Add unit tests for bignum_new.c:mbedtls_mpi_core_montmul()
These tests are also used to test the existing mpi_montmul() function (which
too is renamed with mbedtls_ prefix). Some of these are replays of captured
invocations during unit test runs. Others are generated. They use a mixture
of primes and odd numbers for N, with four randomly-generated cases for each N.
The lines in the .data file were generated by the following script
```
#!/usr/bin/env perl
#
# mpi-test-core-montmul.pl - generate MPI tests in Perl for mbedtls_mpi_core_montmul()
#
use strict;
use warnings;
use Math::BigInt;
use sort 'stable';
generate_tests();
sub generate_tests {
generate_mbedtls_mpi_core_montmul();
}
# XXX mbedtls_mpi_grow() and mbedtls_mpi_shrink() work in little-endian manner
# \brief Montgomery multiplication: X = A * B * R^-1 mod N (HAC 14.36)
#
# \param[out] X The destination MPI, as a big endian array of length \p n.
# On successful completion, X contains the result of
# the multiplication A * B * R^-1 mod N where
# R = (2^ciL)^n.
# \param[in] A Big endian presentation of first operand.
# Must have exactly \p n limbs.
# \param[in] B Big endian presentation of second operand.
# \param[in] B_len The number of limbs in \p B.
# \param[in] N Big endian presentation of the modulus.
# This must be odd and have exactly \p n limbs.
# \param[in] n The number of limbs in \p X, \p A, \p N.
# \param mm The Montgomery constant for \p N: -N^-1 mod 2^ciL.
# This can be calculated by `mbedtls_mpi_montg_init()`.
# \param[in,out] T Temporary storage of size at least 2*n+1 limbs.
# Its initial content is unused and
# its final content is indeterminate.
#
# void mbedtls_mpi_core_montmul( mbedtls_mpi_uint *X,
# const mbedtls_mpi_uint *A,
# const mbedtls_mpi_uint *B, size_t B_len,
# const mbedtls_mpi_uint *N, size_t n,
# mbedtls_mpi_uint mm, mbedtls_mpi_uint *T );
sub generate_mbedtls_mpi_core_montmul {
my $sub_name = (caller(0))[3]; # e.g. main::generate_mbedtls_mpi_sub_mpi
my ($ignore, $test_name) = split("main::generate_", $sub_name);
my @cases = ();
my @replay = (
# [ limbsAN_4, limbsB_4, limbsAN_8, limbsB_8, hexA, hexB, hexN, hexExpected ]
[ 2, 1, 1, 1, "19", "1", "1D", "18" ],
[ 2, 1, 1, 1, "7", "1", "9", "1" ],
[ 2, 1, 1, 1, "4", "1", "9", "7" ],
#montmul:
#A.n = 3
#A.p = FFFE000000008004
# 0000000000007FFC
# 0000000000000000
#B.n = 1
#B.p = 0000000000000001
#N.n = 3
#N.p = 0000000000000001
# 0000000000008000
# 0000000000000000
#mm = FFFFFFFFFFFFFFFF
#res.n = 3
#res.p = EFFF9FFF3FFF8001
# 0000000000007FFF
# 0000000000000000
#[ "MBEDTLS_HAVE_INT32", 3, 1, 3, "7FFCFFFE000000008004", "1", "80000000000000000001", "2000C001800100000000" ],
#[ "MBEDTLS_HAVE_INT64", 3, 1, 3, "7FFCFFFE000000008004", "1", "80000000000000000001", "7FFFEFFF9FFF3FFF8001" ],
[ 12, 1, 6, 1, "3C246D0E059A93A266288A7718419EC741661B474C58C032C5EDAF92709402B07CC8C7CE0B781C641A1EA8DB2F4343", "1", "66A198186C18C10B2F5ED9B522752A9830B69916E535C8F047518A889A43A594B6BED27A168D31D4A52F88925AA8F5", "36E139AEA55215609D2816998ED020BBBD96C37890F65171D948E9BC7CBAA4D9325D24D6A3C12710F10A09FA08AB87" ],
