Commit | Line | Data |
---|---|---|
d3409d5e | 1 | # Test vectors for Montgomery reduction |
d3409d5e | 2 | |
444083ae MW |
3 | mul { |
4 | 6277101735386680763835789423207666416083908700390324961279 | |
5 | 2455155546008943817740293915197451784769108058161191238065 | |
6 | 340282366920938463500268095579187314689 | |
7 | 5646741895976341600220572388698743135318229029826089708489; | |
8 | } | |
9 | ||
d3409d5e | 10 | create { |
11 | 340809809850981098423498794792349 # m | |
12 | 266454859 # -m^{-1} mod b | |
13 | 130655606683780235388773757767708 # R mod m | |
14 | 237786678640282040194246459306177; # R^2 mod m | |
0e70bd46 MW |
15 | |
16 | 6277101735386680763835789423207666416083908700390324961279 | |
17 | 340282366920938463444927863358058659841 | |
18 | 18446744073709551617 | |
19 | 340282366920938463500268095579187314689; | |
d3409d5e | 20 | } |
21 | ||
22 | mul { | |
23 | 43289823545 | |
24 | 234324324 | |
25 | 6456542564 | |
26 | 10807149256; | |
83c017f3 | 27 | |
3119b3ae MW |
28 | 4325987397987458979875737589783 |
29 | 1 | |
30 | 4309747041023999857206910900081 | |
31 | 4309747041023999857206910900081; | |
32 | ||
379829cb MW |
33 | 170141183460469231731687303715884105727 |
34 | 2 | |
35 | 2 | |
36 | 4; | |
37 | ||
0e70bd46 MW |
38 | 6277101735386680763835789423207666416083908700390324961279 |
39 | 2455155546008943817740293915197451784769108058161191238065 | |
40 | 340282366920938463500268095579187314689 | |
41 | 5646741895976341600220572388698743135318229029826089708489; | |
42 | ||
83c017f3 | 43 | 51518627314818829164222247085233898246715229794943812733936714788310185005015428803253311691709787911812368198649776769324928993075889524373913555618270874746833913595051625422038974326537979654635530320271853851973343513053953211672797425464186157719021174955241645388345195723368057041032310152242301620397 |
44 | 7041548659011846562361842096561083537784928869240554198760844555642215260669458833049231069318370838770180094409088437631986867239713464317243824963669990014087444248250948204574690463940534304651099653802302150197753463246181762684347288736386534346725039618007392334267637262008343417972878515511486456037 | |
45 | 21451817224897484023627307128311082613304580637202546848860538836010530320943159719981586919811151828606838777812233053319458755053306547823820900602281867134174742586071226220962576712633552196944784360512851517812225731562588375896089193406088239903885470354101095713609394462435076126493339021945199401247 | |
46 | 48192532305912989641372170084506981675917951543147719789775743631071830656350879578731578070582102149232280305157616093002880139716311910835926678896882798493523792373475521651115163420137602661060123597773253524671874189844988793471524978853764238038494563159505836018994860909028653670132922744758133798212; | |
366e9701 MW |
47 | |
48 | 0x1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 | |
49 | 0 1 0; | |
d3409d5e | 50 | } |
51 | ||
52 | exp { | |
53 | 4325987397987458979875737589783 | |
54 | 435365332435654643667 | |
55 | 8745435676786567758678547 | |
56 | 2439674515119108242643169132064; | |
57 | ||
379829cb MW |
58 | 170141183460469231731687303715884105727 |
59 | 2 | |
60 | 170141183460469231731687303715884105727 | |
61 | 2; | |
62 | ||
890e34fd | 63 | # --- Bizarre bug --- |
64 | # | |
65 | # This was caused by omission of the test-and-subtract step in the | |
66 | # Montgomery reduction. | |
67 | ||
68 | 8939489893434234331 1804289383 454353454354565 6139425926295484741; | |
69 | 8939489893434234331 1804289383 8939489893434234330 1; | |
70 | ||
a69a3efd | 71 | # --- Negative and zero exponents --- |
21bebf11 | 72 | |
45c0fd36 | 73 | 0xfffffffdffffffffffffffffffffffff 0xfffffffdfffffffffffffffffffffffe 0 1; |
21bebf11 | 74 | 8939489893434234331 1804289383 -8939035539979879765 6139425926295484741; |
75 | ||
f790765d | 76 | # --- DSA public key derivation --- |
77 | ||
32ccc3c3 | 78 | 0xc9c7feaeaedb16505389c5582df1858d0fdb3eecfe61c230d612661bef8c1bc5 |
79 | 0x5cd41fc97d0db5322bab7d659354db2ed9f88e39d2c6fae9f29acab5a522131e | |
80 | 0x1234 | |
81 | 0x51812af9600c89ffe0f73902eb09015c03b4e0fbf6ccf073931c12f9aad1fb47; | |
f790765d | 82 | |
32ccc3c3 | 83 | 0xdde5808744e1cd37c88667e7033694b2513a7429f035f11c0bafc4dff2b96a672bd0a3ca16aba2ea526df00c8571106ba4a1d83eb62605fc9274ab70bef0a111cd070cca2d8b10edf042d6c44f863c36fabea8bb0d7340eb8c169da27a4b0ba2713c166152a0244235093391c5f71aee8c03dcaf2335a2e4689ccb27ba365ec7 |
84 | 0x65985e4c2d6027a8afdeb9b44cc619e1c4d46bde873e0d4b45325412a2f8365e51245324f888704295fe8233a6666624d9a4701172dbfcab5c9643e1caab79eb2a0c85284d1b858688b8f16804326321f53a723502a6d6ae08dcbffccf2187a799f6281c2478ef0faed5c5c80adeabc5ee435cff8b9ae0b603e47fb08d73b014 | |
85 | 0x23a252f60bae4907a8ed5b6203e2b1da32848cd9 | |
45c0fd36 | 86 | 0x9720498d8ec1208585635faaf952c1204c37119acccc64ed7942867be24770e33db39ffcfa1194549ead8495a7918a20e15144e68125860ef4f8c1a3d771bad690938bdb2c8817e2b89a8fc615d067084a7a2f2f9280e15fb9ccebfe713584260d5ed30545b69745d7b22977bfd44d60d7c5e657aab1c79dc5cb33ff29ee9074; |
