| 1 | # Test vectors for Montgomery reduction |
| 2 | |
| 3 | mul { |
| 4 | 6277101735386680763835789423207666416083908700390324961279 |
| 5 | 2455155546008943817740293915197451784769108058161191238065 |
| 6 | 340282366920938463500268095579187314689 |
| 7 | 5646741895976341600220572388698743135318229029826089708489; |
| 8 | } |
| 9 | |
| 10 | create { |
| 11 | 340809809850981098423498794792349 # m |
| 12 | 266454859 # -m^{-1} mod b |
| 13 | 130655606683780235388773757767708 # R mod m |
| 14 | 237786678640282040194246459306177; # R^2 mod m |
| 15 | |
| 16 | 6277101735386680763835789423207666416083908700390324961279 |
| 17 | 340282366920938463444927863358058659841 |
| 18 | 18446744073709551617 |
| 19 | 340282366920938463500268095579187314689; |
| 20 | } |
| 21 | |
| 22 | mul { |
| 23 | 43289823545 |
| 24 | 234324324 |
| 25 | 6456542564 |
| 26 | 10807149256; |
| 27 | |
| 28 | 4325987397987458979875737589783 |
| 29 | 1 |
| 30 | 4309747041023999857206910900081 |
| 31 | 4309747041023999857206910900081; |
| 32 | |
| 33 | 6277101735386680763835789423207666416083908700390324961279 |
| 34 | 2455155546008943817740293915197451784769108058161191238065 |
| 35 | 340282366920938463500268095579187314689 |
| 36 | 5646741895976341600220572388698743135318229029826089708489; |
| 37 | |
| 38 | 51518627314818829164222247085233898246715229794943812733936714788310185005015428803253311691709787911812368198649776769324928993075889524373913555618270874746833913595051625422038974326537979654635530320271853851973343513053953211672797425464186157719021174955241645388345195723368057041032310152242301620397 |
| 39 | 7041548659011846562361842096561083537784928869240554198760844555642215260669458833049231069318370838770180094409088437631986867239713464317243824963669990014087444248250948204574690463940534304651099653802302150197753463246181762684347288736386534346725039618007392334267637262008343417972878515511486456037 |
| 40 | 21451817224897484023627307128311082613304580637202546848860538836010530320943159719981586919811151828606838777812233053319458755053306547823820900602281867134174742586071226220962576712633552196944784360512851517812225731562588375896089193406088239903885470354101095713609394462435076126493339021945199401247 |
| 41 | 48192532305912989641372170084506981675917951543147719789775743631071830656350879578731578070582102149232280305157616093002880139716311910835926678896882798493523792373475521651115163420137602661060123597773253524671874189844988793471524978853764238038494563159505836018994860909028653670132922744758133798212; |
| 42 | |
| 43 | 0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 |
| 44 | 0 1 0; |
| 45 | } |
| 46 | |
| 47 | exp { |
| 48 | 4325987397987458979875737589783 |
| 49 | 435365332435654643667 |
| 50 | 8745435676786567758678547 |
| 51 | 2439674515119108242643169132064; |
| 52 | |
| 53 | # --- Bizarre bug --- |
| 54 | # |
| 55 | # This was caused by omission of the test-and-subtract step in the |
| 56 | # Montgomery reduction. |
| 57 | |
| 58 | 8939489893434234331 1804289383 454353454354565 6139425926295484741; |
| 59 | 8939489893434234331 1804289383 8939489893434234330 1; |
| 60 | |
| 61 | # --- Negative and zero exponents --- |
| 62 | |
| 63 | 0xfffffffdffffffffffffffffffffffff 0xfffffffdfffffffffffffffffffffffe 0 1; |
| 64 | 8939489893434234331 1804289383 -8939035539979879765 6139425926295484741; |
| 65 | |
| 66 | # --- DSA public key derivation --- |
| 67 | |
| 68 | 0xc9c7feaeaedb16505389c5582df1858d0fdb3eecfe61c230d612661bef8c1bc5 |
| 69 | 0x5cd41fc97d0db5322bab7d659354db2ed9f88e39d2c6fae9f29acab5a522131e |
| 70 | 0x1234 |
| 71 | 0x51812af9600c89ffe0f73902eb09015c03b4e0fbf6ccf073931c12f9aad1fb47; |
| 72 | |
| 73 | 0xdde5808744e1cd37c88667e7033694b2513a7429f035f11c0bafc4dff2b96a672bd0a3ca16aba2ea526df00c8571106ba4a1d83eb62605fc9274ab70bef0a111cd070cca2d8b10edf042d6c44f863c36fabea8bb0d7340eb8c169da27a4b0ba2713c166152a0244235093391c5f71aee8c03dcaf2335a2e4689ccb27ba365ec7 |
| 74 | 0x65985e4c2d6027a8afdeb9b44cc619e1c4d46bde873e0d4b45325412a2f8365e51245324f888704295fe8233a6666624d9a4701172dbfcab5c9643e1caab79eb2a0c85284d1b858688b8f16804326321f53a723502a6d6ae08dcbffccf2187a799f6281c2478ef0faed5c5c80adeabc5ee435cff8b9ae0b603e47fb08d73b014 |
| 75 | 0x23a252f60bae4907a8ed5b6203e2b1da32848cd9 |
| 76 | 0x9720498d8ec1208585635faaf952c1204c37119acccc64ed7942867be24770e33db39ffcfa1194549ead8495a7918a20e15144e68125860ef4f8c1a3d771bad690938bdb2c8817e2b89a8fc615d067084a7a2f2f9280e15fb9ccebfe713584260d5ed30545b69745d7b22977bfd44d60d7c5e657aab1c79dc5cb33ff29ee9074; |
