElement h1 = basePoint.doubleScalarMultiplyVariableTime(g, f2.toByteArray(), f1.toByteArray()); final GroupElement h2 = MathUtils.doubleScalarMultiplyGroupElements(basePoint, f1, g, f2); // Assert: Assert.assertThat(h1, IsEqual.equalTo(h2)); } } // endregion /** * Test method for {@link GroupElement#isOnCurve(Curve)}. */ @Test public void testIsOnCurve() { assertThat(P2_ZERO.isOnCurve(curve), is(true)); assertThat(GroupElement.p2(curve, ZERO, ZERO, ONE).isOnCurve(curve), is(false)); assertThat(GroupElement.p2(curve, ONE, ONE, ONE).isOnCurve(curve), is(false)); assertThat(GroupElement.p2(curve, TEN, ZERO, ONE).isOnCurve(curve), is(false)); assertThat(GroupElement.p2(curve, ONE, TEN, ONE).isOnCurve(curve), is(false)); assertThat(GroupElement.p2(curve, PKR[0], PKR[1], ONE).isOnCurve(curve), is(true)); } @Test public void isOnCurveReturnsTrueForPointsOnTheCurve() { for (int i=0; i<100; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Assert: Assert.assertThat(g.isOnCurve(), IsEqual.equalTo(true)); } } @Test public void isOnCurveReturnsFalseForPointsNotOnTheCurve() { for (int i=0; i<100; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); final GroupElement h = GroupElement.p2(curve, g.getX(), g.getY(), g.getZ().multiply(curve.getField().TWO)); // Assert (can only fail for 5*Z^2=1): Assert.assertThat(h.isOnCurve(), IsEqual.equalTo(false)); } } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/MathUtils.java000066400000000000000000000456231327341674300254130ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.math.ed25519.*; import net.i2p.crypto.eddsa.spec.*; import org.hamcrest.core.IsEqual; import org.junit.*; import java.math.BigInteger; import java.security.SecureRandom; /** * Utility class to help with calculations. */ public class MathUtils { private static final int[] exponents = {0, 26, 26 + 25, 2*26 + 25, 2*26 + 2*25, 3*26 + 2*25, 3*26 + 3*25, 4*26 + 3*25, 4*26 + 4*25, 5*26 + 4*25}; private static final SecureRandom random = new SecureRandom(); private static final EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); private static final Curve curve = ed25519.getCurve(); private static final BigInteger d = new BigInteger("-121665").multiply(new BigInteger("121666").modInverse(getQ())); private static final BigInteger groupOrder = BigInteger.ONE.shiftLeft(252).add(new BigInteger("27742317777372353535851937790883648493")); /** * Gets q = 2^255 - 19 as BigInteger. */ public static BigInteger getQ() { return new BigInteger("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed", 16); } /** * Gets group order = 2^252 + 27742317777372353535851937790883648493 as BigInteger. */ public static BigInteger getGroupOrder() { return groupOrder; } /** * Gets the underlying finite field with q=2^255 - 19 elements. * * @return The finite field. */ public static Field getField() { return new Field( 256, // b Utils.hexToBytes("edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f"), // q new Ed25519LittleEndianEncoding()); } // region field element /** * Converts a 2^25.5 bit representation to a BigInteger. *

    * Value: 2^exponents[0] * t[0] + 2^exponents[1] * t[1] + ... + 2^exponents[9] * t[9] * * @param t The 2^25.5 bit representation. * @return The BigInteger. */ public static BigInteger toBigInteger(final int[] t) { BigInteger b = BigInteger.ZERO; for (int i=0; i<10; i++) { b = b.add(BigInteger.ONE.multiply(BigInteger.valueOf(t[i])).shiftLeft(exponents[i])); } return b; } /** * Converts a 2^8 bit representation to a BigInteger. *

    * Value: bytes[0] + 2^8 * bytes[1] + ... * * @param bytes The 2^8 bit representation. * @return The BigInteger. */ public static BigInteger toBigInteger(final byte[] bytes) { BigInteger b = BigInteger.ZERO; for (int i=0; i= 0) { throw new RuntimeException("only numbers < 2^256 are allowed"); } final byte[] bytes = new byte[32]; final byte[] original = b.toByteArray(); // Although b < 2^256, original can have length > 32 with some bytes set to 0. final int offset = original.length > 32? original.length - 32 : 0; for (int i=0; i * a, b and c are given in 2^8 bit representation. * * @param a The first integer. * @param b The second integer. * @param c The third integer. * @return The mod group order reduced result. */ public static byte[] multiplyAndAddModGroupOrder(final byte[] a, final byte[] b, final byte[] c) { final BigInteger result = toBigInteger(a).multiply(toBigInteger(b)).add(toBigInteger(c)).mod(groupOrder); return toByteArray(result); } public static byte[] getRandomByteArray(final int length) { final byte[] bytes = new byte[length]; random.nextBytes(bytes); return bytes; } /** * Gets a random field element where |t[i]| <= 2^24 for 0 <= i <= 9. * * @return The field element. */ public static FieldElement getRandomFieldElement() { final int[] t = new int[10]; for (int j=0; j<10; j++) { t[j] = random.nextInt(1 << 25) - (1 << 24); } return new Ed25519FieldElement(getField(), t); } // endregion // region group element /** * Gets a random group element in P3 representation. * * @return The group element. */ public static GroupElement getRandomGroupElement() { return getRandomGroupElement(false); } /** * Gets a random group element in P3 representation, with precmp and dblPrecmp populated. * * @return The group element. */ public static GroupElement getRandomGroupElement(boolean precompute) { final byte[] bytes = new byte[32]; while (true) { try { random.nextBytes(bytes); return new GroupElement(curve, bytes, precompute); } catch (IllegalArgumentException e) { // Will fail in about 87.5%, so try again. } } } /** * Creates a group element from a byte array. *

