#include #include /* * Configuration */ #ifndef LTM_DEMO_TEST_VS_MTEST #define LTM_DEMO_TEST_VS_MTEST 1 #endif #ifndef LTM_DEMO_TEST_REDUCE_2K_L /* This test takes a moment so we disable it by default, but it can be: * 0 to disable testing * 1 to make the test with P = 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF * 2 to make the test with P = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F */ #define LTM_DEMO_TEST_REDUCE_2K_L 0 #endif #ifdef LTM_DEMO_REAL_RAND #define LTM_DEMO_RAND_SEED time(NULL) #else #define LTM_DEMO_RAND_SEED 23 #endif #include "tommath.h" static void ndraw(mp_int *a, const char *name) { char buf[16000]; printf("%s: ", name); mp_toradix(a, buf, 10); printf("%s\n", buf); mp_toradix(a, buf, 16); printf("0x%s\n", buf); } #if LTM_DEMO_TEST_VS_MTEST static void draw(mp_int *a) { ndraw(a, ""); } #endif #if defined(LTM_DEMO_REAL_RAND) && !defined(_WIN32) static FILE *fd_urandom; #endif #if LTM_DEMO_TEST_VS_MTEST == 0 static int myrng(unsigned char *dst, int len, void *dat) { int x; (void)dat; #if defined(LTM_DEMO_REAL_RAND) if (!fd_urandom) { # if !defined(_WIN32) fprintf(stderr, "\nno /dev/urandom\n"); # endif } else { return fread(dst, 1uL, len, fd_urandom); } #endif for (x = 0; x < len;) { unsigned int r = (unsigned int)rand(); do { dst[x++] = r & 0xFFu; r >>= 8; } while ((r != 0u) && (x < len)); } return len; } #endif #if LTM_DEMO_TEST_VS_MTEST != 0 static void _panic(int l) { fprintf(stderr, "\n%d: fgets failed\n", l); exit(EXIT_FAILURE); } #endif #define FGETS(str, size, stream) \ { \ char *ret = fgets(str, size, stream); \ if (!ret) { _panic(__LINE__); } \ } static mp_int a, b, c, d, e, f; static void _cleanup(void) { mp_clear_multi(&a, &b, &c, &d, &e, &f, NULL); printf("\n"); #ifdef LTM_DEMO_REAL_RAND if (fd_urandom) fclose(fd_urandom); #endif } #if LTM_DEMO_TEST_VS_MTEST == 0 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 } }; struct mp_jacobi_st { unsigned long n; int c[16]; }; static struct 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 } }, }; 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 } } }; #endif #if LTM_DEMO_TEST_VS_MTEST != 0 static char cmd[4096]; #endif static char buf[4096]; int main(void) { unsigned rr; int cnt, ix; #if LTM_DEMO_TEST_VS_MTEST unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n; #else unsigned long s, t; long k, m; unsigned long long q, r; mp_digit mp; int i, n, err, should; #endif if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY) return EXIT_FAILURE; atexit(_cleanup); #if defined(LTM_DEMO_REAL_RAND) if (!fd_urandom) { fd_urandom = fopen("/dev/urandom", "r"); if (!fd_urandom) { # if !defined(_WIN32) fprintf(stderr, "\ncould not open /dev/urandom\n"); # endif } } #endif srand(LTM_DEMO_RAND_SEED); #ifdef MP_8BIT printf("Digit size 8 Bit \n"); #endif #ifdef MP_16BIT printf("Digit size 16 Bit \n"); #endif #ifdef MP_32BIT printf("Digit size 32 Bit \n"); #endif #ifdef MP_64BIT printf("Digit size 64 Bit \n"); #endif printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit)); printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word)); printf("DIGIT_BIT: %d\n", DIGIT_BIT); printf("MP_PREC: %d\n", MP_PREC); #if LTM_DEMO_TEST_VS_MTEST == 0 /* trivial stuff */ /* a: 0->5 */ mp_set_int(&a, 5); /* a: 5-> b: -5 */ mp_neg(&a, &b); if (mp_cmp(&a, &b) != MP_GT) { return EXIT_FAILURE; } if (mp_cmp(&b, &a) != MP_LT) { return EXIT_FAILURE; } /* a: 5-> a: -5 */ mp_neg(&a, &a); if (mp_cmp(&b, &a) != MP_EQ) { return EXIT_FAILURE; } /* a: -5-> b: 5 */ mp_abs(&a, &b); if (mp_isneg(&b) != MP_NO) { return EXIT_FAILURE; } /* a: -5-> b: -4 */ mp_add_d(&a, 1uL, &b); if (mp_isneg(&b) != MP_YES) { return EXIT_FAILURE; } if (mp_get_int(&b) != 4) { return EXIT_FAILURE; } /* a: -5-> b: 1 */ mp_add_d(&a, 6uL, &b); if (mp_get_int(&b) != 1) { return EXIT_FAILURE; } /* a: -5-> a: 1 */ mp_add_d(&a, 6uL, &a); if (mp_get_int(&a) != 1) { return EXIT_FAILURE; } mp_zero(&a); /* a: 0-> a: 6 */ mp_add_d(&a, 6uL, &a); if (mp_get_int(&a) != 