| 77 | |
| 78 | # --- Quick RSA test --- |
| 79 | |
| 80 | 905609324890967090294090970600361 # This is p |
| 81 | 3 |
| 82 | 905609324890967090294090970600360 # This is (p - 1) |
| 83 | 1; # Fermat test: p is prime |
| 84 | |
| 85 | 734589569806680985408670989082927 # This is q |
| 86 | 5 |
| 87 | 734589569806680985408670989082926 # And this is (q - 1) |
| 88 | 1; # Fermat again: q is prime |
| 89 | |
| 90 | # --- Encrypt a message --- |
| 91 | # |
| 92 | # The public and private exponents are from the GCD test. The message |
| 93 | # is just obvious. The modulus is the product of the two primes above. |
| 94 | |
| 95 | 665251164384574309450646977867045404520085938543622535546005136647 |
| 96 | 123456789012345678901234567890123456789012345678901234567890 |
| 97 | 5945908509680983480596809586040589085680968709809890671 |
| 98 | 25906467774034212974484417859588980567136610347807401817990462701; |
| 99 | |
| 100 | # --- And decrypt it again --- |
| 101 | |
| 102 | 665251164384574309450646977867045404520085938543622535546005136647 |
| 103 | 25906467774034212974484417859588980567136610347807401817990462701 |
| 104 | 514778499400157641662814932021958856708417966520837469125919104431 |
| 105 | 123456789012345678901234567890123456789012345678901234567890; |
| 106 | |
| 107 | # --- Regression --- |
| 108 | |
| 109 | 3986624077014487421577005607434178981611827907415414229383186257799185035259267946499319317546248903815958429965343062841026732183070884484415037389112766124480881891335541864933360040451772640848433986354946570483859801429553601029855169093153120649968457991955067742589996787220443833463413655161718521778024152687493646856649224308444934694934177848997119462792993163729623894124424825605063456003809024630116233635811919734143467917391222413748618664640084816819791040047135721631646389562380726980090637225607902904093720467390446340147754975063914238763877962986901317873962501987398883284691263121949707967483 |
| 110 | 2169501609694605731113683435915932024263931111070470928071742781553833481227229665038394569450673541955381439893533586899516369125587996614390351130855433932967123352056637148142399218614659226596196082977912512097782590337133839376057748669786776861900003976657975002808400242688631641605350346310303557783077961976578644612942618488786721156576047036803063809499458142391930097492829437793780428298460587910313123127299017105180518995858168981798364124607742910479678852164938149352363613709839015911625193499208078080300810729238501127706236236987807659841302058153641198634312186169690290317377895433013774581020 |
| 111 | 51190650099377934681679689372059155651634030541122059023228371179527051284414 |
| 112 | 2182336244564627050476203952083643687109210844491929333865487949231032236266424033053219865356293652087346833773990958617081657598928894294027838097457060132084513275728637155311686562443969707442331856969523833049082440569661820589637161378175422424940183890787723213162895088451684485064228413121825045190532424942855250521728705814032313019282814300698512615465322506857392325469773301168485302267577566759375501214494771698910873834970265937979350795050000891405548412798945017578510891723221844676960980502437259841806090144299798005080365645221451715661064400809603224286845878809241930399832108000526121054958; |
| 113 | } |
| 114 | |
| 115 | # --- Simultaneous exponentiation --- |
| 116 | |
| 117 | mexp-1 { |
| 118 | 4325987397987458979875737589783 |
| 119 | 435365332435654643667 |
| 120 | 8745435676786567758678547 |
| 121 | 2439674515119108242643169132064; |
| 122 | } |
| 123 | |
| 124 | mexp-2 { |
| 125 | 0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291 |
| 126 | 0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802 |
| 127 | 0xbf655bd046f0b35ec791b004804afcbb8ef7d69d |
| 128 | 0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333 |
| 129 | 0x821a926312e97adeabcc8d082b5278978a2df4b0 |
| 130 | 0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e; |
| 131 | |
| 132 | 0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291 |
| 133 | 0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802 |
| 134 | 0xbf655bd046f0b35ec791b004804afcbb8ef7d69d |
| 135 | 0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333 |
| 136 | -0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adabb090e849367fc31d4c6a97bac0b4be56a79a0de0 |
| 137 | 0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e; |
| 138 | } |