    * Bit 0 to 254 are the affine y-coordinate, bit 255 is the sign of the affine x-coordinate. * * @param bytes the byte array. * @return The group element. */ public static GroupElement toGroupElement(final byte[] bytes) { final boolean shouldBeNegative = (bytes[31] >> 7) != 0; bytes[31] &= 0x7f; final BigInteger y = MathUtils.toBigInteger(bytes); // x = sign(x) * sqrt((y^2 - 1) / (d * y^2 + 1)) final BigInteger u = y.multiply(y).subtract(BigInteger.ONE).mod(getQ()); final BigInteger v = d.multiply(y).multiply(y).add(BigInteger.ONE).mod(getQ()); final BigInteger tmp = u.multiply(v.pow(7)).modPow(BigInteger.ONE.shiftLeft(252).subtract(new BigInteger("3")), getQ()).mod(getQ()); BigInteger x = tmp.multiply(u).multiply(v.pow(3)).mod(getQ()); if (!v.multiply(x).multiply(x).subtract(u).mod(getQ()).equals(BigInteger.ZERO)) { if (!v.multiply(x).multiply(x).add(u).mod(getQ()).equals(BigInteger.ZERO)) { throw new IllegalArgumentException("not a valid GroupElement"); } x = x.multiply(toBigInteger(curve.getI())).mod(getQ()); } final boolean isNegative = x.mod(new BigInteger("2")).equals(BigInteger.ONE); if ((shouldBeNegative && !isNegative) || (!shouldBeNegative && isNegative)) { x = x.negate().mod(getQ()); } return GroupElement.p3(curve, toFieldElement(x), toFieldElement(y), getField().ONE, toFieldElement(x.multiply(y).mod(getQ()))); } /** * Converts a group element from one representation to another. * This method is a helper used to test various methods in GroupElement. * * @param g The group element. * @param repr The desired representation. * @return The same group element in the new representation. */ public static GroupElement toRepresentation(final GroupElement g, final GroupElement.Representation repr) { BigInteger x; BigInteger y; final BigInteger gX = toBigInteger(g.getX().toByteArray()); final BigInteger gY = toBigInteger(g.getY().toByteArray()); final BigInteger gZ = toBigInteger(g.getZ().toByteArray()); final BigInteger gT = null == g.getT()? null : toBigInteger(g.getT().toByteArray()); // Switch to affine coordinates. switch (g.getRepresentation()) { case P2: case P3: case P3PrecomputedDouble: x = gX.multiply(gZ.modInverse(getQ())).mod(getQ()); y = gY.multiply(gZ.modInverse(getQ())).mod(getQ()); break; case P1P1: x = gX.multiply(gZ.modInverse(getQ())).mod(getQ()); y = gY.multiply(gT.modInverse(getQ())).mod(getQ()); break; case CACHED: x = gX.subtract(gY).multiply(gZ.multiply(new BigInteger("2")).modInverse(getQ())).mod(getQ()); y = gX.add(gY).multiply(gZ.multiply(new BigInteger("2")).modInverse(getQ())).mod(getQ()); break; case PRECOMP: x = gX.subtract(gY).multiply(new BigInteger("2").modInverse(getQ())).mod(getQ()); y = gX.add(gY).multiply(new BigInteger("2").modInverse(getQ())).mod(getQ()); break; default: throw new UnsupportedOperationException(); } // Now back to the desired representation. switch (repr) { case P2: return GroupElement.p2( curve, toFieldElement(x), toFieldElement(y), getField().ONE); case P3: return GroupElement.p3( curve, toFieldElement(x), toFieldElement(y), getField().ONE, toFieldElement(x.multiply(y).mod(getQ())), false); case P3PrecomputedDouble: return GroupElement.p3( curve, toFieldElement(x), toFieldElement(y), getField().ONE, toFieldElement(x.multiply(y).mod(getQ())), true); case P1P1: return GroupElement.p1p1( curve, toFieldElement(x), toFieldElement(y), getField().ONE, getField().ONE); case CACHED: return GroupElement.cached( curve, toFieldElement(y.add(x).mod(getQ())), toFieldElement(y.subtract(x).mod(getQ())), getField().ONE, toFieldElement(d.multiply(new BigInteger("2")).multiply(x).multiply(y).mod(getQ()))); case PRECOMP: return GroupElement.precomp( curve, toFieldElement(y.add(x).mod(getQ())), toFieldElement(y.subtract(x).mod(getQ())), toFieldElement(d.multiply(new BigInteger("2")).multiply(x).multiply(y).mod(getQ()))); default: throw new UnsupportedOperationException(); } } /** * Adds two group elements and returns the result in P3 representation. * It uses BigInteger arithmetic and the affine representation. * This method is a helper used to test the projective group addition formulas in GroupElement. * * @param g1 The first group element. * @param g2 The second group element. * @return The result of the addition. */ public static GroupElement addGroupElements(final GroupElement g1, final GroupElement g2) { // Relying on a special representation of the group elements. if ((g1.getRepresentation() != GroupElement.Representation.P2 && g1.getRepresentation() != GroupElement.Representation.P3) || (g2.getRepresentation() != GroupElement.Representation.P2 && g2.getRepresentation() != GroupElement.Representation.P3)) { throw new IllegalArgumentException("g1 and g2 must have representation P2 or P3"); } // Projective coordinates final BigInteger g1X = toBigInteger(g1.getX().toByteArray()); final BigInteger g1Y = toBigInteger(g1.getY().toByteArray()); final BigInteger g1Z = toBigInteger(g1.getZ().toByteArray()); final BigInteger g2X = toBigInteger(g2.getX().toByteArray()); final BigInteger g2Y = toBigInteger(g2.getY().toByteArray()); final BigInteger g2Z = toBigInteger(g2.getZ().toByteArray()); // Affine coordinates final BigInteger g1x = g1X.multiply(g1Z.modInverse(getQ())).mod(getQ()); final BigInteger g1y = g1Y.multiply(g1Z.modInverse(getQ())).mod(getQ()); final BigInteger g2x = g2X.multiply(g2Z.modInverse(getQ())).mod(getQ()); final BigInteger g2y = g2Y.multiply(g2Z.modInverse(getQ())).mod(getQ()); // Addition formula for affine coordinates. The formula is complete in our case. // // (x3, y3) = (x1, y1) + (x2, y2) where // // x3 = (x1 * y2 + x2 * y1) / (1 + d * x1 * x2 * y1 * y2) and // y3 = (x1 * x2 + y1 * y2) / (1 - d * x1 * x2 * y1 * y2) and // d = -121665/121666 BigInteger dx1x2y1y2 = d.multiply(g1x).multiply(g2x).multiply(g1y).multiply(g2y).mod(getQ()); BigInteger x3 = g1x.multiply(g2y).add(g2x.multiply(g1y)) .multiply(BigInteger.ONE.add(dx1x2y1y2).modInverse(getQ())).mod(getQ()); BigInteger y3 = g1x.multiply(g2x).add(g1y.multiply(g2y)) .multiply(BigInteger.ONE.subtract(dx1x2y1y2).modInverse(getQ())).mod(getQ()); BigInteger t3 = x3.multiply(y3).mod(getQ()); return GroupElement.p3(g1.getCurve(), toFieldElement(x3), toFieldElement(y3), getField().ONE, toFieldElement(t3)); } /** * Doubles a group element and returns the result in P3 representation. * It uses BigInteger arithmetic and the affine representation. * This method is a helper used to test the projective group doubling formula in GroupElement. * * @param g The group element. * @return g+g. */ public static GroupElement doubleGroupElement(final GroupElement g) { return addGroupElements(g, g); } /** * Scalar multiply the group element by the field element. * * @param g The group element. * @param f The field element. * @return The resulting group element. */ public static GroupElement scalarMultiplyGroupElement(final GroupElement g, final FieldElement f) { final byte[] bytes = f.toByteArray(); GroupElement h = curve.getZero(GroupElement.Representation.P3); for (int i=254; i>=0; i--) { h = doubleGroupElement(h); if (Utils.bit(bytes, i) == 1) { h = addGroupElements(h, g); } } return h; } /** * Calculates f1 * g1 + f2 * g2. * * @param g1 The first group element. * @param f1 The first multiplier. * @param g2 The second group element. * @param f2 The second multiplier. * @return The resulting group element. */ public static GroupElement doubleScalarMultiplyGroupElements( final GroupElement g1, final FieldElement f1, final GroupElement g2, final FieldElement f2) { final GroupElement h1 = scalarMultiplyGroupElement(g1, f1); final GroupElement h2 = scalarMultiplyGroupElement(g2, f2); return addGroupElements(h1, h2); } /** * Negates a group element. * * @param g The group element. * @return The negated group element. */ public static GroupElement negateGroupElement(final GroupElement g) { if (g.getRepresentation() != GroupElement.Representation.P3) { throw new IllegalArgumentException("g must have representation P3"); } return GroupElement.p3(g.getCurve(), g.getX().negate(), g.getY(), g.getZ(), g.getT().negate()); } // Start TODO BR: Remove when finished! @Test public void mathUtilsWorkAsExpected() { final GroupElement neutral = GroupElement.p3(curve, curve.getField().ZERO, curve.getField().ONE, curve.getField().ONE, curve.getField().ZERO); for (int i=0; i<1000; i++) { final GroupElement g = getRandomGroupElement(); // Act: final GroupElement h1 = addGroupElements(g, neutral); final GroupElement h2 = addGroupElements(neutral, g); // Assert: Assert.assertThat(g, IsEqual.equalTo(h1)); Assert.assertThat(g, IsEqual.equalTo(h2)); } for (int i=0; i<1000; i++) { GroupElement g = getRandomGroupElement(); // P3 -> P2. GroupElement h = toRepresentation(g, GroupElement.Representation.P2); Assert.assertThat(h, IsEqual.equalTo(g)); // P3 -> P1P1. h = toRepresentation(g, GroupElement.Representation.P1P1); Assert.assertThat(g, IsEqual.equalTo(h)); // P3 -> CACHED. h = toRepresentation(g, GroupElement.Representation.CACHED); Assert.assertThat(h, IsEqual.equalTo(g)); // P3 -> P2 -> P3. g = toRepresentation(g, GroupElement.Representation.P2); h = toRepresentation(g, GroupElement.Representation.P3); Assert.assertThat(g, IsEqual.equalTo(h)); // P3 -> P2 -> P1P1. g = toRepresentation(g, GroupElement.Representation.P2); h = toRepresentation(g, GroupElement.Representation.P1P1); Assert.assertThat(g, IsEqual.equalTo(h)); } for (int i=0; i<10; i++) { // Arrange: final GroupElement g = MathUtils.getRandomGroupElement(); // Act: final GroupElement h = MathUtils.scalarMultiplyGroupElement(g, curve.getField().ZERO); // Assert: Assert.assertThat(curve.getZero(GroupElement.Representation.P3), IsEqual.equalTo(h)); } } // End TODO BR: Remove when finished! } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/PrecomputationTestVectors.java000066400000000000000000000113601327341674300307070ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math; import java.io.BufferedReader; import java.io.IOException; import java.io.InputStream; import java.io.InputStreamReader; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveSpec; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; public class PrecomputationTestVectors { // Test files were generated using base.py and base2.py from ref10 // (by printing hex(x%q) instead of the radix-255 representation). static GroupElement[][] testPrecmp = getPrecomputation("basePrecmp"); static GroupElement[] testDblPrecmp = getDoublePrecomputation("baseDblPrecmp"); public static GroupElement[][] getPrecomputation(String fileName) { EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Curve curve = ed25519.getCurve(); Field field = curve.getField(); GroupElement[][] precmp = new GroupElement[32][8]; BufferedReader file = null; int row = 0, col = 0; try { InputStream is = PrecomputationTestVectors.class.getResourceAsStream(fileName); if (is == null) throw new IOException("Resource not found: " + fileName); file = new BufferedReader(new InputStreamReader(is)); String line; while ((line = file.readLine()) != null) { if (line.equals(" },")) col += 1; else if (line.equals("},")) { col = 0; row += 1; } else if (line.startsWith(" { ")) { String ypxStr = line.substring(4, line.lastIndexOf(' ')); FieldElement ypx = field.fromByteArray( Utils.hexToBytes(ypxStr)); line = file.readLine(); String ymxStr = line.substring(4, line.lastIndexOf(' ')); FieldElement ymx = field.fromByteArray( Utils.hexToBytes(ymxStr)); line = file.readLine(); String xy2dStr = line.substring(4, line.lastIndexOf(' ')); FieldElement xy2d = field.fromByteArray( Utils.hexToBytes(xy2dStr)); precmp[row][col] = GroupElement.precomp(curve, ypx, ymx, xy2d); } } } catch (IOException e) { e.printStackTrace(); } finally { if (file != null) try { file.close(); } catch (IOException e) {} } return precmp; } public static GroupElement[] getDoublePrecomputation(String fileName) { EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); Curve curve = ed25519.getCurve(); Field field = curve.getField(); GroupElement[] dblPrecmp = new GroupElement[8]; BufferedReader file = null; int row = 0; try { InputStream is = PrecomputationTestVectors.class.getResourceAsStream(fileName); if (is == null) throw new IOException("Resource not found: " + fileName); file = new BufferedReader(new InputStreamReader(is)); String line; while ((line = file.readLine()) != null) { if (line.equals(" },")) { row += 1; } else if (line.startsWith(" { ")) { String ypxStr = line.substring(4, line.lastIndexOf(' ')); FieldElement ypx = field.fromByteArray( Utils.hexToBytes(ypxStr)); line = file.readLine(); String ymxStr = line.substring(4, line.lastIndexOf(' ')); FieldElement ymx = field.fromByteArray( Utils.hexToBytes(ymxStr)); line = file.readLine(); String xy2dStr = line.substring(4, line.lastIndexOf(' ')); FieldElement xy2d = field.fromByteArray( Utils.hexToBytes(xy2dStr)); dblPrecmp[row] = GroupElement.precomp(curve, ypx, ymx, xy2d); } } } catch (IOException e) { e.printStackTrace(); } finally { if (file != null) try { file.close(); } catch (IOException e) {} } return dblPrecmp; } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/baseDblPrecmp000066400000000000000000000033701327341674300252550ustar00rootroot00000000000000 { { 853b8cf5c693bc2f190e8cfbc62d93cfc2423d6498480b2765bad4333a9dcf07 }, { 3e9140d70539109db3be40d1059f39fd098a8f683484c1a56712f898922ffd44 }, { 68aa7a870512c9ab9ec4aacc23e8d9268c5943ddcb7d1b5aa8650c9f687b116f }, }, { { 3097ee4ca8b025af8a4b86e830845a023267019f02501bc1f4f8809a1b4e167a }, { 65d2fca4e81f61567dbac1e5fd53d33bbdd64b211af3318162da5b558715b92a }, { 89d8d00d3f93ae1462da351c222394584cdbf28c45e570d1c6b4b912af26285a }, }, { { 33bba50844bc12a202ed5ec7c348508d44ecbf5a0ceb1bddeb06e246f1cc4529 }, { bad647a4c382917fb729274bd11400d587a064b81cf13ce3f3551beb737e4a15 }, { 85822a81f1dbbbbcfcd1bdd007080e272da7bd1b0b671bb49ab63b6b69beaa43 }, }, { { bfa34e94d05c1a6bd2c09db33a357074492e54288252b2717e923c2869ea1b46 }, { b12132aa9a2c6fbaa723ba3b5321a06c3a2c19924f76ea9de017532e5ddd6e1d }, { a2b3b801c86d83f19aa43e05475f03b3f3ad7758ba419c52a7900f6a1cbb9f7a }, }, { { 2f63a8a68a672e9bc546bc516f9e50a6b5f586c6c933b2ce597fdd8a33edb934 }, { 64809d037e216ef39b4120f5b681a09844b05ee708c6cb968f9cdcfa515ac049 }, { 1baf4590bfe8b4062fd219a7e883ffe216cfd49329fcf6aa068b001b0272c173 }, }, { { de2a808a8400bf2f272e3002cffed9e50634701771843e11af8f6d54e2aa7542 }, { 48438649025b5f318183087769b3d63e95eb8d6a5575a0a37fc7d5298059ab18 }, { e98960fdc52c2bd8a4e48232a1b41e0322861ab59911314448f93db52255c63d }, }, { { 6d7f00a222c270bfdbdebcb59ab384bf07ba07fb120e7a5341f246c3eed74f23 }, { 93bf7f323b016f506b6f779bc9ebfcae6859adaa32b2129da72460172d886702 }, { 