#A.n = 5
#A.p = 340E918CE03C6211
# 9888165CB75BFA1F
# FCCE74B999E470CA
# 1E442976B0E63D64
# 0000000000000000
#B.n = 1
#B.p = 0000000000000001
#N.n = 4
#N.p = 8054B3D124D0E561
# 92A338655DCE4CA8
# E28581ECD892E0F5
# B3A119602EE213CD
#mm = E41CFB909805815F
#res.n = 5
#res.p = 0E65383B59F8CA5B
# B103B17A2EEF84E6
# F23BC08FD0801C55
# 38EB7749F4A5DA80
# 0000000000000000
[ 8, 1, 4, 1, "1E442976B0E63D64FCCE74B999E470CA9888165CB75BFA1F340E918CE03C6211", "1", "B3A119602EE213CDE28581ECD892E0F592A338655DCE4CA88054B3D124D0E561", "38EB7749F4A5DA80F23BC08FD0801C55B103B17A2EEF84E60E65383B59F8CA5B" ],
#A.n = 12
#A.p = 542306BCA7A2366E
# D2780B2B4968F8D8
# CBDFC696104353E4
# 7776839B0AC9DB23
# B7E125BE407E7415
# D711917FD7537E13
# 82392870D6D08F87
# D83ED5FA38560FFB
# 9994B0FED1D2A8D3
# 63C65413F57249F5
# 007CF5AC97304E0B
# 0000000000000000
#B.n = 1
#B.p = 0000000000000001
#N.n = 11
#N.p = E1AD22CEB7BA0123
# 32B2A6AA42ADA923
# C56C62082912B661
# C6F0EAD752500A32
# DBC8D651793E93C9
# 0B2F60D99CC1950C
# 5B4CDCB5734C58F9
# 09D3CB5BC5585472
# 9A2C2BE12ED487A8
# BE09A8111926AAA3
# 0284139EA19C139E
#mm = C02E2164B293C975
#res.n = 12
#res.p = F6B14471839D8D31
# FF843ED3B17C44D7
# 1C3D52C7CB9E0BA6
# 82F3590C866BF9F8
# 49C371DB2A4FB164
# 964ECA2527A031ED
# FAACEC6982E0E5BE
# 1F70C4CB2426AEE1
# 2C92B02886267AB4
# 0630B14113BEAD74
# 01E4426A3D6C425F
# 0000000000000000
[ 22, 1, 11, 1, "7CF5AC97304E0B63C65413F57249F59994B0FED1D2A8D3D83ED5FA38560FFB82392870D6D08F87D711917FD7537E13B7E125BE407E74157776839B0AC9DB23CBDFC696104353E4D2780B2B4968F8D8542306BCA7A2366E", "1", "284139EA19C139EBE09A8111926AAA39A2C2BE12ED487A809D3CB5BC55854725B4CDCB5734C58F90B2F60D99CC1950CDBC8D651793E93C9C6F0EAD752500A32C56C62082912B66132B2A6AA42ADA923E1AD22CEB7BA0123", "1E4426A3D6C425F0630B14113BEAD742C92B02886267AB41F70C4CB2426AEE1FAACEC6982E0E5BE964ECA2527A031ED49C371DB2A4FB16482F3590C866BF9F81C3D52C7CB9E0BA6FF843ED3B17C44D7F6B14471839D8D31" ],
);
for my $c (@replay) {
# For all of these, la4 = 2 * la8, so $xh4 == $xh8 (so we just have $xh)
my ($la4, $lb4, $la8, $lb8, $ah, $bh, $nh, $xh) = @$c; # limbs(A), limbs(B), limbs(N), (A, B, N, expected) hex
my $a = Math::BigInt->from_hex($ah);
my $b = Math::BigInt->from_hex($bh);
my $n = Math::BigInt->from_hex($nh);
my $desc = "$test_name #NUMBER (replay)";
# mbedtls_mpi_core_montmul:mpiSize:limbs(A,N):limbs(B):<A>:<B>:<N>:<expected4>:<expected8>
# (just repeat $xh, as la4 = 2 * la8, so $xh4 == $xh8)
my $case = output($test_name, $la4, $lb4, $la8, $lb8, str($ah), str($bh), str($nh), str($xh), str($xh));
push(@cases, [$case, $desc]);
}
# see mpi-modmul-gen.pl for the source of these test cases
my @generate = (
# [ hexN, hexA, hexB, info ]
[ "3", "2", "2", "" ],
[ "3", "1", "2", "" ],
[ "3", "2", "1", "" ],
[ "7", "6", "5", "" ],
[ "7", "3", "4", "" ],
[ "7", "1", "6", "" ],
[ "7", "5", "6", "" ],
[ "B", "3", "4", "" ],
[ "B", "7", "4", "" ],