6) { return EXIT_FAILURE; } mp_set_int(&a, 42); mp_set_int(&b, 1); mp_neg(&b, &b); mp_set_int(&c, 1); mp_exptmod(&a, &b, &c, &d); mp_set_int(&c, 7); mp_exptmod(&a, &b, &c, &d); mp_set_int(&a, 0); mp_set_int(&b, 1); if ((err = mp_jacobi(&a, &b, &i)) != MP_OKAY) { printf("Failed executing mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err)); return EXIT_FAILURE; } if (i != 1) { printf("Failed trivial mp_jacobi(0 | 1) %d != 1\n", i); return EXIT_FAILURE; } 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, 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 = mp_jacobi(&a, &b, &i)) != should) { printf("Failed executing mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err)); return EXIT_FAILURE; } if (err == MP_OKAY && i != jacobi[cnt].c[n + 5]) { printf("Failed trivial mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]); return EXIT_FAILURE; } } } mp_set_int(&a, 0); mp_set_int(&b, 1u); if ((err = mp_kronecker(&a, &b, &i)) != MP_OKAY) { printf("Failed executing mp_kronecker(0 | 1) %s.\n", mp_error_to_string(err)); return EXIT_FAILURE; } if (i != 1) { printf("Failed trivial mp_kronecker(0 | 1) %d != 1\n", i); return EXIT_FAILURE; } 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)); return EXIT_FAILURE; } 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]); return EXIT_FAILURE; } } } /* test mp_complement */ printf("\n\nTesting: mp_complement"); for (i = 0; i < 1000; ++i) { int l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&a, labs(l)); if (l < 0) mp_neg(&a, &a); mp_complement(&a, &b); l = ~l; mp_set_int(&c, labs(l)); if (l < 0) mp_neg(&c, &c); if (mp_cmp(&b, &c) != MP_EQ) { printf("\nmp_complement() bad result!"); return EXIT_FAILURE; } } /* test mp_tc_div_2d */ printf("\n\nTesting: mp_tc_div_2d"); for (i = 0; i < 1000; ++i) { int l, em; l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&a, labs(l)); if (l < 0) mp_neg(&a, &a); em = rand() % 32; mp_set_int(&d, labs(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!"); return EXIT_FAILURE; } } /* test mp_tc_xor */ printf("\n\nTesting: mp_tc_xor"); for (i = 0; i < 1000; ++i) { int l, em; l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&a, labs(l)); if (l < 0) mp_neg(&a, &a); em = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&b, labs(em)); if (em < 0) mp_neg(&b, &b); mp_set_int(&d, labs(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!"); return EXIT_FAILURE; } } /* test mp_tc_or */ printf("\n\nTesting: mp_tc_or"); for (i = 0; i < 1000; ++i) { int l, em; l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&a, labs(l)); if (l < 0) mp_neg(&a, &a); em = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&b, labs(em)); if (em < 0) mp_neg(&b, &b); mp_set_int(&d, labs(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!"); return EXIT_FAILURE; } } /* test mp_tc_and */ printf("\n\nTesting: mp_tc_and"); for (i = 0; i < 1000; ++i) { int l, em; l = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&a, labs(l)); if (l < 0) mp_neg(&a, &a); em = (rand() * rand() + 1) * (rand() % 1 ? -1 : 1); mp_set_int(&b, labs(em)); if (em < 0) mp_neg(&b, &b); mp_set_int(&d, labs(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!"); return EXIT_FAILURE; } } /* mp_invmod corner-case of https://github.com/libtom/libtommath/issues/118 */ printf("\n\nTesting: mp_invmod"); { 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!"); return EXIT_FAILURE; } if (mp_read_radix(&b, b_, 16) != MP_OKAY) { printf("\nmp_read_radix(b) failed!"); return EXIT_FAILURE; } if (mp_read_radix(&c, should_, 16) != MP_OKAY) { printf("\nmp_read_radix(should) failed!"); return EXIT_FAILURE; } if (mp_invmod(&a, &b, &d) != MP_OKAY) { printf("\nmp_invmod() failed!"); return EXIT_FAILURE; } if (mp_cmp(&c, &d) != MP_EQ) { printf("\nmp_invmod() bad result!"); return EXIT_FAILURE; } } /* test mp_get_double/mp_set_double */ #if defined(__STDC_IEC_559__) || defined(__GCC_IEC_559) printf("\n\nTesting: mp_get_double"); if (mp_set_double(&a, +1.