78a32e7319a1605371d48ddfb1e6372433e5a791f837efa2637809aafda67b49 }, }, { { a0eacf1303ccce246d249c188dc24886d0d4f2c1fabdbd2d2be72df11729e261 }, { 0bcf8c4686cd0b04d610992aa49b82d39251b20708300875bf5ed01842cdb543 }, { 16b5d09b2f769a5deede3f374eaf38eb7042d6937d5a2e0342d8e40a21611d51 }, }, str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/basePrecmp000066400000000000000000001576401327341674300246450ustar00rootroot00000000000000{ { { 853b8cf5c693bc2f190e8cfbc62d93cfc2423d6498480b2765bad4333a9dcf07 }, { 3e9140d70539109db3be40d1059f39fd098a8f683484c1a56712f898922ffd44 }, { 68aa7a870512c9ab9ec4aacc23e8d9268c5943ddcb7d1b5aa8650c9f687b116f }, }, { { d7713c93fce72492b5f50f7a969d469f0207d6e1659aa65a2e2e7da83f060c59 }, { a8d5b44260a5998af6ac604e0c812b8faa376eb16b239ee05525c969a695b56b }, { 5f7a9ba5b3a8fa4378cf9a5ddd6bc136316a3d0b84a00f50730ba53eb1f51a70 }, }, { { 3097ee4ca8b025af8a4b86e830845a023267019f02501bc1f4f8809a1b4e167a }, { 65d2fca4e81f61567dbac1e5fd53d33bbdd64b211af3318162da5b558715b92a }, { 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}, { d93492f3ed5da7e2f958b5e180763d96fb233c6eac41272cc3010e32a124903a }, { 1a91a2c9d9f5c1e7d7a7cc8b7871a3b8322ab60e19126463954ecc2e5c7c9026 }, }, }, { { { 1d9c2f630eddcc2e1531897696b6d051587a63a86bb7df5239ef0ea0497dd36d }, { 5e51aa4954635bed3a82c60b9fc465a8c4d1425be91f0c85b915d3036f6dd730 }, { c7e406211744446c697f8d9280d653fb263f4d69a49e73b4b04b862e1197c610 }, }, { { 05c85883a02aa60c4742207ae34a3d6adced113ba6d36474ef060855af9bbf03 }, { de5fbe7d27c49364a27ead19ad4f5d2690453046c8df000e09fe66edab1ce625 }, { 046658cc28e1133f7e7459b4ec73586ff56812cced3db6a02ce2864563786d56 }, }, { { d02f5ac6854205a1c36716f32a11646c58ee1a7340e20a682ab29347f3a5fb14 }, { 3408c19c9fa4371651c49ba8d5568ebcdbd27f7f0fecb51cd935cc5eca5b9733 }, { d4f785691646d73c5700c8c9845e3e591e13617bb6f2c32f6c52fc83ea9c8214 }, }, { { b8ec714e2f0be721e377a440b9dd56e6804f1dcece5665bf7e7b5d53c43bfc05 }, { c295dd97847b43ffa7b54eaa304e746c8be8853c615d0c9e7381755f1ec7d92f }, { 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If not, see . * */ package net.i2p.crypto.eddsa.math.bigint; import static org.hamcrest.Matchers.*; import static org.junit.Assert.*; import java.math.BigInteger; import java.util.Random; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.math.Field; import net.i2p.crypto.eddsa.math.FieldElement; import net.i2p.crypto.eddsa.math.MathUtils; import net.i2p.crypto.eddsa.math.AbstractFieldElementTest; import org.junit.Test; /** * @author str4d * */ public class BigIntegerFieldElementTest extends AbstractFieldElementTest { static final byte[] BYTES_ZERO = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_ONE = Utils.hexToBytes("0100000000000000000000000000000000000000000000000000000000000000"); static final byte[] BYTES_TEN = Utils.hexToBytes("0a00000000000000000000000000000000000000000000000000000000000000"); static final Field ed25519Field = new Field( 256, // b Utils.hexToBytes("edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f"), // q new BigIntegerLittleEndianEncoding()); static final FieldElement ZERO = new BigIntegerFieldElement(ed25519Field, BigInteger.ZERO); static final FieldElement ONE = new BigIntegerFieldElement(ed25519Field, BigInteger.ONE); static final FieldElement TWO = new BigIntegerFieldElement(ed25519Field, BigInteger.valueOf(2)); protected FieldElement getRandomFieldElement() { BigInteger r; Random rnd = new Random(); do { r = new BigInteger(255, rnd); } while (r.compareTo(getQ()) >= 0); return new BigIntegerFieldElement(ed25519Field, r); } protected BigInteger toBigInteger(FieldElement f) { return ((BigIntegerFieldElement)f).bi; } protected BigInteger getQ() { return MathUtils.getQ(); } protected Field getField() { return ed25519Field; } /** * Test method for {@link BigIntegerFieldElement#BigIntegerFieldElement(Field, BigInteger)}. */ @Test public void testFieldElementBigInteger() { assertThat(new BigIntegerFieldElement(ed25519Field, BigInteger.ZERO).bi, is(BigInteger.ZERO)); assertThat(new BigIntegerFieldElement(ed25519Field, BigInteger.ONE).bi, is(BigInteger.ONE)); assertThat(new BigIntegerFieldElement(ed25519Field, BigInteger.valueOf(2)).bi, is(BigInteger.valueOf(2))); } /** * Test method for {@link FieldElement#toByteArray()}. */ @Test public void testToByteArray() { byte[] zero = ZERO.toByteArray(); assertThat(zero.length, is(equalTo(BYTES_ZERO.length))); assertThat(zero, is(equalTo(BYTES_ZERO))); byte[] one = ONE.toByteArray(); assertThat(one.length, is(equalTo(BYTES_ONE.length))); assertThat(one, is(equalTo(BYTES_ONE))); byte[] ten = new BigIntegerFieldElement(ed25519Field, BigInteger.TEN).toByteArray(); assertThat(ten.length, is(equalTo(BYTES_TEN.length))); assertThat(ten, is(equalTo(BYTES_TEN))); } // region isNonZero protected FieldElement getZeroFieldElement() { return ZERO; } protected FieldElement getNonZeroFieldElement() { return TWO; } // endregion /** * Test method for {@link FieldElement#equals(java.lang.Object)}. */ @Test public void testEqualsObject() { assertThat(new BigIntegerFieldElement(ed25519Field, BigInteger.ZERO), is(equalTo(ZERO))); assertThat(new BigIntegerFieldElement(ed25519Field, BigInteger.valueOf(1000)), is(equalTo(new BigIntegerFieldElement(ed25519Field, BigInteger.valueOf(1000))))); assertThat(ONE, is(not(equalTo(TWO)))); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/bigint/BigIntegerScalarOpsTest.java000066400000000000000000000060761327341674300314430ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.bigint; import static org.hamcrest.Matchers.