#include "shared.h" static long rand_long(void) { long x; if (s_mp_rand_source(&x, sizeof(x)) != MP_OKAY) { fprintf(stderr, "s_mp_rand_source failed\n"); exit(EXIT_FAILURE); } return x; } static int rand_int(void) { int x; if (s_mp_rand_source(&x, sizeof(x)) != MP_OKAY) { fprintf(stderr, "s_mp_rand_source failed\n"); exit(EXIT_FAILURE); } return x; } static unsigned long ulabs(long x) { return x > 0 ? (unsigned long)x : -(unsigned long)x; } static int test_trivial_stuff(void) { mp_int a, b, c, d; mp_err e; if ((e = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { return EXIT_FAILURE; } (void)mp_error_to_string(e); /* a: 0->5 */ mp_set_int(&a, 5uL); /* a: 5-> b: -5 */ mp_neg(&a, &b); if (mp_cmp(&a, &b) != MP_GT) { goto LBL_ERR; } if (mp_cmp(&b, &a) != MP_LT) { goto LBL_ERR; } /* a: 5-> a: -5 */ mp_neg(&a, &a); if (mp_cmp(&b, &a) != MP_EQ) { goto LBL_ERR; } /* a: -5-> b: 5 */ mp_abs(&a, &b); if (mp_isneg(&b) != MP_NO) { goto LBL_ERR; } /* a: -5-> b: -4 */ mp_add_d(&a, 1uL, &b); if (mp_isneg(&b) != MP_YES) { goto LBL_ERR; } if (mp_get_int(&b) != 4) { goto LBL_ERR; } /* a: -5-> b: 1 */ mp_add_d(&a, 6uL, &b); if (mp_get_int(&b) != 1) { goto LBL_ERR; } /* a: -5-> a: 1 */ mp_add_d(&a, 6uL, &a); if (mp_get_int(&a) != 1) { goto LBL_ERR; } mp_zero(&a); /* a: 0-> a: 6 */ mp_add_d(&a, 6uL, &a); if (mp_get_int(&a) != 6) { goto LBL_ERR; } mp_set_int(&a, 42uL); mp_set_int(&b, 1uL); mp_neg(&b, &b); mp_set_int(&c, 1uL); mp_exptmod(&a, &b, &c, &d); mp_set_int(&c, 7uL); mp_exptmod(&a, &b, &c, &d); if (mp_iseven(&a) == mp_isodd(&a)) { goto LBL_ERR; } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_fread_fwrite(void) { mp_int a, b; mp_err e; FILE *tmp = NULL; if ((e = mp_init_multi(&a, &b, NULL)) != MP_OKAY) { return EXIT_FAILURE; } mp_set_int(&a, 123456uL); tmp = tmpfile(); if ((e = mp_fwrite(&a, 64, tmp)) != MP_OKAY) { goto LBL_ERR; } rewind(tmp); if ((e = mp_fread(&b, 64, tmp)) != MP_OKAY) { goto LBL_ERR; } if (mp_get_int(&b) != 123456uL) { goto LBL_ERR; } fclose(tmp); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: if (tmp != NULL) fclose(tmp); mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static mp_err very_random_source(void *out, size_t size) { memset(out, 0xff, size); return MP_OKAY; } static int test_mp_rand(void) { mp_int a, b; int n; mp_err err; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } mp_rand_source(very_random_source); for (n = 1; n < 1024; ++n) { if ((err = mp_rand(&a, n)) != MP_OKAY) { printf("Failed mp_rand() %s.\n", mp_error_to_string(err)); break; } if ((err = mp_incr(&a)) != MP_OKAY) { printf("Failed mp_incr() %s.\n", mp_error_to_string(err)); break; } if ((err = mp_div_2d(&a, n * MP_DIGIT_BIT, &b, NULL)) != MP_OKAY) { printf("Failed mp_div_2d() %s.\n", mp_error_to_string(err)); break; } if (mp_cmp_d(&b, 1) != MP_EQ) { ndraw(&a, "mp_rand() a"); ndraw(&b, "mp_rand() b"); err = MP_ERR; break; } } mp_rand_source(s_mp_rand_jenkins); mp_clear_multi(&a, &b, NULL); return err == MP_OKAY ? EXIT_SUCCESS : EXIT_FAILURE; } static int test_s_mp_jacobi(void) { struct s_mp_jacobi_st { unsigned long n; int c[16]; }; static struct s_mp_jacobi_st jacobi[] = { { 3, { 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1 } }, { 5, { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0 } }, { 7, { 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1 } }, { 9, { -1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 } }, }; int i, n, cnt; mp_err err, should; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } mp_set_int(&a, 0uL); mp_set_int(&b, 1uL); if ((err = s_mp_jacobi(&a, &b, &i)) != MP_OKAY) { printf("Failed executing s_mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err)); goto LBL_ERR; } if (i != 1) { printf("Failed trivial s_mp_jacobi(0 | 1) %d != 1\n", i); goto LBL_ERR; } for (cnt = 0; cnt < (int)(sizeof(jacobi)/sizeof(jacobi[0])); ++cnt) { mp_set_int(&b, jacobi[cnt].n); /* only test positive values of a */ for (n = -5; n <= 10; ++n) { mp_set_int(&a, (unsigned int)abs(n)); should = MP_OKAY; if (n < 0) { mp_neg(&a, &a); /* Until #44 is fixed the negative a's must fail */ should = MP_VAL; } if ((err = s_mp_jacobi(&a, &b, &i)) != should) { printf("Failed executing s_mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err)); goto LBL_ERR; } if ((err == MP_OKAY) && (i != jacobi[cnt].c[n + 5])) { printf("Failed trivial s_mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]); goto LBL_ERR; } } } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_kronecker(void) { struct mp_kronecker_st { long n; int c[21]; }; static struct mp_kronecker_st kronecker[] = { /*-10, -9, -8, -7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10*/ { -10, { 0, -1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0 } }, { -9, { -1, 0, -1, 1, 0, -1, -1, 0, -1, -1, 0, 1, 1, 0, 1, 1, 0, -1, 1, 0, 1 } }, { -8, { 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0 } }, { -7, { 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1 } }, { -6, { 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0 } }, { -5, { 0, -1, 1, -1, 1, 0, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, -1, 1, -1, 1, 0 } }, { -4, { 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0 } }, { -3, { -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1 } }, { -2, { 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0 } }, { -1, { -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1 } }, { 0, { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 } }, { 1, { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 } }, { 2, { 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0 } }, { 3, { 1, 0, -1, -1, 0, -1, 1, 0, -1, 1, 0, 1, -1, 0, 1, -1, 0, -1, -1, 0, 1 } }, { 4, { 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0 } }, { 5, { 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0 } }, { 6, { 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0 } }, { 7, { -1, 1, 1, 0, 1, -1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -1, 1, 0, 1, 1, -1 } }, { 8, { 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0 } }, { 9, { 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1 } }, { 10, { 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0 } } }; long k, m; int i, cnt; mp_err err; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } mp_set_int(&a, 0uL); mp_set_int(&b, 1uL); if ((err = mp_kronecker(&a, &b, &i)) != MP_OKAY) { printf("Failed executing mp_kronecker(0 | 1) %s.