[ "B", "9", "7", "" ],
[ "B", "2", "a", "" ],
[ "29", "25", "16", "(0x29 is prime)" ],
[ "29", "8", "28", "" ],
[ "29", "18", "21", "" ],
[ "29", "15", "f", "" ],
[ "FF", "e2", "ea", "" ],
[ "FF", "43", "72", "" ],
[ "FF", "d8", "70", "" ],
[ "FF", "3c", "7c", "" ],
[ "101", "99", "b9", "(0x101 is prime)" ],
[ "101", "65", "b2", "" ],
[ "101", "81", "32", "" ],
[ "101", "51", "dd", "" ],
[ "38B", "d5", "143", "(0x38B is prime)" ],
[ "38B", "3d", "387", "" ],
[ "38B", "160", "2e5", "" ],
[ "38B", "10f", "137", "" ],
[ "8003", "7dac", "25a", "(0x8003 is prime)" ],
[ "8003", "6f1c", "3286", "" ],
[ "8003", "59ed", "2f3f", "" ],
[ "8003", "6893", "736d", "" ],
[ "10001", "d199", "2832", "(0x10001 is prime)" ],
[ "10001", "c3b2", "3e5b", "" ],
[ "10001", "abe4", "214e", "" ],
[ "10001", "4360", "a05d", "" ],
[ "7F7F7", "3f5a1", "165b2", "" ],
[ "7F7F7", "3bd29", "37863", "" ],
[ "7F7F7", "60c47", "64819", "" ],
[ "7F7F7", "16584", "12c49", "" ],
[ "800009", "1ff03f", "610347", "(0x800009 is prime)" ],
[ "800009", "340fd5", "19812e", "" ],
[ "800009", "3fe2e8", "4d0dc7", "" ],
[ "800009", "40356", "e6392", "" ],
[ "100002B", "dd8a1d", "266c0e", "(0x100002B is prime)" ],
[ "100002B", "3fa1cb", "847fd6", "" ],
[ "100002B", "5f439d", "5c3196", "" ],
[ "100002B", "18d645", "f72dc6", "" ],
[ "37EEE9D", "20051ad", "37def6e", "(0x37EEE9D is prime)" ],
[ "37EEE9D", "2ec140b", "3580dbf", "" ],
[ "37EEE9D", "1d91b46", "190d4fc", "" ],
[ "37EEE9D", "34e488d", "1224d24", "" ],
[ "8000000B", "2a4fe2cb", "263466a9", "(0x8000000B is prime)" ],
[ "8000000B", "5643fe94", "29a1aefa", "" ],
[ "8000000B", "29633513", "7b007ac4", "" ],
[ "8000000B", "2439cef5", "5c9d5a47", "" ],
[ "8CD626B9", "4de3cfaa", "50dea178", "(0x8CD626B9 is prime)" ],
[ "8CD626B9", "b8b8563", "10dbbbac", "" ],
[ "8CD626B9", "4e8a6151", "5574ec19", "" ],
[ "8CD626B9", "69224878", "309cfc23", "" ],
[ "10000000F", "fb6f7fb6", "afb05423", "(0x10000000F is prime)" ],
[ "10000000F", "8391a243", "26034dcd", "" ],
[ "10000000F", "d26b98c", "14b2d6aa", "" ],
[ "10000000F", "6b9f1371", "a21daf1d", "" ],
[ "174876E7E9", "9f49435ad", "c8264ade8", "0x174876E7E9 is prime (dec) 99999999977" ],
[ "174876E7E9", "c402da434", "1fb427acf", "" ],
[ "174876E7E9", "f6ebc2bb1", "1096d39f2a", "" ],
[ "174876E7E9", "153b7f7b6b", "878fda8ff", "" ],
[ "8000000017", "2c1adbb8d6", "4384d2d3c6", "(0x8000000017 is prime)" ],
[ "8000000017", "2e4f9cf5fb", "794f3443d9", "" ],
[ "8000000017", "149e495582", "3802b8f7b7", "" ],
[ "8000000017", "7b9d49df82", "69c68a442a", "" ],
[ "864CB9076D", "683a134600", "6dd80ea9f6", "(0x864CB9076D is prime)" ],
[ "864CB9076D", "13a870ff0d", "59b099694a", "" ],
[ "864CB9076D", "37d06b0e63", "4d2147e46f", "" ],
[ "864CB9076D", "661714f8f4", "22e55df507", "" ],
[ "F7F7F7F7F7", "2f0a96363", "52693307b4", "" ],
[ "F7F7F7F7F7", "3c85078e64", "f2275ecb6d", "" ],
[ "F7F7F7F7F7", "352dae68d1", "707775b4c6", "" ],
[ "F7F7F7F7F7", "37ae0f3e0b", "912113040f", "" ],