*; import static org.junit.Assert.*; import java.math.BigInteger; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.math.Field; import net.i2p.crypto.eddsa.math.ScalarOps; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveSpec; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import org.junit.Test; /** * @author str4d * */ public class BigIntegerScalarOpsTest { static final EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); static final Field ed25519Field = ed25519.getCurve().getField(); /** * Test method for {@link net.i2p.crypto.eddsa.math.bigint.BigIntegerScalarOps#reduce(byte[])}. */ @Test public void testReduce() { ScalarOps sc = new BigIntegerScalarOps(ed25519Field, new BigInteger("5")); assertThat(sc.reduce(new byte[] {7}), is(equalTo(Utils.hexToBytes("0200000000000000000000000000000000000000000000000000000000000000")))); ScalarOps sc2 = new BigIntegerScalarOps(ed25519Field, new BigInteger("7237005577332262213973186563042994240857116359379907606001950938285454250989")); // Example from test case 1 byte[] r = Utils.hexToBytes("b6b19cd8e0426f5983fa112d89a143aa97dab8bc5deb8d5b6253c928b65272f4044098c2a990039cde5b6a4818df0bfb6e40dc5dee54248032962323e701352d"); assertThat(sc2.reduce(r), is(equalTo(Utils.hexToBytes("f38907308c893deaf244787db4af53682249107418afc2edc58f75ac58a07404")))); } /** * Test method for {@link net.i2p.crypto.eddsa.math.bigint.BigIntegerScalarOps#multiplyAndAdd(byte[], byte[], byte[])}. */ @Test public void testMultiplyAndAdd() { ScalarOps sc = new BigIntegerScalarOps(ed25519Field, new BigInteger("5")); assertThat(sc.multiplyAndAdd(new byte[] {7}, new byte[] {2}, new byte[] {5}), is(equalTo(Utils.hexToBytes("0400000000000000000000000000000000000000000000000000000000000000")))); ScalarOps sc2 = new BigIntegerScalarOps(ed25519Field, new BigInteger("7237005577332262213973186563042994240857116359379907606001950938285454250989")); // Example from test case 1 byte[] h = Utils.hexToBytes("86eabc8e4c96193d290504e7c600df6cf8d8256131ec2c138a3e7e162e525404"); byte[] a = Utils.hexToBytes("307c83864f2833cb427a2ef1c00a013cfdff2768d980c0a3a520f006904de94f"); byte[] r = Utils.hexToBytes("f38907308c893deaf244787db4af53682249107418afc2edc58f75ac58a07404"); byte[] S = Utils.hexToBytes("5fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b"); assertThat(sc2.multiplyAndAdd(h, a, r), is(equalTo(S))); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/ed25519/000077500000000000000000000000001327341674300236225ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/ed25519/Ed25519FieldElementTest.java000066400000000000000000000052431327341674300305450ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.ed25519; import net.i2p.crypto.eddsa.math.*; import org.hamcrest.core.*; import org.junit.*; import java.math.BigInteger; /** * Tests rely on the BigInteger class. */ public class Ed25519FieldElementTest extends AbstractFieldElementTest { protected FieldElement getRandomFieldElement() { return MathUtils.getRandomFieldElement(); } protected BigInteger toBigInteger(FieldElement f) { return MathUtils.toBigInteger(f); } protected BigInteger getQ() { return MathUtils.getQ(); } protected Field getField() { return MathUtils.getField(); } // region constructor @Test public void canConstructFieldElementFromArrayWithCorrectLength() { // Assert: new Ed25519FieldElement(MathUtils.getField(), new int[10]); } @Test (expected = IllegalArgumentException.class) public void cannotConstructFieldElementFromArrayWithIncorrectLength() { // Assert: new Ed25519FieldElement(MathUtils.getField(), new int[9]); } @Test (expected = IllegalArgumentException.class) public void cannotConstructFieldElementWithoutField() { // Assert: new Ed25519FieldElement(null, new int[9]); } // endregion // region isNonZero protected FieldElement getZeroFieldElement() { return new Ed25519FieldElement(MathUtils.getField(), new int[10]); } protected FieldElement getNonZeroFieldElement() { final int[] t = new int[10]; t[0] = 5; return new Ed25519FieldElement(MathUtils.getField(), t); } // endregion // region toString @Test public void toStringReturnsCorrectRepresentation() { // Arrange: final byte[] bytes = new byte[32]; for (int i=0; i<32; i++) { bytes[i] = (byte)(i+1); } final FieldElement f = MathUtils.getField().getEncoding().decode(bytes); // Act: final String fAsString = f.toString(); final StringBuilder builder = new StringBuilder(); builder.append("[Ed25519FieldElement val="); for (byte b : bytes) { builder.append(String.format("%02x", b)); } builder.append("]"); // Assert: Assert.assertThat(fAsString, IsEqual.equalTo(builder.toString())); } // endregion } Ed25519LittleEndianEncodingTest.java000066400000000000000000000101571327341674300321540ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/ed25519/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.ed25519; import net.i2p.crypto.eddsa.math.