\n", mp_error_to_string(err)); goto LBL_ERR; } if (i != 1) { printf("Failed trivial mp_kronecker(0 | 1) %d != 1\n", i); goto LBL_ERR; } for (cnt = 0; cnt < (int)(sizeof(kronecker)/sizeof(kronecker[0])); ++cnt) { k = kronecker[cnt].n; if (k < 0) { mp_set_int(&a, (unsigned long)(-k)); mp_neg(&a, &a); } else { mp_set_int(&a, (unsigned long) k); } /* only test positive values of a */ for (m = -10; m <= 10; m++) { if (m < 0) { mp_set_int(&b,(unsigned long)(-m)); mp_neg(&b, &b); } else { mp_set_int(&b, (unsigned long) m); } if ((err = mp_kronecker(&a, &b, &i)) != MP_OKAY) { printf("Failed executing mp_kronecker(%ld | %ld) %s.\n", kronecker[cnt].n, m, mp_error_to_string(err)); goto LBL_ERR; } if ((err == MP_OKAY) && (i != kronecker[cnt].c[m + 10])) { printf("Failed trivial mp_kronecker(%ld | %ld) %d != %d\n", kronecker[cnt].n, m, i, kronecker[cnt].c[m + 10]); goto LBL_ERR; } } } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_complement(void) { int i; mp_int a, b, c; if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { long l = rand_long(); mp_set_long(&a, ulabs(l)); if (l < 0) mp_neg(&a, &a); mp_complement(&a, &b); l = ~l; mp_set_long(&c, ulabs(l)); if (l < 0) mp_neg(&c, &c); if (mp_cmp(&b, &c) != MP_EQ) { printf("\nmp_complement() bad result!"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } static int test_mp_tc_div_2d(void) { int i; mp_int a, b, d; if (mp_init_multi(&a, &b, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { long l; int em; l = rand_long(); mp_set_long(&a, ulabs(l)); if (l < 0) mp_neg(&a, &a); em = abs(rand_int()) % 32; mp_set_long(&d, ulabs(l >> em)); if ((l >> em) < 0) mp_neg(&d, &d); mp_tc_div_2d(&a, em, &b); if (mp_cmp(&b, &d) != MP_EQ) { printf("\nmp_tc_div_2d() bad result!"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &d, NULL); return EXIT_FAILURE; } static int test_mp_tc_xor(void) { int i; mp_int a, b, c, d; if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { long l, em; l = rand_long(); mp_set_int(&a, ulabs(l)); if (l < 0) mp_neg(&a, &a); em = rand_long(); mp_set_int(&b, ulabs(em)); if (em < 0) mp_neg(&b, &b); mp_set_int(&d, ulabs(l ^ em)); if ((l ^ em) < 0) mp_neg(&d, &d); mp_tc_xor(&a, &b, &c); if (mp_cmp(&c, &d) != MP_EQ) { printf("\nmp_tc_xor() bad result!"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_tc_or(void) { int i; mp_int a, b, c, d; if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { long l, em; l = rand_long(); mp_set_long(&a, ulabs(l)); if (l < 0) mp_neg(&a, &a); em = rand_long(); mp_set_long(&b, ulabs(em)); if (em < 0) mp_neg(&b, &b); mp_set_long(&d, ulabs(l | em)); if ((l | em) < 0) mp_neg(&d, &d); mp_tc_or(&a, &b, &c); if (mp_cmp(&c, &d) != MP_EQ) { printf("\nmp_tc_or() bad result!"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_tc_and(void) { int i; mp_int a, b, c, d; if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { long l, em; l = rand_long(); mp_set_long(&a, ulabs(l)); if (l < 0) mp_neg(&a, &a); em = rand_long(); mp_set_long(&b, ulabs(em)); if (em < 0) mp_neg(&b, &b); mp_set_long(&d, ulabs(l & em)); if ((l & em) < 0) mp_neg(&d, &d); mp_tc_and(&a, &b, &c); if (mp_cmp(&c, &d) != MP_EQ) { printf("\nmp_tc_and() bad result!"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_invmod(void) { mp_int a, b, c, d; if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* mp_invmod corner-case of https://github.com/libtom/libtommath/issues/118 */ { const char *a_ = "47182BB8DF0FFE9F61B1F269BACC066B48BA145D35137D426328DC3F88A5EA44"; const char *b_ = "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF"; const char *should_ = "0521A82E10376F8E4FDEF9A32A427AC2A0FFF686E00290D39E3E4B5522409596"; if (mp_read_radix(&a, a_, 16) != MP_OKAY) { printf("\nmp_read_radix(a) failed!"); goto LBL_ERR; } if (mp_read_radix(&b, b_, 16) != MP_OKAY) { printf("\nmp_read_radix(b) failed!"); goto LBL_ERR; } if (mp_read_radix(&c, should_, 16) != MP_OKAY) { printf("\nmp_read_radix(should) failed!"); goto LBL_ERR; } if (mp_invmod(&a, &b, &d) != MP_OKAY) { printf("\nmp_invmod() failed!"); goto LBL_ERR; } if (mp_cmp(&c, &d) != MP_EQ) { printf("\nmp_invmod() bad result!"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_set_double(void) { int i; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test mp_get_double/mp_set_double */ #if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) if (mp_set_double(&a, +1.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for +inf"); goto LBL_ERR; } if (mp_set_double(&a, -1.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for -inf"); goto LBL_ERR; } if (mp_set_double(&a, +0.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for NaN"); goto LBL_ERR; } if (mp_set_double(&a, -0.