[ "1000000000F", "6dada15e31", "f58ed9eff7", "(0x1000000000F is prime)" ],
[ "1000000000F", "69627a7c89", "cfb5ebd13d", "" ],
[ "1000000000F", "a5e1ad239b", "afc030c731", "" ],
[ "1000000000F", "f1cc45f4c5", "c64ad607c8", "" ],
[ "800000000005", "2ebad87d2e31", "4c72d90bca78", "(0x800000000005 is prime)" ],
[ "800000000005", "a30b3cc50d", "29ac4fe59490", "" ],
[ "800000000005", "33674e9647b4", "5ec7ee7e72d3", "" ],
[ "800000000005", "3d956f474f61", "74070040257d", "" ],
[ "800795D9BA47", "48348e3717d6", "43fcb4399571", "(0x800795D9BA47 is prime)" ],
[ "800795D9BA47", "5234c03cc99b", "2f3cccb87803", "" ],
[ "800795D9BA47", "3ed13db194ab", "44b8f4ba7030", "" ],
[ "800795D9BA47", "1c11e843bfdb", "95bd1b47b08", "" ],
[ "1000000000015", "a81d11cb81fd", "1e5753a3f33d", "(0x1000000000015 is prime)" ],
[ "1000000000015", "688c4db99232", "36fc0cf7ed", "" ],
[ "1000000000015", "f0720cc07e07", "fc76140ed903", "" ],
[ "1000000000015", "2ec61f8d17d1", "d270c85e36d2", "" ],
[ "100000000000051", "6a24cd3ab63820", "ed4aad55e5e348", "(0x100000000000051 is prime)" ],
[ "100000000000051", "e680c160d3b248", "31e0d8840ed510", "" ],
[ "100000000000051", "a80637e9aebc38", "bb81decc4e1738", "" ],
[ "100000000000051", "9afa5a59e9d630", "be9e65a6d42938", "" ],
[ "ABCDEF0123456789", "ab5e104eeb71c000", "2cffbd639e9fea00", "" ],
[ "ABCDEF0123456789", "197b867547f68a00", "44b796cf94654800", "" ],
[ "ABCDEF0123456789", "329f9483a04f2c00", "9892f76961d0f000", "" ],
[ "ABCDEF0123456789", "4a2e12dfb4545000", "1aa3e89a69794500", "" ],
[ "25A55A46E5DA99C71C7", "8b9acdf013d140f000", "12e4ceaefabdf2b2f00", "0x25A55A46E5DA99C71C7 is the 3rd repunit prime (dec) 11111111111111111111111" ],
[ "25A55A46E5DA99C71C7", "1b8d960ea277e3f5500", "14418aa980e37dd000", "" ],
[ "25A55A46E5DA99C71C7", "7314524977e8075980", "8172fa45618ccd0d80", "" ],
[ "25A55A46E5DA99C71C7", "ca14f031769be63580", "147a2f3cf2964ca9400", "" ],
[ "314DC643FB763F2B8C0E2DE00879", "18532ba119d5cd0cf39735c0000", "25f9838e31634844924733000000", "0x314DC643FB763F2B8C0E2DE00879 is (dec)99999999977^3" ],
[ "314DC643FB763F2B8C0E2DE00879", "a56e2d2517519e3970e70c40000", "ec27428d4bb380458588fa80000", "" ],
[ "314DC643FB763F2B8C0E2DE00879", "1cb5e8257710e8653fff33a00000", "15fdd42fe440fd3a1d121380000", "" ],
[ "314DC643FB763F2B8C0E2DE00879", "e50d07a65fc6f93e538ce040000", "1f4b059ca609f3ce597f61240000", "" ],
[ "47BF19662275FA2F6845C74942ED1D852E521", "1ea3ade786a095d978d387f30df9f20000000", "127c448575f04af5a367a7be06c7da0000000", "0x47BF19662275FA2F6845C74942ED1D852E521 is (dec) 99999999977^4" ],
[ "47BF19662275FA2F6845C74942ED1D852E521", "16e15b0ca82764e72e38357b1f10a20000000", "43e2355d8514bbe22b0838fdc3983a0000000", "" ],
[ "47BF19662275FA2F6845C74942ED1D852E521", "be39332529d93f25c3d116c004c620000000", "5cccec42370a0a2c89c6772da801a0000000", "" ],
[ "47BF19662275FA2F6845C74942ED1D852E521", "ecaa468d90de0eeda474d39b3e1fc0000000", "1e714554018de6dc0fe576bfd3b5660000000", "" ],