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for +inf"); return EXIT_FAILURE; } if (mp_set_double(&a, -1.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for -inf"); return EXIT_FAILURE; } if (mp_set_double(&a, +0.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for NaN"); return EXIT_FAILURE; } if (mp_set_double(&a, -0.0/0.0) != MP_VAL) { printf("\nmp_set_double should return MP_VAL for NaN"); return EXIT_FAILURE; } for (i = 0; i < 1000; ++i) { int tmp = rand(); double dbl = (double)tmp * rand() + 1; if (mp_set_double(&a, dbl) != MP_OKAY) { printf("\nmp_set_double() failed"); return EXIT_FAILURE; } if (dbl != mp_get_double(&a)) { printf("\nmp_get_double() bad result!"); return EXIT_FAILURE; } if (mp_set_double(&a, -dbl) != MP_OKAY) { printf("\nmp_set_double() failed"); return EXIT_FAILURE; } if (-dbl != mp_get_double(&a)) { printf("\nmp_get_double() bad result!"); return EXIT_FAILURE; } } #endif /* test mp_get_int */ printf("\n\nTesting: mp_get_int"); for (i = 0; i < 1000; ++i) { t = (unsigned long)(rand() * rand() + 1) & 0xFFFFFFFFuL; mp_set_int(&a, t); if (t != mp_get_int(&a)) { printf("\nmp_get_int() bad result!"); return EXIT_FAILURE; } } mp_set_int(&a, 0); if (mp_get_int(&a) != 0) { printf("\nmp_get_int() bad result!"); return EXIT_FAILURE; } mp_set_int(&a, 0xFFFFFFFFuL); if (mp_get_int(&a) != 0xFFFFFFFFuL) { printf("\nmp_get_int() bad result!"); return EXIT_FAILURE; } printf("\n\nTesting: mp_get_long\n"); for (i = 0; i < (int)(sizeof(unsigned long)*CHAR_BIT) - 1; ++i) { t = (1ULL << (i+1)) - 1; if (!t) t = -1; printf(" t = 0x%lx i = %d\r", t, i); do { if (mp_set_long(&a, t) != MP_OKAY) { printf("\nmp_set_long() error!"); return EXIT_FAILURE; } s = mp_get_long(&a); if (s != t) { printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t); return EXIT_FAILURE; } t <<= 1; } while (t); } printf("\n\nTesting: mp_get_long_long\n"); for (i = 0; i < (int)(sizeof(unsigned long long)*CHAR_BIT) - 1; ++i) { r = (1ULL << (i+1)) - 1; if (!r) r = -1; printf(" r = 0x%llx i = %d\r", r, i); do { if (mp_set_long_long(&a, r) != MP_OKAY) { printf("\nmp_set_long_long() error!"); return EXIT_FAILURE; } q = mp_get_long_long(&a); if (q != r) { printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r); return EXIT_FAILURE; } r <<= 1; } while (r); } /* test mp_sqrt */ printf("\n\nTesting: mp_sqrt\n"); for (i = 0; i < 1000; ++i) { printf("%6d\r", i); fflush(stdout); n = (rand() & 15) + 1; mp_rand(&a, n); if (mp_sqrt(&a, &b) != MP_OKAY) { printf("\nmp_sqrt() error!"); return EXIT_FAILURE; } mp_n_root_ex(&a, 2, &c, 0); mp_n_root_ex(&a, 2, &d, 1); if (mp_cmp_mag(&c, &d) != MP_EQ) { printf("\nmp_n_root_ex() bad result!"); return EXIT_FAILURE; } if (mp_cmp_mag(&b, &c) != MP_EQ) { printf("mp_sqrt() bad result!\n"); return EXIT_FAILURE; } } printf("\n\nTesting: mp_is_square\n"); for (i = 0; i < 1000; ++i) { printf("%6d\r", i); fflush(stdout); /* test mp_is_square false negatives */ n = (rand() & 7) + 1; mp_rand(&a, n); mp_sqr(&a, &a); if (mp_is_square(&a, &n) != MP_OKAY) { printf("\nfn:mp_is_square() error!"); return EXIT_FAILURE; } if (n == 0) { printf("\nfn:mp_is_square() bad result!"); return EXIT_FAILURE; } /* test for false positives */ mp_add_d(&a, 1uL, &a); if (mp_is_square(&a, &n) != MP_OKAY) { printf("\nfp:mp_is_square() error!"); return EXIT_FAILURE; } if (n == 1) { printf("\nfp:mp_is_square() bad result!"); return EXIT_FAILURE; } } printf("\n\n"); /* 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)); return EXIT_FAILURE; } if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) { printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1)); ndraw(&c, "r"); 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_random_ex(&a, 8, ix, (rand() & 1) ? 0 : LTM_PRIME_2MSB_ON, myrng, NULL); if (err != MP_OKAY) { printf("failed with err code %d\n", err); return EXIT_FAILURE; } if (mp_count_bits(&a) != ix) { printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); return EXIT_FAILURE; } } printf("\n"); /* 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, 8, &cnt); if (cnt == MP_YES) { printf("Arnault's pseudoprime is not prime but mp_prime_is_prime says it is.