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for NaN"); goto LBL_ERR; } for (i = 0; i < 1000; ++i) { int tmp = rand_int(); double dbl = (double)tmp * rand_int() + 1; if (mp_set_double(&a, dbl) != MP_OKAY) { printf("\nmp_set_double() failed"); goto LBL_ERR; } if (dbl != mp_get_double(&a)) { printf("\nmp_get_double() bad result!"); goto LBL_ERR; } if (mp_set_double(&a, -dbl) != MP_OKAY) { printf("\nmp_set_double() failed"); goto LBL_ERR; } if (-dbl != mp_get_double(&a)) { printf("\nmp_get_double() bad result!"); goto LBL_ERR; } } #endif mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_get_int(void) { unsigned long t; int i; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { t = (unsigned long)rand_long() & 0xFFFFFFFFuL; mp_set_int(&a, t); if (t != mp_get_int(&a)) { printf("\nmp_get_int() bad result!"); goto LBL_ERR; } } mp_set_int(&a, 0uL); if (mp_get_int(&a) != 0) { printf("\nmp_get_int() bad result!"); goto LBL_ERR; } mp_set_int(&a, 0xFFFFFFFFuL); if (mp_get_int(&a) != 0xFFFFFFFFuL) { printf("\nmp_get_int() bad result!"); goto LBL_ERR; } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_get_long(void) { unsigned long s, t; int i; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < ((int)(sizeof(unsigned long)*CHAR_BIT) - 1); ++i) { t = (1UL << (i+1)) - 1; if (!t) t = ~0UL; printf(" t = 0x%lx i = %d\r", t, i); do { mp_set_long(&a, t); s = mp_get_long(&a); if (s != t) { printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t); goto LBL_ERR; } t <<= 1; } while (t != 0uL); } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_get_long_long(void) { unsigned long long q, r; int i; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < ((int)(sizeof(unsigned long long)*CHAR_BIT) - 1); ++i) { r = (1ULL << (i+1)) - 1; if (!r) r = ~0ULL; printf(" r = 0x%llx i = %d\r", r, i); do { mp_set_long_long(&a, r); q = mp_get_long_long(&a); if (q != r) { printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r); goto LBL_ERR; } r <<= 1; } while (r != 0uLL); } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_sqrt(void) { int i, n; mp_int a, b, c, d; if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { printf("%6d\r", i); fflush(stdout); n = (rand_int() & 15) + 1; mp_rand(&a, n); if (mp_sqrt(&a, &b) != MP_OKAY) { printf("\nmp_sqrt() error!"); goto LBL_ERR; } mp_n_root_ex(&a, 2uL, &c, 0); mp_n_root_ex(&a, 2uL, &d, 1); if (mp_cmp_mag(&c, &d) != MP_EQ) { printf("\nmp_n_root_ex() bad result!"); goto LBL_ERR; } if (mp_cmp_mag(&b, &c) != MP_EQ) { printf("mp_sqrt() bad result!\n"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_is_square(void) { int i, n; mp_int a, b; mp_bool res; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { printf("%6d\r", i); fflush(stdout); /* test mp_is_square false negatives */ n = (rand_int() & 7) + 1; mp_rand(&a, n); mp_sqr(&a, &a); if (mp_is_square(&a, &res) != MP_OKAY) { printf("\nfn:mp_is_square() error!"); goto LBL_ERR; } if (res == MP_NO) { printf("\nfn:mp_is_square() bad result!"); goto LBL_ERR; } /* test for false positives */ mp_add_d(&a, 1uL, &a); if (mp_is_square(&a, &res) != MP_OKAY) { printf("\nfp:mp_is_square() error!"); goto LBL_ERR; } if (res == MP_YES) { printf("\nfp:mp_is_square() bad result!"); goto LBL_ERR; } } printf("\n\n"); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_sqrtmod_prime(void) { struct mp_sqrtmod_prime_st { unsigned long p; unsigned long n; mp_digit r; }; static struct mp_sqrtmod_prime_st sqrtmod_prime[] = { { 5, 14, 3 }, { 7, 9, 4 }, { 113, 2, 62 } }; int i; mp_int a, b, c; if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* r^2 = n (mod p) */ for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) { mp_set_int(&a, sqrtmod_prime[i].p); mp_set_int(&b, sqrtmod_prime[i].n); if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) { printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1)); goto LBL_ERR; } if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) { printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1)); ndraw(&c, "r"); goto LBL_ERR; } } mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } static int test_mp_prime_rand(void) { int ix; mp_err err; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test for size */ for (ix = 10; ix < 128; ix++) { printf("Testing (not safe-prime): %9d bits \r", ix); fflush(stdout); err = mp_prime_rand(&a, 8, ix, (rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON); if (err != MP_OKAY) { printf("\nfailed with error: %s\n", mp_error_to_string(err)); goto LBL_ERR; } if (mp_count_bits(&a) != ix) { printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); goto LBL_ERR; } } printf("\n"); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_prime_is_prime(void) { int ix; mp_err err; mp_bool cnt, fu; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* strong Miller-Rabin pseudoprime to the first 200 primes (F. Arnault) */ puts("Testing mp_prime_is_prime() with Arnault's pseudoprime 803...901 \n"); mp_read_radix(&a, "91xLNF3roobhzgTzoFIG6P13ZqhOVYSN60Fa7Cj2jVR1g0k89zdahO9/kAiRprpfO1VAp1aBHucLFV/qLKLFb+zonV7R2Vxp1K13ClwUXStpV0oxTNQVjwybmFb5NBEHImZ6V7P6+udRJuH8VbMEnS0H8/pSqQrg82OoQQ2fPpAk6G1hkjqoCv5s/Yr", 64); mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt); if (cnt == MP_YES) { printf("Arnault's pseudoprime is not prime but mp_prime_is_prime says it is.\n"); goto LBL_ERR; } /* About the same size as Arnault's pseudoprime */ puts("Testing mp_prime_is_prime() with certified prime 2^1119 + 53\n"); mp_set(&a, 1uL); mp_mul_2d(&a,1119,&a); mp_add_d(&a, 53uL, &a); err = mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt); /* small problem */ if (err != MP_OKAY) { printf("\nfailed with error: %s\n", mp_error_to_string(err)); } /* large problem */ if (cnt == MP_NO) { printf("A certified prime is a prime but mp_prime_is_prime says it is not.