[ "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "32298816711c5dce46f9ba06e775c4bedfc770e6700000000000000", "8ee751fd5fb24f0b4a653cb3a0c8b7d9e724574d168000000000000", "0x97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931 is (dec) 99999999977^6" ],
[ "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "29213b9df3cfd15f4b428645b67b677c29d1378d810000000000000", "6cbb732c65e10a28872394dfdd1936d5171c3c3aac0000000000000", "" ],
[ "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "6f18db06ad4abc52c0c50643dd13098abccd4a232f0000000000000", "7e6bf41f2a86098ad51f98dfc10490ba3e8081bc830000000000000", "" ],
[ "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "62d3286cd706ad9d73caff63f1722775d7e8c731208000000000000", "530f7ba02ae2b04c2fe3e3d27ec095925631a6c2528000000000000", "" ],
[ "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "a6c6503e3c031fdbf6009a89ed60582b7233c5a85de28b16000000000000000", "75c8ed18270b583f16d442a467d32bf95c5e491e9b8523798000000000000000", "0xDD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499 is (dec) 99999999977^7" ],
[ "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "bf84d1f85cf6b51e04d2c8f4ffd03532d852053cf99b387d4000000000000000", "397ba5a743c349f4f28bc583ecd5f06e0a25f9c6d98f09134000000000000000", "" ],
[ "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "6db11c3a4152ed1a2aa6fa34b0903ec82ea1b88908dcb482000000000000000", "ac8ac576a74ad6ca48f201bf89f77350ce86e821358d85920000000000000000", "" ],
[ "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "3001d96d7fe8b733f33687646fc3017e3ac417eb32e0ec708000000000000000", "925ddbdac4174e8321a48a32f79640e8cf7ec6f46ea235a80000000000000000", "" ],
[ "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", "1029048755f2e60dd98c8de6d9989226b6bb4f0db8e46bd1939de560000000000000000000", "51bb7270b2e25cec0301a03e8275213bb6c2f6e6ec93d4d46d36ca0000000000000000000", "0x141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41 is 99999999977^8" ],
[ "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", "1c5337ff982b3ad6611257dbff5bbd7a9920ba2d4f5838a0cc681ce000000000000000000", "520c5d049ca4702031ba728591b665c4d4ccd3b2b86864d4c160fd2000000000000000000", "" ],
[ "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", "57074dfa00e42f6555bae624b7f0209f218adf57f73ed34ab0ff90c000000000000000000", "41eb14b6c07bfd3d1fe4f4a610c17cc44fcfcda695db040e011065000000000000000000", "" ],
[ "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", "d8ed7feed2fe855e6997ad6397f776158573d425031bf085a615784000000000000000000", "6f121dcd18c578ab5e229881006007bb6d319b179f11015fe958b9c000000000000000000", "" ],
[ "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451", "2a462b156180ea5fe550d3758c764e06fae54e626b5f503265a09df76edbdfbfa1e6000000000000000000000000", "1136f41d1879fd4fb9e49e0943a46b6704d77c068ee237c3121f9071cfd3e6a00315800000000000000000000000", "0x2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451 is (dec) 99999999977^10" ],