f790765d | 87 | |
d3409d5e | 88 | # --- Quick RSA test --- |
89 | ||
90 | 905609324890967090294090970600361 # This is p | |
91 | 3 | |
92 | 905609324890967090294090970600360 # This is (p - 1) | |
93 | 1; # Fermat test: p is prime | |
94 | ||
95 | 734589569806680985408670989082927 # This is q | |
96 | 5 | |
97 | 734589569806680985408670989082926 # And this is (q - 1) | |
98 | 1; # Fermat again: q is prime | |
99 | ||
100 | # --- Encrypt a message --- | |
101 | # | |
102 | # The public and private exponents are from the GCD test. The message | |
103 | # is just obvious. The modulus is the product of the two primes above. | |
104 | ||
105 | 665251164384574309450646977867045404520085938543622535546005136647 | |
106 | 123456789012345678901234567890123456789012345678901234567890 | |
107 | 5945908509680983480596809586040589085680968709809890671 | |
108 | 25906467774034212974484417859588980567136610347807401817990462701; | |
109 | ||
45c0fd36 | 110 | # --- And decrypt it again --- |
d3409d5e | 111 | |
112 | 665251164384574309450646977867045404520085938543622535546005136647 | |
113 | 25906467774034212974484417859588980567136610347807401817990462701 | |
114 | 514778499400157641662814932021958856708417966520837469125919104431 | |
115 | 123456789012345678901234567890123456789012345678901234567890; | |
c5f2543f | 116 | |
117 | # --- Regression --- | |
118 | ||
119 | 3986624077014487421577005607434178981611827907415414229383186257799185035259267946499319317546248903815958429965343062841026732183070884484415037389112766124480881891335541864933360040451772640848433986354946570483859801429553601029855169093153120649968457991955067742589996787220443833463413655161718521778024152687493646856649224308444934694934177848997119462792993163729623894124424825605063456003809024630116233635811919734143467917391222413748618664640084816819791040047135721631646389562380726980090637225607902904093720467390446340147754975063914238763877962986901317873962501987398883284691263121949707967483 | |
120 | 2169501609694605731113683435915932024263931111070470928071742781553833481227229665038394569450673541955381439893533586899516369125587996614390351130855433932967123352056637148142399218614659226596196082977912512097782590337133839376057748669786776861900003976657975002808400242688631641605350346310303557783077961976578644612942618488786721156576047036803063809499458142391930097492829437793780428298460587910313123127299017105180518995858168981798364124607742910479678852164938149352363613709839015911625193499208078080300810729238501127706236236987807659841302058153641198634312186169690290317377895433013774581020 | |
121 | 51190650099377934681679689372059155651634030541122059023228371179527051284414 | |
122 | 2182336244564627050476203952083643687109210844491929333865487949231032236266424033053219865356293652087346833773990958617081657598928894294027838097457060132084513275728637155311686562443969707442331856969523833049082440569661820589637161378175422424940183890787723213162895088451684485064228413121825045190532424942855250521728705814032313019282814300698512615465322506857392325469773301168485302267577566759375501214494771698910873834970265937979350795050000891405548412798945017578510891723221844676960980502437259841806090144299798005080365645221451715661064400809603224286845878809241930399832108000526121054958; | |
d3409d5e | 123 | } |
890e34fd | 124 | |
125 | # --- Simultaneous exponentiation --- | |
126 | ||
127 | mexp-1 { | |
128 | 4325987397987458979875737589783 | |
129 | 435365332435654643667 | |
130 | 8745435676786567758678547 | |
131 | 2439674515119108242643169132064; | |
132 | } | |
133 | ||
134 | mexp-2 { | |
32ccc3c3 | 135 | 0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291 |
136 | 0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802 | |
137 | 0xbf655bd046f0b35ec791b004804afcbb8ef7d69d | |
138 | 0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333 | |
139 | 0x821a926312e97adeabcc8d082b5278978a2df4b0 | |
140 | 0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e; | |
21bebf11 | 141 | |
142 | 0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adac32ab7aac49693dfbf83724c2ec0736ee31c80291 | |
143 | 0x626d027839ea0a13413163a55b4cb500299d5522956cefcb3bff10f399ce2c2e71cb9de5fa24babf58e5b79521925c9cc42e9f6f464b088cc572af53e6d78802 | |
144 | 0xbf655bd046f0b35ec791b004804afcbb8ef7d69d | |
145 | 0x19131871d75b1612a819f29d78d1b0d7346f7aa77bb62a859bfd6c5675da9d212d3a36ef1672ef660b8c7c255cc0ec74858fba33f44c06699630a76b030ee333 | |
146 | -0x8df2a494492276aa3d25759bb06869cbeac0d83afb8d0cf7cbb8324f0d7882e5d0762fc5b7210eafc2e9adabb090e849367fc31d4c6a97bac0b4be56a79a0de0 | |
147 | 0x2fc6cb9ac3be0eac3daf02eefb96fca3846708a28dd05730165fe50942f7f07edfef8e52fcb9369e3814aa24607e80475d0e61ad461d6b16b6cec5baae58946e; | |
890e34fd | 148 | } |