*; import org.hamcrest.core.IsEqual; import org.junit.*; import java.math.BigInteger; import java.security.SecureRandom; /** * Tests rely on the BigInteger class. */ public class Ed25519LittleEndianEncodingTest { private static final SecureRandom random = new SecureRandom(); @Test public void encodeReturnsCorrectByteArrayForSimpleFieldElements() { // Arrange: final int[] t1 = new int[10]; final int[] t2 = new int[10]; t2[0] = 1; final FieldElement fieldElement1 = new Ed25519FieldElement(MathUtils.getField(), t1); final FieldElement fieldElement2 = new Ed25519FieldElement(MathUtils.getField(), t2); // Act: final byte[] bytes1 = MathUtils.getField().getEncoding().encode(fieldElement1); final byte[] bytes2 = MathUtils.getField().getEncoding().encode(fieldElement2); // Assert: Assert.assertThat(bytes1, IsEqual.equalTo(MathUtils.toByteArray(BigInteger.ZERO))); Assert.assertThat(bytes2, IsEqual.equalTo(MathUtils.toByteArray(BigInteger.ONE))); } @Test public void encodeReturnsCorrectByteArray() { for (int i=0; i<10000; i++){ // Arrange: final int[] t = new int[10]; for (int j=0; j<10; j++) { t[j] = random.nextInt(1 << 28) - (1 << 27); } final FieldElement fieldElement1 = new Ed25519FieldElement(MathUtils.getField(), t); final BigInteger b = MathUtils.toBigInteger(t); // Act: final byte[] bytes = MathUtils.getField().getEncoding().encode(fieldElement1); // Assert: Assert.assertThat(bytes, IsEqual.equalTo(MathUtils.toByteArray(b.mod(MathUtils.getQ())))); } } @Test public void decodeReturnsCorrectFieldElementForSimpleByteArrays() { // Arrange: final byte[] bytes1 = new byte[32]; final byte[] bytes2 = new byte[32]; bytes2[0] = 1; // Act: final Ed25519FieldElement f1 = (Ed25519FieldElement)MathUtils.getField().getEncoding().decode(bytes1); final Ed25519FieldElement f2 = (Ed25519FieldElement)MathUtils.getField().getEncoding().decode(bytes2); final BigInteger b1 = MathUtils.toBigInteger(f1.t); final BigInteger b2 = MathUtils.toBigInteger(f2.t); // Assert: Assert.assertThat(b1, IsEqual.equalTo(BigInteger.ZERO)); Assert.assertThat(b2, IsEqual.equalTo(BigInteger.ONE)); } @Test public void decodeReturnsCorrectFieldElement() { for (int i=0; i<10000; i++) { // Arrange: final byte[] bytes = new byte[32]; random.nextBytes(bytes); bytes[31] = (byte)(bytes[31] & 0x7f); final BigInteger b1 = MathUtils.toBigInteger(bytes); // Act: final Ed25519FieldElement f = (Ed25519FieldElement)MathUtils.getField().getEncoding().decode(bytes); final BigInteger b2 = MathUtils.toBigInteger(f.t).mod(MathUtils.getQ()); // Assert: Assert.assertThat(b2, IsEqual.equalTo(b1)); } } @Test public void isNegativeReturnsCorrectResult() { for (int i=0; i<10000; i++) { // Arrange: final int[] t = new int[10]; for (int j=0; j<10; j++) { t[j] = random.nextInt(1 << 28) - (1 << 27); } final boolean isNegative = MathUtils.toBigInteger(t).mod(MathUtils.getQ()).mod(new BigInteger("2")).equals(BigInteger.ONE); final FieldElement f = new Ed25519FieldElement(MathUtils.getField(), t); // Assert: Assert.assertThat(MathUtils.getField().getEncoding().isNegative(f), IsEqual.equalTo(isNegative)); } } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/math/ed25519/Ed25519ScalarOpsTest.java000066400000000000000000000071311327341674300300750ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.math.ed25519; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.math.*; import org.hamcrest.core.IsEqual; import org.junit.*; import java.math.BigInteger; import static org.hamcrest.Matchers.equalTo; import static org.hamcrest.Matchers.is; import static org.junit.Assert.assertThat; /** * @author str4d * Additional tests by the NEM project team. * */ public class Ed25519ScalarOpsTest { private static final Ed25519ScalarOps scalarOps = new Ed25519ScalarOps(); /** * Test method for {@link net.i2p.crypto.eddsa.math.bigint.BigIntegerScalarOps#reduce(byte[])}. */ @Test public void testReduce() { // Example from test case 1 byte[] r = Utils.hexToBytes("b6b19cd8e0426f5983fa112d89a143aa97dab8bc5deb8d5b6253c928b65272f4044098c2a990039cde5b6a4818df0bfb6e40dc5dee54248032962323e701352d"); assertThat(scalarOps.reduce(r), is(equalTo(Utils.hexToBytes("f38907308c893deaf244787db4af53682249107418afc2edc58f75ac58a07404")))); } @Test public void reduceReturnsExpectedResult() { for (int i=0; i<1000; i++) { // Arrange: final byte[] bytes = MathUtils.getRandomByteArray(64); // Act: final byte[] reduced1 = scalarOps.reduce(bytes); final byte[] reduced2 = MathUtils.reduceModGroupOrder(bytes); // Assert: Assert.assertThat(MathUtils.toBigInteger(reduced1).compareTo(MathUtils.getGroupOrder()), IsEqual.equalTo(-1)); Assert.assertThat(MathUtils.toBigInteger(reduced1).compareTo(new BigInteger("-1")), IsEqual.equalTo(1)); Assert.assertThat(reduced1, IsEqual.equalTo(reduced2)); } } /** * Test method for {@link