[ "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451", "c1ac3800dfb3c6954dea391d206200cf3c47f795bf4a5603b4cb88ae7e574de4740800000000000000000000000", "c0d16eda0549ede42fa0deb4635f7b7ce061fadea02ee4d85cba4c4f7096034193c800000000000000000000000", "" ],
[ "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451", "19e45bb7633094d272588ad2e43bcb3ee341991c6731b6fa9d47c4018d7ce7bba5ee800000000000000000000000", "1e4f83166ae59f6b9cc8fd3e7677ed8bfc01bb99c98bd3eb084246b64c1e18c3365b800000000000000000000000", "" ],
[ "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451", "1aa93395fad5f9b7f20b8f9028a054c0bb7c11bb8520e6a95e5a34f06cb70bcdd01a800000000000000000000000", "54b45afa5d4310192f8d224634242dd7dcfb342318df3d9bd37b4c614788ba13b8b000000000000000000000000", "" ],
[ "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051", "544f2628a28cfb5ce0a1b7180ee66b49716f1d9476c466c57f0c4b2308991784306d48f78686115ee19e25400000000000000000000000000000000", "677eb31ef8d66c120fa872a60cd47f6e10cbfdf94f90501bd7883cba03d185be0a0148d1625745e9c4c827300000000000000000000000000000000", "0x8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051 is prime, (dec) 10^143 + 3^4" ],
[ "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051", "76bb3470985174915e9993522aec989666908f9e8cf5cb9f037bf4aee33d8865cb6464174795d07e30015b80000000000000000000000000000000", "6aaaf60d5784dcef612d133613b179a317532ecca0eed40b8ad0c01e6d4a6d8c79a52af190abd51739009a900000000000000000000000000000000", "" ],
[ "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051", "6cfdd6e60912e441d2d1fc88f421b533f0103a5322ccd3f4db84861643ad63fd63d1d8cfbc1d498162786ba00000000000000000000000000000000", "1177246ec5e93814816465e7f8f248b350d954439d35b2b5d75d917218e7fd5fb4c2f6d0667f9467fdcf33400000000000000000000000000000000", "" ],
[ "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051", "7a09a0b0f8bbf8057116fb0277a9bdf3a91b5eaa8830d448081510d8973888be5a9f0ad04facb69aa3715f00000000000000000000000000000000", "764dec6c05a1c0d87b649efa5fd94c91ea28bffb4725d4ab4b33f1a3e8e3b314d799020e244a835a145ec9800000000000000000000000000000000", "" ],
);
my %described = ();
for my $g (@generate) {
my ($nh, $ah, $bh, $info) = @$g;
my $a = Math::BigInt->from_hex($ah);
my $b = Math::BigInt->from_hex($bh);
my $n = Math::BigInt->from_hex($nh);
my $ln4 = mpi4s($n);
my $la4 = mpi4s($a);
my $lb4 = mpi4s($b);
my $ln8 = mpi8s($n);
my $la8 = mpi8s($a);
my $lb8 = mpi8s($b);
my $r4 = bound_mpi4($n->copy());
my $i4 = $r4->copy()->bmodinv($n);
my $x4 = $a * $b * $i4;
$x4->bmod($n);
my $xh4 = Math::BigInt->new($x4)->to_hex();
my $r8 = bound_mpi8($n->copy());
my $i8 = $r8->copy()->bmodinv($n);
my $x8 = $a * $b * $i8;
$x8->bmod($n);
my $xh8 = Math::BigInt->new($x8)->to_hex();
die("") if $la4 > $ln4 || $la8 > $ln8;
my $desc = "$test_name #NUMBER (gen)";
if ($ln4 > 1) {
if (!$described{"2-MPI4"}) {
$desc .= " (start of 2-MPI 4-byte bignums)";
$described{"2-MPI4"} = 1;
}
}
if ($ln8 > 1) {
if (!$described{"2-MPI8"}) {
$desc .= " (start of 2-MPI 8-byte bignums)";
$described{"2-MPI8"} = 1;