\n"); } if ((err != MP_OKAY) || (cnt == MP_NO)) { printf("prime tested was: "); mp_fwrite(&a,16,stdout); putchar('\n'); goto LBL_ERR; } for (ix = 16; ix < 128; ix++) { printf("Testing ( safe-prime): %9d bits \r", ix); fflush(stdout); err = mp_prime_rand(&a, 8, ix, ((rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON) | MP_PRIME_SAFE); if (err != MP_OKAY) { printf("\nfailed with error: %s\n", mp_error_to_string(err)); goto LBL_ERR; } if (mp_count_bits(&a) != ix) { printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); goto LBL_ERR; } /* let's see if it's really a safe prime */ mp_sub_d(&a, 1uL, &b); mp_div_2(&b, &b); err = mp_prime_is_prime(&b, mp_prime_rabin_miller_trials(mp_count_bits(&b)), &cnt); /* small problem */ if (err != MP_OKAY) { printf("\nfailed with error: %s\n", mp_error_to_string(err)); } /* large problem */ if (cnt == MP_NO) { printf("\nsub is not prime!\n"); } mp_prime_frobenius_underwood(&b, &fu); if (fu == MP_NO) { printf("\nfrobenius-underwood says sub is not prime!\n"); } if ((err != MP_OKAY) || (cnt == MP_NO)) { printf("prime tested was: "); mp_fwrite(&a,16,stdout); putchar('\n'); printf("sub tested was: "); mp_fwrite(&b,16,stdout); putchar('\n'); goto LBL_ERR; } } /* Check regarding problem #143 */ #ifndef MP_8BIT mp_read_radix(&a, "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF", 16); err = mp_prime_strong_lucas_selfridge(&a, &cnt); /* small problem */ if (err != MP_OKAY) { printf("\nmp_prime_strong_lucas_selfridge failed with error: %s\n", mp_error_to_string(err)); } /* large problem */ if (cnt == MP_NO) { printf("\n\nissue #143 - mp_prime_strong_lucas_selfridge FAILED!\n"); } if ((err != MP_OKAY) || (cnt == MP_NO)) { printf("prime tested was: "); mp_fwrite(&a,16,stdout); putchar('\n'); goto LBL_ERR; } #endif printf("\n\n"); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_montgomery_reduce(void) { mp_digit mp; int ix, i, n; char buf[4096]; mp_int a, b, c, d, e; if (mp_init_multi(&a, &b, &c, &d, &e, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test montgomery */ for (i = 1; i <= 10; i++) { if (i == 10) i = 1000; printf(" digit size: %2d\r", i); fflush(stdout); for (n = 0; n < 1000; n++) { mp_rand(&a, i); a.dp[0] |= 1; /* let's see if R is right */ mp_montgomery_calc_normalization(&b, &a); mp_montgomery_setup(&a, &mp); /* now test a random reduction */ for (ix = 0; ix < 100; ix++) { mp_rand(&c, 1 + abs(rand_int()) % (2*i)); mp_copy(&c, &d); mp_copy(&c, &e); mp_mod(&d, &a, &d); mp_montgomery_reduce(&c, &a, mp); mp_mulmod(&c, &b, &a, &c); if (mp_cmp(&c, &d) != MP_EQ) { /* *INDENT-OFF* */ printf("d = e mod a, c = e MOD a\n"); mp_todecimal(&a, buf); printf("a = %s\n", buf); mp_todecimal(&e, buf); printf("e = %s\n", buf); mp_todecimal(&d, buf); printf("d = %s\n", buf); mp_todecimal(&c, buf); printf("c = %s\n", buf); printf("compare no compare!\n"); goto LBL_ERR; /* *INDENT-ON* */ } /* only one big montgomery reduction */ if (i > 10) { n = 1000; ix = 100; } } } } printf("\n\n"); mp_clear_multi(&a, &b, &c, &d, &e, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, &e, NULL); return EXIT_FAILURE; } static int test_mp_read_radix(void) { char buf[4096]; mp_int a; if (mp_init_multi(&a, NULL)!= MP_OKAY) { return EXIT_FAILURE; } mp_read_radix(&a, "123456", 10); mp_toradix_n(&a, buf, 10, 3); printf("a == %s\n", buf); mp_toradix_n(&a, buf, 10, 4); printf("a == %s\n", buf); mp_toradix_n(&a, buf, 10, 30); printf("a == %s\n", buf); #if 0 for (;;) { fgets(buf, sizeof(buf), stdin); mp_read_radix(&a, buf, 10); mp_prime_next_prime(&a, 5, 1); mp_toradix(&a, buf, 10); printf("%s, %lu\n", buf, a.dp[0] & 3); } #endif mp_clear_multi(&a, NULL); return EXIT_SUCCESS; } static int test_mp_cnt_lsb(void) { int ix; mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } mp_set(&a, 1uL); for (ix = 0; ix < 1024; ix++) { if (mp_cnt_lsb(&a) != ix) { printf("Failed at %d, %d\n", ix, mp_cnt_lsb(&a)); goto LBL_ERR; } mp_mul_2(&a, &a); } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_reduce_2k(void) { int ix, cnt; mp_int a, b, c, d; if (mp_init_multi(&a, &b, &c, &d, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test mp_reduce_2k */ for (cnt = 3; cnt <= 128; ++cnt) { mp_digit tmp; mp_2expt(&a, cnt); mp_sub_d(&a, 2uL, &a); /* a = 2**cnt - 2 */ printf("\r %4d bits", cnt); printf("(%d)", mp_reduce_is_2k(&a)); mp_reduce_2k_setup(&a, &tmp); printf("(%lu)", (unsigned long) tmp); for (ix = 0; ix < 1000; ix++) { if (!(ix & 127)) { printf("."); fflush(stdout); } mp_rand(&b, (cnt / MP_DIGIT_BIT + 1) * 2); mp_copy(&c, &b); mp_mod(&c, &a, &c); mp_reduce_2k(&b, &a, 2uL); if (mp_cmp(&c, &b) != MP_EQ) { printf("FAILED\n"); goto LBL_ERR; } } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_mp_div_3(void) { int cnt; mp_int a, b, c, d, e; if (mp_init_multi(&a, &b, &c, &d, &e, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test mp_div_3 */ mp_set(&d, 3uL); for (cnt = 0; cnt < 10000;) { mp_digit r2; if (!(++cnt & 127)) { printf("%9d\r", cnt); fflush(stdout); } mp_rand(&a, abs(rand_int()) % 128 + 1); mp_div(&a, &d, &b, &e); mp_div_3(&a, &c, &r2); if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) { printf("\nmp_div_3 => Failure\n"); goto LBL_ERR; } } printf("\nPassed div_3 testing"); mp_clear_multi(&a, &b, &c, &d, &e, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, &d, &e, NULL); return EXIT_FAILURE; } static int test_mp_dr_reduce(void) { mp_digit mp; int cnt; unsigned rr; int ix; mp_int a, b, c; if (mp_init_multi(&a, &b, &c, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test the DR reduction */ for (cnt = 2; cnt < 32; cnt++) { printf("\r%d digit modulus", cnt); mp_grow(&a, cnt); mp_zero(&a); for (ix = 1; ix < cnt; ix++) { a.dp[ix] = MP_MASK; } a.used = cnt; a.dp[0] = 3; mp_rand(&b, cnt - 1); mp_copy(&b, &c); rr = 0; do { if (!