git.distorted.org.uk Git - u/mdw/catacomb/blob - tests/mpmont

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