}
}
if (length($info) && !$described{$info}) {
$desc .= " " . $info;
$described{$info} = 1;
}
my $case = output($test_name, $ln4, $lb4, $ln8, $lb8, str($ah), str($bh), str($nh), str($xh4), str($xh8));
#push(@cases, [$case, $desc, "MBEDTLS_HAVE_INT64"]); -- now doing it differently
push(@cases, [$case, $desc]);
}
output_cases("", @cases);
}
sub output_cases {
my ($explain, @cases) = @_;
my $count = 1;
for my $c (@cases) {
my ($case, $desc, $dep) = @$c;
$desc =~ s/NUMBER/$count/; $count++;
if (defined($explain) && $desc =~ /EXPLAIN/) {
$desc =~ s/EXPLAIN/$explain/;
$explain = "";
}
my $depends = "";
$depends = "depends_on:$dep\n" if defined($dep) && length($dep);
print <<EOF;
$desc
$depends$case
EOF
}
}
# The first number (a power of 2) that won't fit in the number of MPIs
# needed for the given number
sub bound_mpi4 {
my $one = Math::BigInt->new(1); # blsft modifies caller
return $one->blsft(bits_mpi4($_[0]));
}
sub bound_mpi8 {
my $one = Math::BigInt->new(1); # blsft modifies caller
return $one->blsft(bits_mpi8($_[0]));
}
# How many bits (a multiple of 32) needed to store the specified number
# when using 4-byte MPIs
sub bits_mpi4 {
return 32 * mpi4s($_[0]);
}
# How many bits (a multiple of 64) needed to store the specified number
# when using 8-byte MPIs
sub bits_mpi8 {
return 64 * mpi8s($_[0]);
}
# How many 4-byte MPIs needed to store the specified number
sub mpi4s {
my ($n) = @_;
my $h = $n->to_hex();
return int((length($h) + 7) / 8);
}
# How many 8-byte MPIs needed to store the specified number
sub mpi8s {
my ($n) = @_;
my $h = $n->to_hex();
return int((length($h) + 15) / 16);
}
sub output {
#run_test(@_);
return join(":", @_);
}
sub str {
return '"' . $_[0] . '"';
}
```
The data for the generated test cases (@generate) for mpi-test-core-montmul.pl
was created by
```
#!/usr/bin/env perl
#
# mpi-modmul-gen.pl - randomly generate test cases for mpi-test-core-montmul.pl
#
use strict;
use warnings;
use Math::BigInt;
use sort 'stable';
my %seen = ();
my @primes = (
"3",
"7",
"B",
"29",
"101",
"38B",
"8003",
"10001",
"800009",
"100002B",
"37EEE9D",
"8000000B",
"8CD626B9",
# From here they require > 1 4-byte MPI
"10000000F",
"174876E7E9",
"8000000017",
"864CB9076D",
"1000000000F",
"800000000005",
"800795D9BA47",
"1000000000015",
"100000000000051",
# From here they require > 1 8-byte MPI
"25A55A46E5DA99C71C7", # this is 11111111111111111111111 decimal
# 10^143 + 3^4: (which is prime)
# 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000081
"8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051",
);
my %prime = map { $_ => 1 } @primes;
my @moduli = (
[ "3", "" ],
[ "7", "" ],
[ "B", "" ],
[ "29", "" ],
[ "FF", "" ],
[ "101", "" ],
[ "38B", "" ],
[ "8003", "" ],
[ "10001", "" ],
[ "7F7F7", "" ],
[ "800009", "" ],
[ "100002B", "" ],
[ "37EEE9D", "" ],
[ "8000000B", "" ],
[ "8CD626B9", "" ],
[ "10000000F", "" ],
[ "174876E7E9", "0x174876E7E9 is prime (dec) 99999999977" ],
[ "8000000017", "" ],
[ "864CB9076D", "" ],
