/* * Copyright (c) 2017 Dag-Erling Smørgrav * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. The name of the author may not be used to endorse or promote * products derived from this software without specific prior written * permission. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include "cryb/impl.h" #include #include #include #include #include #include #include "t_mpi.h" /*************************************************************************** * Test cases */ static struct t_gcd_case { const char *desc; uint8_t a[16]; size_t amsb; int aneg:1; uint8_t b[16]; size_t bmsb; int bneg:1; uint8_t e[16]; size_t emsb; int eneg:1; } t_gcd_cases[] = { { "gcd(0, 0) == 0", { }, 0, 0, { }, 0, 0, { }, 0, 0, }, { "gcd(0x20140901, 0x20140901) == 0x20140901", { 0x20, 0x14, 0x09, 0x01 }, 30, 0, { 0x20, 0x14, 0x09, 0x01 }, 30, 0, { 0x20, 0x14, 0x09, 0x01 }, 30, 0, }, /* exercise both sides of the 0 check */ { "gcd(0x20140901, 0) == 0", { 0x20, 0x14, 0x09, 0x01 }, 30, 0, { }, 0, 0, { }, 0, 0, }, { "gcd(0, 0x20140901) == 0", { }, 0, 0, { 0x20, 0x14, 0x09, 0x01 }, 30, 0, { }, 0, 0, }, /* exercise both sides of the parity reduction */ { "gcd(512, 2048) == 512", { 0x02, 0x00 }, 10, 0, { 0x08, 0x00 }, 12, 0, { 0x02, 0x00 }, 10, 0, }, { "gcd(2048, 512) == 512", { 0x08, 0x00 }, 12, 0, { 0x02, 0x00 }, 10, 0, { 0x02, 0x00 }, 10, 0, }, /* HAC 14.55 */ { "gcd(1764, 868) == 28", { 0x06, 0xe4 }, 11, 0, { 0x03, 0x64 }, 10, 0, { 0x1c }, 5, 0, }, /* HAC 14.60 (small coprimes) */ { "gcd(768454923, 542167814) == 1", { 0x2d, 0xcd, 0xb1, 0x0b }, 30, 0, { 0x20, 0x50, 0xd3, 0x06 }, 30, 0, { 0x01 }, 1, 0, }, /* largish primes */ { "gcd(83464029052373107673, 52563826518442013507) == 1", { 0x04, 0x86, 0x4b, 0xcc, 0x36, 0x35, 0x95, 0x03, 0xd9 }, 59, 0, { 0x02, 0xd9, 0x78, 0x39, 0xb9, 0x32, 0xfe, 0x73, 0x43 }, 58, 0, { 0x01 }, 1, 0, }, /* * Two examples of a pathological case for Stein's algorithm: * gcd(k * n, k) where k and n are prime and n >> k. The code * goes into a loop which makes the absolute minimum amount of * progress per iteration: * * gcd(k * n, k) = gcd(k * (n - 1) / 2, k) * = gcd(k * ((n - 1) / 2 - 1) / 2, k) * = ... * * for approximately log2(k * n) iterations. */ { "gcd(2^61-1, 1) == 1", { 0x1f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff }, 61, 0, { 0x01 }, 1, 0, { 0x01 }, 1, 0, }, { "gcd((2^61-1)*3, 3) == 3", { 0x5f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfd }, 63, 0, { 0x03 }, 2, 0, { 0x03 }, 2, 0, }, }; /*************************************************************************** * Test functions */ static int t_mpi_gcd_tc(char **desc CRYB_UNUSED, void *arg) { struct t_gcd_case *tc = arg; cryb_mpi a = CRYB_MPI_ZERO, b = CRYB_MPI_ZERO, e = CRYB_MPI_ZERO; cryb_mpi x = CRYB_MPI_ZERO; int ret = 1; mpi_load(&a, tc->a, (tc->amsb + 7) / 8); a.neg = tc->aneg; mpi_load(&b, tc->b, (tc->bmsb + 7) / 8); b.neg = tc->bneg; mpi_load(&e, tc->e, (tc->emsb + 7) / 8); e.neg = tc->eneg; ret &= t_is_zero_i(mpi_gcd_abs(&x, &a, &b)); ret &= t_compare_mpi(&e, &x); mpi_destroy(&a); mpi_destroy(&b); mpi_destroy(&e); mpi_destroy(&x); return (ret); } static int t_mpi_gcd_ident_ab(char **desc CRYB_UNUSED, void *arg CRYB_UNUSED) { cryb_mpi a = CRYB_MPI_ZERO, x = CRYB_MPI_ZERO; int ret = 1; mpi_set(&a, 0x20140901); ret &= t_is_zero_i(mpi_gcd_abs(&x, &a, &a)); ret &= t_compare_mpi_u32(0x20140901, &x); mpi_destroy(&a); mpi_destroy(&x); return (ret); } static int t_mpi_gcd_ident_xa(char **desc CRYB_UNUSED, void *arg CRYB_UNUSED) { cryb_mpi a = CRYB_MPI_ZERO, b = CRYB_MPI_ZERO; int ret = 1; mpi_set(&a, 0x20140901); mpi_set(&b, 0x20140901); ret &= t_is_zero_i(mpi_gcd_abs(&a, &a, &b)); ret &= t_compare_mpi_u32(0x20140901, &a); mpi_destroy(&a); mpi_destroy(&b); return (ret); } static int t_mpi_gcd_ident_xb(char **desc CRYB_UNUSED, void *arg CRYB_UNUSED) { cryb_mpi a = CRYB_MPI_ZERO, b = CRYB_MPI_ZERO; int ret = 1; mpi_set(&a, 0x20140901); mpi_set(&b, 0x20140901); ret &= t_is_zero_i(mpi_gcd_abs(&b, &a, &b)); ret &= t_compare_mpi_u32(0x20140901, &b); mpi_destroy(&a); mpi_destroy(&b); return (ret); } /*************************************************************************** * Boilerplate */ static int t_prepare(int argc, char *argv[]) { unsigned int i; (void)argc; (void)argv; t_mpi_prepare(); for (i = 0; i < sizeof t_gcd_cases / sizeof t_gcd_cases[0]; ++i) t_add_test(t_mpi_gcd_tc, &t_gcd_cases[i], "%s", t_gcd_cases[i].desc); t_add_test(t_mpi_gcd_ident_ab, NULL, "x = gcd(a, a)"); t_add_test(t_mpi_gcd_ident_xa, NULL, "a = gcd(a, b)"); t_add_test(t_mpi_gcd_ident_xb, NULL, "b = gcd(a, b)"); return (0); } static void t_cleanup(void) { t_mpi_cleanup(); } int main(int argc, char *argv[]) { t_main(t_prepare, t_cleanup, argc, argv); }