(rr & 127)) { printf("."); fflush(stdout); } mp_sqr(&b, &b); mp_add_d(&b, 1uL, &b); mp_copy(&b, &c); mp_mod(&b, &a, &b); mp_dr_setup(&a, &mp); mp_dr_reduce(&c, &a, mp); if (mp_cmp(&b, &c) != MP_EQ) { printf("Failed on trial %u\n", rr); goto LBL_ERR; } } while (++rr < 500); printf(" passed"); fflush(stdout); } mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } static int test_mp_reduce_2k_l(void) { # if LTM_DEMO_TEST_REDUCE_2K_L mp_int a, b; if (mp_init_multi(&a, &b, NULL)!= MP_OKAY) { return EXIT_FAILURE; } /* test the mp_reduce_2k_l code */ # if LTM_DEMO_TEST_REDUCE_2K_L == 1 /* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */ mp_2expt(&a, 1024); mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16); mp_sub(&a, &b, &a); # elif LTM_DEMO_TEST_REDUCE_2K_L == 2 /* p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */ mp_2expt(&a, 2048); mp_read_radix(&b, "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F", 16); mp_sub(&a, &b, &a); # else # error oops # endif mp_todecimal(&a, buf); printf("\n\np==%s\n", buf); /* now mp_reduce_is_2k_l() should return */ if (mp_reduce_is_2k_l(&a) != 1) { printf("mp_reduce_is_2k_l() return 0, should be 1\n"); goto LBL_ERR; } mp_reduce_2k_setup_l(&a, &d); /* now do a million square+1 to see if it varies */ mp_rand(&b, 64); mp_mod(&b, &a, &b); mp_copy(&b, &c); printf("Testing: mp_reduce_2k_l..."); fflush(stdout); for (cnt = 0; cnt < (int)(1uL << 20); cnt++) { mp_sqr(&b, &b); mp_add_d(&b, 1uL, &b); mp_reduce_2k_l(&b, &a, &d); mp_sqr(&c, &c); mp_add_d(&c, 1uL, &c); mp_mod(&c, &a, &c); if (mp_cmp(&b, &c) != MP_EQ) { printf("mp_reduce_2k_l() failed at step %d\n", cnt); mp_tohex(&b, buf); printf("b == %s\n", buf); mp_tohex(&c, buf); printf("c == %s\n", buf); goto LBL_ERR; } } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; #else return EXIT_SUCCESS; # endif /* LTM_DEMO_TEST_REDUCE_2K_L */ } /* stripped down version of mp_radix_size. The faster version can be off by up t o +3 */ static mp_err s_rs(const mp_int *a, int radix, int *size) { mp_err res; int digs = 0; mp_int t; mp_digit d; *size = 0; if (mp_iszero(a) == MP_YES) { *size = 2; return MP_OKAY; } if (radix == 2) { *size = mp_count_bits(a) + 1; return MP_OKAY; } if ((res = mp_init_copy(&t, a)) != MP_OKAY) { return res; } t.sign = MP_ZPOS; while (mp_iszero(&t) == MP_NO) { if ((res = mp_div_d(&t, (mp_digit)radix, &t, &d)) != MP_OKAY) { mp_clear(&t); return res; } ++digs; } mp_clear(&t); *size = digs + 1; return MP_OKAY; } static int test_mp_ilogb(void) { mp_int a, lb; mp_digit d, base; int size; if (mp_init_multi(&a, &lb, NULL) != MP_OKAY) { goto LBL_ERR; } /* base a result 0 x MP_VAL 1 x MP_VAL */ mp_set(&a, 42uL); base = 0uL; if (mp_ilogb(&a, base, &lb) != MP_VAL) { goto LBL_ERR; } base = 1uL; if (mp_ilogb(&a, base, &lb) != MP_VAL) { goto LBL_ERR; } /* base a result 2 0 MP_VAL 2 1 0 2 2 1 2 3 1 */ base = 2uL; mp_zero(&a); if (mp_ilogb(&a, base, &lb) != MP_VAL) { goto LBL_ERR; } for (d = 1; d < 4; d++) { mp_set(&a, d); if (mp_ilogb(&a, base, &lb) != MP_OKAY) { goto LBL_ERR; } if (mp_cmp_d(&lb, (d == 1)?0uL:1uL) != MP_EQ) { goto LBL_ERR; } } /* base a result 3 0 MP_VAL 3 1 0 3 2 0 3 3 1 */ base = 3uL; mp_zero(&a); if (mp_ilogb(&a, base, &lb) != MP_VAL) { goto LBL_ERR; } for (d = 1; d < 4; d++) { mp_set(&a, d); if (mp_ilogb(&a, base, &lb) != MP_OKAY) { goto LBL_ERR; } if (mp_cmp_d(&lb, (d < base)?0uL:1uL) != MP_EQ) { goto LBL_ERR; } } /* bases 2..64 with "a" a random large constant. The range of bases tested allows to check with radix_size. */ if (mp_rand(&a, 10) != MP_OKAY) { goto LBL_ERR; } for (base = 2uL; base < 65uL; base++) { if (mp_ilogb(&a, base, &lb) != MP_OKAY) { goto LBL_ERR; } if (s_rs(&a,(int)base, &size) != MP_OKAY) { goto LBL_ERR; } /* radix_size includes the memory needed for '\0', too*/ size -= 2; if (mp_cmp_d(&lb, (mp_digit)size) != MP_EQ) { goto LBL_ERR; } } /* bases 2..64 with "a" a random small constant to test the part of mp_ilogb that uses native types. */ if (mp_rand(&a, 1) != MP_OKAY) { goto LBL_ERR; } for (base = 2uL; base < 65uL; base++) { if (mp_ilogb(&a, base, &lb) != MP_OKAY) { goto LBL_ERR; } if (s_rs(&a,(int)base, &size) != MP_OKAY) { goto LBL_ERR; } size -= 2; if (mp_cmp_d(&lb, (mp_digit)size) != MP_EQ) { goto LBL_ERR; } } /*Test upper edgecase with base MP_MASK and number (MP_MASK/2)*MP_MASK^10 */ mp_set(&a, MP_MASK); if (mp_expt_d(&a, 10uL, &a) != MP_OKAY) { goto LBL_ERR; } if (mp_add_d(&a, (MP_MASK>>1), &a) != MP_OKAY) { goto LBL_ERR; } if (mp_ilogb(&a, MP_MASK, &lb) != MP_OKAY) { goto LBL_ERR; } if (mp_cmp_d(&lb, 10uL) != MP_EQ) { goto LBL_ERR; } mp_clear_multi(&a, &lb, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &lb, NULL); return EXIT_FAILURE; } static int test_mp_incr(void) { mp_int a, b; mp_err e = MP_OKAY; if ((e = mp_init_multi(&a, &b, NULL)) != MP_OKAY) { goto LTM_ERR; } /* Does it increment inside the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK/2); if ((e = mp_incr(&a)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp_d(&a, (MP_MASK/2uL) + 1uL) != MP_EQ) { goto LTM_ERR; } /* Does it increment outside of the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK); mp_set(&b, MP_MASK); if ((e = mp_incr(&a)) != MP_OKAY) { goto LTM_ERR; } if ((e = mp_add_d(&b, 1uL, &b)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&a, &b) != MP_EQ) { goto LTM_ERR; } /* Does it increment from -1 to 0? */ mp_set(&a, 1uL); a.sign = MP_NEG; if ((e = mp_incr(&a)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp_d(&a, 0uL) != MP_EQ) { goto