[ "F7F7F7F7F7", "" ],
[ "1000000000F", "" ],
[ "800000000005", "" ],
[ "800795D9BA47", "" ],
[ "1000000000015", "" ],
[ "100000000000051", "" ],
[ "ABCDEF0123456789", "" ],
[ "25A55A46E5DA99C71C7", "0x25A55A46E5DA99C71C7 is the 3rd repunit prime (dec) 11111111111111111111111" ],
[ "314DC643FB763F2B8C0E2DE00879", "0x314DC643FB763F2B8C0E2DE00879 is (dec)99999999977^3" ],
[ "47BF19662275FA2F6845C74942ED1D852E521", "0x47BF19662275FA2F6845C74942ED1D852E521 is (dec) 99999999977^4" ],
[ "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", "0x97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931 is (dec) 99999999977^6" ],
[ "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", "0xDD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499 is (dec) 99999999977^7" ],
[ "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41", "0x141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41 is 99999999977^8" ],
[ "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451", "0x2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451 is (dec) 99999999977^10" ],
[ "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051", "0x8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11DABD6E6144BEF37C6800000000000000000000000000000000051 is prime, (dec) 10^143 + 3^4" ], # 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000081
);
#99999999977^2:
#ibase=16 ; obase=10 ; 174876E7E9*174876E7E9
#99999999977^3:
#ibase=16 ; obase=10 ; 174876E7E9*174876E7E9*174876E7E9
#99999999977^2: 21E19E0C58BACE25211
#99999999977^3: 314DC643FB763F2B8C0E2DE00879
#99999999977^4: 47BF19662275FA2F6845C74942ED1D852E521
#99999999977^5: 6867A5A664437D20ED7941408583AADA2193CE95695209
#99999999977^6: 97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931
#99999999977^7: DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499
#99999999977^8: 141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41
#99999999977^9: 1D42AEA1837AA78C6339224E9B39A483E4AAAF12CE7752E1EA1681082CBC8AB056A36B6299557D7A029
#99999999977^10: 2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC902713E40F51E3B3C214EDFABC451
my %mentioned = ();
for my $mod (@moduli) {
my ($nh, $info) = @$mod;
my $n = Math::BigInt->from_hex($nh);
my $xxx = $n->to_hex();
die("$xxx != $nh") unless lc($xxx) eq lc($nh);
my $cases = ($n < 5) ? 3 : 4;
for (my $case = 0; $case < $cases; $case++) {
my ($a, $b);
for ($a = 0; $a == 0; ) {
$a = int(rand($n));
}
for ($b = 0; $b == 0; ) {
$b = int(rand($n));
}
my $cstr = "$a|$b|$n";
if (exists($seen{$cstr})) { # don't repeat ourselves
$case--;
next;
}
$seen{$cstr} = 1;
my $ah = Math::BigInt->new($a)->to_hex();
my $bh = Math::BigInt->new($b)->to_hex();
my $desc = "";
if (length($info)) {
$desc = $info if !$mentioned{$info};
$mentioned{$info} = 1;
} elsif (length($nh) > 1 && $prime{$nh} && !$mentioned{$nh}) {
$desc = "(0x$nh is prime)";
$mentioned{$nh} = 1;
}
print <<EOF;
[ "$nh", "$ah", "$bh", "$desc" ],
EOF
}
}
```
Signed-off-by: Tom Cosgrove <tom.cosgrove@arm.com>
f334d9622b