net.i2p.crypto.eddsa.math.bigint.BigIntegerScalarOps#multiplyAndAdd(byte[], byte[], byte[])}. */ @Test public void testMultiplyAndAdd() { // Example from test case 1 byte[] h = Utils.hexToBytes("86eabc8e4c96193d290504e7c600df6cf8d8256131ec2c138a3e7e162e525404"); byte[] a = Utils.hexToBytes("307c83864f2833cb427a2ef1c00a013cfdff2768d980c0a3a520f006904de94f"); byte[] r = Utils.hexToBytes("f38907308c893deaf244787db4af53682249107418afc2edc58f75ac58a07404"); byte[] S = Utils.hexToBytes("5fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b"); assertThat(scalarOps.multiplyAndAdd(h, a, r), is(equalTo(S))); } @Test public void multiplyAndAddReturnsExpectedResult() { for (int i=0; i<1000; i++) { // Arrange: final byte[] bytes1 = MathUtils.getRandomByteArray(32); final byte[] bytes2 = MathUtils.getRandomByteArray(32); final byte[] bytes3 = MathUtils.getRandomByteArray(32); // Act: final byte[] result1 = scalarOps.multiplyAndAdd(bytes1, bytes2, bytes3); final byte[] result2 = MathUtils.multiplyAndAddModGroupOrder(bytes1, bytes2, bytes3); // Assert: Assert.assertThat(MathUtils.toBigInteger(result1).compareTo(MathUtils.getGroupOrder()), IsEqual.equalTo(-1)); Assert.assertThat(MathUtils.toBigInteger(result1).compareTo(new BigInteger("-1")), IsEqual.equalTo(1)); Assert.assertThat(result1, IsEqual.equalTo(result2)); } } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/spec/000077500000000000000000000000001327341674300226255ustar00rootroot00000000000000str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/spec/EdDSANamedCurveTableTest.java000066400000000000000000000025621327341674300301370ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import static net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable.ED_25519; import static net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable.ED_25519_CURVE_SPEC; import static org.hamcrest.Matchers.*; import static org.junit.Assert.*; import org.junit.Test; /** * @author str4d * */ public class EdDSANamedCurveTableTest { /** * Ensure curve names are case-inspecific */ @Test public void curveNamesAreCaseInspecific() { EdDSANamedCurveSpec mixed = EdDSANamedCurveTable.getByName("Ed25519"); EdDSANamedCurveSpec lower = EdDSANamedCurveTable.getByName("ed25519"); EdDSANamedCurveSpec upper = EdDSANamedCurveTable.getByName("ED25519"); assertThat(lower, is(equalTo(mixed))); assertThat(upper, is(equalTo(mixed))); } @Test public void testConstants() { EdDSANamedCurveSpec spec = EdDSANamedCurveTable.getByName(ED_25519); assertThat("Named curve and constant should match", spec, is(equalTo(ED_25519_CURVE_SPEC))); } } str4d-ed25519-java-7c26a63/test/net/i2p/crypto/eddsa/spec/EdDSAPrivateKeySpecTest.java000066400000000000000000000054031327341674300300310ustar00rootroot00000000000000/** * EdDSA-Java by str4d * * To the extent possible under law, the person who associated CC0 with * EdDSA-Java has waived all copyright and related or neighboring rights * to EdDSA-Java. * * You should have received a copy of the CC0 legalcode along with this * work. If not, see . * */ package net.i2p.crypto.eddsa.spec; import static org.hamcrest.Matchers.*; import static org.junit.Assert.*; import net.i2p.crypto.eddsa.Utils; import net.i2p.crypto.eddsa.spec.EdDSANamedCurveTable; import org.junit.Rule; import org.junit.Test; import org.junit.rules.ExpectedException; /** * @author str4d * */ public class EdDSAPrivateKeySpecTest { static final byte[] ZERO_SEED = Utils.hexToBytes("0000000000000000000000000000000000000000000000000000000000000000"); static final byte[] ZERO_H = Utils.hexToBytes("5046adc1dba838867b2bbbfdd0c3423e58b57970b5267a90f57960924a87f1960a6a85eaa642dac835424b5d7c8d637c00408c7a73da672b7f498521420b6dd3"); static final byte[] ZERO_PK = Utils.hexToBytes("3b6a27bcceb6a42d62a3a8d02a6f0d73653215771de243a63ac048a18b59da29"); static final EdDSANamedCurveSpec ed25519 = EdDSANamedCurveTable.getByName(EdDSANamedCurveTable.ED_25519); @Rule public ExpectedException exception = ExpectedException.none(); /** * Test method for {@link net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec#EdDSAPrivateKeySpec(byte[], net.i2p.crypto.eddsa.spec.EdDSAParameterSpec)}. */ @Test public void testEdDSAPrivateKeySpecFromSeed() { EdDSAPrivateKeySpec key = new EdDSAPrivateKeySpec(ZERO_SEED, ed25519); assertThat(key.getSeed(), is(equalTo(ZERO_SEED))); assertThat(key.getH(), is(equalTo(ZERO_H))); assertThat(key.getA().toByteArray(), is(equalTo(ZERO_PK))); } @Test public void incorrectSeedLengthThrows() { exception.expect(IllegalArgumentException.class); exception.expectMessage("seed length is wrong"); EdDSAPrivateKeySpec key = new EdDSAPrivateKeySpec(new byte[2], ed25519); } /** * Test method for {@link net.i2p.crypto.eddsa.spec.EdDSAPrivateKeySpec#EdDSAPrivateKeySpec(net.i2p.crypto.eddsa.spec.EdDSAParameterSpec, byte[])}. */ @Test public void testEdDSAPrivateKeySpecFromH() { EdDSAPrivateKeySpec key = new EdDSAPrivateKeySpec(ed25519, ZERO_H); assertThat(key.getSeed(), is(nullValue())); assertThat(key.getH(), is(equalTo(ZERO_H))); 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