LTM_ERR; } /* Does it increment from -(MP_MASK + 1) to -MP_MASK? */ mp_set(&a, MP_MASK); if ((e = mp_add_d(&a, 1uL, &a)) != MP_OKAY) { goto LTM_ERR; } a.sign = MP_NEG; if ((e = mp_incr(&a)) != MP_OKAY) { goto LTM_ERR; } if (a.sign != MP_NEG) { goto LTM_ERR; } a.sign = MP_ZPOS; if (mp_cmp_d(&a, MP_MASK) != MP_EQ) { goto LTM_ERR; } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_decr(void) { mp_int a, b; mp_err e = MP_OKAY; if ((e = mp_init_multi(&a, &b, NULL)) != MP_OKAY) { goto LTM_ERR; } /* Does it decrement inside the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK/2); if ((e = mp_decr(&a)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp_d(&a, (MP_MASK/2uL) - 1uL) != MP_EQ) { goto LTM_ERR; } /* Does it decrement outside of the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK); if ((e = mp_add_d(&a, 1uL, &a)) != MP_OKAY) { goto LTM_ERR; } if ((e = mp_decr(&a)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp_d(&a, MP_MASK) != MP_EQ) { goto LTM_ERR; } /* Does it decrement from 0 to -1? */ mp_zero(&a); if ((e = mp_decr(&a)) != MP_OKAY) { goto LTM_ERR; } if (a.sign == MP_NEG) { a.sign = MP_ZPOS; if (mp_cmp_d(&a, 1uL) != MP_EQ) { goto LTM_ERR; } } else { goto LTM_ERR; } /* Does it decrement from -MP_MASK to -(MP_MASK + 1)? */ mp_set(&a, MP_MASK); a.sign = MP_NEG; mp_set(&b, MP_MASK); b.sign = MP_NEG; if ((e = mp_sub_d(&b, 1uL, &b)) != MP_OKAY) { goto LTM_ERR; } if ((e = mp_decr(&a)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&a, &b) != MP_EQ) { goto LTM_ERR; } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } /* Cannot test mp_exp(_d) without mp_n_root and vice versa. So one of the two has to be tested from scratch. Numbers generated by for i in {1..10} do seed=$(head -c 10000 /dev/urandom | tr -dc '[:digit:]' | head -c 120); echo $seed; convertbase $seed 10 64; done (The program "convertbase" uses libtommath's to/from_radix functions) Roots were precalculated with Pari/GP default(realprecision,1000); for(n=3,100,r = floor(a^(1/n));printf("\"" r "\", ")) All numbers as strings to simplifiy things, especially for the low-mp branch. */ static int test_mp_n_root(void) { mp_int a, c, r; mp_err e; int i, j; const char *input[] = { "4n9cbk886QtLQmofprid3l2Q0GD8Yv979Lh8BdZkFE8g2pDUUSMBET/+M/YFyVZ3mBp", "5NlgzHhmIX05O5YoW5yW5reAlVNtRAlIcN2dfoATnNdc1Cw5lHZUTwNthmK6/ZLKfY6", "3gweiHDX+ji5utraSe46IJX+uuh7iggs63xIpMP5MriU4Np+LpHI5are8RzS9pKh9xP", "5QOJUSKMrfe7LkeyJOlupS8h7bjT+TXmZkDzOjZtfj7mdA7cbg0lRX3CuafhjIrpK8S", "4HtYFldVkyVbrlg/s7kmaA7j45PvLQm+1bbn6ehgP8tVoBmGbv2yDQI1iQQze4AlHyN", "3bwCUx79NAR7c68OPSp5ZabhZ9aBEr7rWNTO2oMY7zhbbbw7p6shSMxqE9K9nrTNucf", "4j5RGb78TfuYSzrXn0z6tiAoWiRI81hGY3el9AEa9S+gN4x/AmzotHT2Hvj6lyBpE7q", "4lwg30SXqZhEHNsl5LIXdyu7UNt0VTWebP3m7+WUL+hsnFW9xJe7UnzYngZsvWh14IE", "1+tcqFeRuGqjRADRoRUJ8gL4UUSFQVrVVoV6JpwVcKsuBq5G0pABn0dLcQQQMViiVRj", "hXwxuFySNSFcmbrs/coz4FUAaUYaOEt+l4V5V8vY71KyBvQPxRq/6lsSrG2FHvWDax" }; /* roots 3-100 of the above */ const char *root[10][100] = { { "9163694094944489658600517465135586130944", "936597377180979771960755204040", "948947857956884030956907", "95727185767390496595", "133844854039712620", "967779611885360", "20926191452627", "974139547476", "79203891950", "9784027073", "1667309744", "365848129", "98268452", "31109156", "11275351", "4574515", "2040800", "986985", "511525", "281431", "163096", "98914", "62437", "40832", "27556", "19127", "13614", "9913", "7367", "5577", "4294", "3357", "2662", "2138", "1738", "1428", "1185", "993", "839", "715", "613", "530", "461", "403", "355", "314", "279", "249", "224", "202", "182", "166", "151", "138", "126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61", "57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", "32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "9534798256755061606359588498764080011382", "964902943621813525741417593772", "971822399862464674540423", "97646291566833512831", "136141536090599560", "982294733581430", "21204945933335", "985810529393", "80066084985", "9881613813", "1682654547", "368973625", "99051783", "31341581", "11354620", "4604882", "2053633", "992879", "514434", "282959", "163942", "99406", "62736", "41020", "27678", "19208", "13670", "9952", "7395", "5598", "4310", "3369", "2671", "2145", "1744", "1433", "1189", "996", "842", "717", "615", "531", "462", "404", "356", "315", "280", "250", "224", "202", "183", "166", "151", "138", "127", "116", "107", "99", "92", "85", "80", "74", "70", "65", "61", "58", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", "32", "31", "30", "29", "27", "26", "25", "24", "23", "23", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "8398539113202579297642815367509019445624", "877309458945432597462853440936", "900579899458998599215071", "91643543761699761637", "128935656335800903", "936647990947203", "20326748623514", "948988882684", "77342677787", "9573063447", "1634096832", "359076114", "96569670", "30604705", "11103188", "4508519", "2012897", "974160", "505193", "278105", "161251", "97842", "61788", "40423", "27291", "18949", "13492", "9826", "7305", "5532", "4260", "3332", "2642", "2123", "1726", "1418", "1177", "986", "834", "710", "610", "527", "458", "401", "353", "312", "278", "248", "223", "201", "181", "165", "150", "137", "126", "116", "107", "99", "91", "85", "79", "74", "69", "65", "61", "57", "54", "51", "48", "46", "43", "41", "39", "37", "35", "34", "32", "31", "30", "28", "27", "26", "25", "24", "23", "22", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "9559098494021810340217797724866627755195", "966746709063325235560830083787", "973307706084821682248292", "97770642291138756434", "136290128605981259", "983232784778520", "21222944848922", "986563584410", "80121684894", "9887903837", "1683643206", "369174929", "99102220", "31356542", "11359721", "4606836", "2054458", "993259", "514621", "283057", "163997", "99437", "62755", "41032", "27686", "19213", "13674", "9955", "7397", "5599", "4311", "3370", "2672", "2146", "1744", "1433", "1189", "996", "842", "717", "615", "532", "462", "404", "356", "315", "280", "250", "224", "202", "183", "166", "151", "138", "127", "116", "107", "99", "92", "86", "80", "74", "70", "65", "61", "58", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", "32", "31", "30", "29", "27", "26", "25", "24", "23", "23", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "8839202025813295923132694443541993309220", "911611499784863252820288596270", "928640961450376817534853", "94017030509441723821", "131792686685970629", "954783483196511", "20676214073400", "963660189823", "78428929840", "9696237956", "1653495486", "363032624", "97562430", "30899570", "11203842", "4547110", "2029216", "981661", "508897", "280051", "162331", "98469", "62168", "40663", "27446", "19053", "13563", "9877", "7341", "5558", "4280", "3347", "2654", "2132", "1733", "1424", "1182", "990", "837", "713", "612", "529", "460", "402", "354", "313", "279", "249", "223", "201", "182", "165", "150", "138", "126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61", "57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", "32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "8338442683973420410660145045849076963795", "872596990706967613912664152945", "896707843885562730147307", "91315073695274540969", "128539440806486007", "934129001105825", "20278149285734", "946946589774", "77191347471", "9555892093", "1631391010", "358523975", "96431070", "30563524", "11089126", "4503126", "2010616", "973111", "504675", "277833", "161100", "97754", "61734", "40390", "27269", "18934", "13482", "9819", "7300", "5528", "4257", "3330", "2641", "2122", "1725", "1417", "1177", "986", "833", "710", "609", "527", "458", "401", "353", "312", "278", "248", "222", "200", "181", "165", "150", "137", "126", "116", "107", "99", "91", "85", "79", "74", "69", "65", "61", "57", "54", "51", "48", "46", "43", "41", "39", "37", "35", "34", "32", "31", "30", "28", "27", "26", "25", "24", "23", "22", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "9122818552483814953977703257848970704164", "933462289569511464780529972314", "946405863353935713909178", "95513446972056321834", "133588658082928446", "966158521967027", "20895030642048", "972833934108", "79107381638", "9773098125", "1665590516", "365497822", "98180628", "31083090", "11266459", "4571108", "2039360", "986323", "511198", "281260", "163001", "98858", "62404", "40811", "27543", "19117", "13608", "9908", "7363", "5575", "4292", "3356", "2661", "2138", "1737", "1428", "1185", "993", "839", "714", "613", "530", "461", "403", "355", "314", "279", "249", "224", "202", "182", "165", "151", "138", "126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61", "57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", "32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "9151329724083804100369546479681933027521", "935649419557299174433860420387", "948179413831316112751907", "95662582675170358900", "133767426788182384", "967289728859610", "20916775466497", "973745045600", "79174731802", "9780725058", "1666790321", "365742295", "98241919", "31101281", "11272665", "4573486", "2040365", "986785", "511426", "281380", "163067", "98897", "62427", "40826", "27552", "19124", "13612", "9911", "7366", "5576", "4294", "3357", "2662", "2138", "1738", "1428", "1185", "993", "839", "715", "613", "530", "461", "403", "355", "314", "279", "249", "224", "202", "182", "165", "151", "138", "126", "116", "107", "99", "92", "85", "79", "74", "69", "65", "61", "57", "54", "51", "48", "46", "43", "41", "39", "37", "36", "34", "32", "31", "30", "28", "27", "26", "25", "24", "23", "23", "22", "21", "20", "20", "19", "18", "18", "17", "17", "16", "16", "15" }, { "6839396355168045468586008471269923213531", "752078770083218822016981965090", "796178899357307807726034", "82700643015444840424", "118072966296549115", "867224751770392", "18981881485802", "892288574037", "73130030771", "9093989389", "1558462688", "343617470", "92683740", "29448679", "10708016", "4356820", "1948676", "944610", "490587", "270425", "156989", "95362", "60284", "39477", "26675", "18536", "13208", "9627", "7161", "5426", "4181", "3272", "2596", "2087", "1697", "1395", "1159", "971", "821", "700", "601", "520", "452", "396", "348", "308", "274", "245", "220", "198", "179", "163", "148", "136", "124", "114", "106", "98", "91", "84", "78", "73", "68", "64", "60", "57", "53", "50", "48", "45", "43", "41", "39", "37", "35", "34", "32", "31", "29", "28", "27", "26", "25", "24", "23", "22", "22", "21", "20", "19", "19", "18", "18", "17", "17", "16", "16", "15" }, { "4788090721380022347683138981782307670424", "575601315594614059890185238256", "642831903229558719812840", "69196031110028430211", "101340693763170691", "758683936560287", "16854690815260", "801767985909", "66353290503", "8318415180", "1435359033", "318340531", "86304307", "27544217", "10054988", "4105446", "1841996", "895414", "466223", "257591", "149855", "91205", "57758", "37886", "25639", "17842", "12730", "9290", "6918", "5248", "4048", "3170", "2518", "2026", "1649", "1357", "1128", "946", "800", "682", "586", "507", "441", "387", "341", "302", "268", "240", "215", "194", "176", "160", "146", "133", "122", "112", "104", "96", "89", "83", "77", "72", "67", "63", "59", "56", "53", "50", "47", "45", "42", "40", "38", "36", "35", "33", "32", "30", "29", "28", "27", "26", "25", "24", "23", "22", "21", "21", "20", "19", "19", "18", "17", "17", "16", "16", "15", "15" } }; if ((e = mp_init_multi(&a, &c, &r, NULL)) != MP_OKAY) { return EXIT_FAILURE; } #ifdef MP_8BIT for (i = 0; i < 1; i++) { #else for (i = 0; i < 10; i++) { #endif mp_read_radix(&a, input[i], 64); #ifdef MP_8BIT for (j = 3; j < 10; j++) { #else for (j = 3; j < 100; j++) { #endif mp_n_root(&a, (mp_digit) j, &c); mp_read_radix(&r, root[i][j-3], 10); if (mp_cmp(&r, &c) != MP_EQ) { fprintf(stderr, "mp_n_root failed at input #%d, root #%d\n", i, j); goto LTM_ERR; } } } mp_clear_multi(&a, &c, &r, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &c, &r, NULL); return EXIT_FAILURE; } static int test_s_mp_balance_mul(void) { mp_int a, b, c; mp_err e = MP_OKAY; const char *na = "4b0I5uMTujCysw+1OOuOyH2FX2WymrHUqi8BBDb7XpkV/4i7vXTbEYUy/kdIfCKu5jT5JEqYkdmnn3jAYo8XShPzNLxZx9yoLjxYRyptSuOI2B1DspvbIVYXY12sxPZ4/HCJ4Usm2MU5lO/006KnDMxuxiv1rm6YZJZ0eZU"; const char *nb = "3x9vs0yVi4hIq7poAeVcggC3WoRt0zRLKO"; const char *nc = "HzrSq9WVt1jDTVlwUxSKqxctu2GVD+N8+SVGaPFRqdxyld6IxDBbj27BPJzYUdR96k3sWpkO8XnDBvupGPnehpQe4KlO/KmN1PjFov/UTZYM+LYzkFcBPyV6hkkL8ePC1rlFLAHzgJMBCXVp4mRqtkQrDsZXXlcqlbTFu69wF6zDEysiX2cAtn/kP9ldblJiwYPCD8hG"; if ((e = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { goto LTM_ERR; } if ((e = mp_read_radix(&a, na, 64)) != MP_OKAY) { goto LTM_ERR; } if ((e = mp_read_radix(&b, nb, 64)) != MP_OKAY) { goto LTM_ERR; } if ((e = s_mp_balance_mul(&a, &b, &c)) != MP_OKAY) { goto LTM_ERR; } if ((e = mp_read_radix(&b, nc, 64)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&b, &c) != MP_EQ) { goto LTM_ERR; } mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) static int test_s_mp_karatsuba_mul(void) { mp_int a, b, c, d; int size, err; if ((err = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { goto LTM_ERR; } for (size = MP_KARATSUBA_MUL_CUTOFF; size < MP_KARATSUBA_MUL_CUTOFF + 20; size++) { if ((err = mp_rand(&a, size)) != MP_OKAY) { goto LTM_ERR; } if ((err = mp_rand(&b, size)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_karatsuba_mul(&a, &b, &c)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_mul(&a,&b,&d)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&c, &d) != MP_EQ) { fprintf(stderr, "Karatsuba multiplication failed at size %d\n", size); goto LTM_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_s_mp_karatsuba_sqr(void) { mp_int a, b, c; int size, err; if ((err = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { goto LTM_ERR; } for (size = MP_KARATSUBA_SQR_CUTOFF; size < MP_KARATSUBA_SQR_CUTOFF + 20; size++) { if ((err = mp_rand(&a, size)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_karatsuba_sqr(&a, &b)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_sqr(&a, &c)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&b, &c) != MP_EQ) { fprintf(stderr, "Karatsuba squaring failed at size %d\n", size); goto LTM_ERR; } } mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } static int test_s_mp_toom_mul(void) { mp_int a, b, c, d; int size, err; if ((err = mp_init_multi(&a, &b, &c, &d, NULL)) != MP_OKAY) { goto LTM_ERR; } for (size = MP_TOOM_MUL_CUTOFF; size < MP_TOOM_MUL_CUTOFF + 20; size++) { if ((err = mp_rand(&a, size)) != MP_OKAY) { goto LTM_ERR; } if ((err = mp_rand(&b, size)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_toom_mul(&a, &b, &c)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_mul(&a,&b,&d)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&c, &d) != MP_EQ) { fprintf(stderr, "Toom-Cook 3-way multiplication failed at size %d\n", size); goto LTM_ERR; } } mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, &c, &d, NULL); return EXIT_FAILURE; } static int test_s_mp_toom_sqr(void) { mp_int a, b, c; int size, err; if ((err = mp_init_multi(&a, &b, &c, NULL)) != MP_OKAY) { goto LTM_ERR; } for (size = MP_TOOM_SQR_CUTOFF; size < MP_TOOM_SQR_CUTOFF + 20; size++) { if ((err = mp_rand(&a, size)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_toom_sqr(&a, &b)) != MP_OKAY) { goto LTM_ERR; } if ((err = s_mp_sqr(&a, &c)) != MP_OKAY) { goto LTM_ERR; } if (mp_cmp(&b, &c) != MP_EQ) { fprintf(stderr, "Toom-Cook 3-way squaring failed at size %d\n", size); goto LTM_ERR; } } mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LTM_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } int unit_tests(int argc, char **argv) { static const struct { const char *name; int (*fn)(void); } test[] = { #define T(n) { #n, test_##n } T(trivial_stuff), T(mp_cnt_lsb), T(mp_complement), T(mp_decr), T(mp_div_3), T(mp_dr_reduce), T(mp_fread_fwrite), T(mp_get_int), T(mp_get_long), T(mp_get_long_long), T(mp_ilogb), T(mp_incr), T(mp_invmod), T(mp_is_square), T(mp_kronecker), T(mp_montgomery_reduce), T(mp_n_root), T(mp_prime_is_prime), T(mp_prime_rand), T(mp_rand), T(mp_read_radix), T(mp_reduce_2k), T(mp_reduce_2k_l), T(mp_set_double), T(mp_sqrt), T(mp_sqrtmod_prime), T(mp_tc_and), T(mp_tc_div_2d), T(mp_tc_or), T(mp_tc_xor), T(s_mp_balance_mul), T(s_mp_jacobi), T(s_mp_karatsuba_mul), T(s_mp_karatsuba_sqr), T(s_mp_toom_mul), T(s_mp_toom_sqr) #undef T }; unsigned long i; int res = EXIT_SUCCESS, j; s_mp_rand_jenkins_init((uint64_t)time(NULL)); mp_rand_source(s_mp_rand_jenkins); for (i = 0; i < sizeof(test) / sizeof(test[0]); ++i) { if (argc > 1) { for (j = 1; j < argc; ++j) { if (strstr(test[i].name, argv[j]) != NULL) { break; } } if (j == argc) continue; } printf("TEST %s\n\n", test[i].name); if (test[i].fn() != EXIT_SUCCESS) { printf("\n\nFAIL %s\n\n", test[i].name); res = EXIT_FAILURE; break; } printf("\n\n"); } return res; }