\n"); return EXIT_FAILURE; } /* About the same size as Arnault's pseudoprime */ puts("Testing mp_prime_is_prime() with certified prime 2^1119 + 53\n"); mp_set(&a,1u); mp_mul_2d(&a,1119,&a); mp_add_d(&a,53,&a); mp_prime_is_prime(&a, 8, &cnt); if (cnt == MP_NO) { printf("A certified prime is a prime but mp_prime_is_prime says it not.\n"); return EXIT_FAILURE; } for (ix = 16; ix < 128; ix++) { printf("Testing ( safe-prime): %9d bits \r", ix); fflush(stdout); err = mp_prime_random_ex( &a, 8, ix, ((rand() & 1) ? 0 : LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE, myrng, NULL); if (err != MP_OKAY) { printf("failed with err code %d\n", err); return EXIT_FAILURE; } if (mp_count_bits(&a) != ix) { printf("Prime is %d not %d bits!!!\n", mp_count_bits(&a), ix); return EXIT_FAILURE; } /* let's see if it's really a safe prime */ mp_sub_d(&a, 1uL, &a); mp_div_2(&a, &a); mp_prime_is_prime(&a, 8, &cnt); if (cnt != MP_YES) { printf("sub is not prime!\n"); return EXIT_FAILURE; } } printf("\n\n"); /* test montgomery */ printf("Testing: montgomery...\n"); 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()) % (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"); return EXIT_FAILURE; /* *INDENT-ON* */ } /* only one big montgomery reduction */ if (i > 10) { n = 1000; ix = 100; } } } } printf("\n\n"); 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 /* test mp_cnt_lsb */ printf("\n\nTesting: mp_cnt_lsb"); 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)); return EXIT_FAILURE; } mp_mul_2(&a, &a); } /* test mp_reduce_2k */ printf("\n\nTesting: mp_reduce_2k\n"); 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 / DIGIT_BIT + 1) * 2); mp_copy(&c, &b); mp_mod(&c, &a, &c); mp_reduce_2k(&b, &a, 2uL); if (mp_cmp(&c, &b)) { printf("FAILED\n"); return EXIT_FAILURE; } } } /* test mp_div_3 */ printf("\n\nTesting: mp_div_3...\n"); 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()) % 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"); } } printf("\nPassed div_3 testing"); /* test the DR reduction */ printf("\n\nTesting: mp_dr_reduce...\n"); 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); return EXIT_FAILURE; } } while (++rr < 500); printf(" passed"); fflush(stdout); } # if LTM_DEMO_TEST_REDUCE_2K_L /* 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"); return EXIT_FAILURE; } 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); return EXIT_FAILURE; } } printf("...Passed\n"); # endif /* LTM_DEMO_TEST_REDUCE_2K_L */ #else div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n = sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = add_d_n = sub_d_n = 0; /* force KARA and TOOM to enable despite cutoffs */ KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8; TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16; for (;;) { /* randomly clear and re-init one variable, this has the affect of triming the alloc space */ switch (abs(rand()) % 7) { case 0: mp_clear(&a); mp_init(&a); break; case 1: mp_clear(&b); mp_init(&b); break; case 2: mp_clear(&c); mp_init(&c); break; case 3: mp_clear(&d); mp_init(&d); break; case 4: mp_clear(&e); mp_init(&e); break; case 5: mp_clear(&f); mp_init(&f); break; case 6: break; /* don't clear any */ } printf("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ", add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n, expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n); FGETS(cmd, 4095, stdin); cmd[strlen(cmd) - 1u] = '\0'; printf("%-6s ]\r", cmd); fflush(stdout); if (strcmp(cmd, "mul2d") == 0) { ++mul2d_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); sscanf(buf, "%u", &rr); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_mul_2d(&a, rr, &a); a.sign = b.sign; if (mp_cmp(&a, &b) != MP_EQ) { printf("mul2d failed, rr == %u\n", rr); draw(&a); draw(&b); return EXIT_FAILURE; } } else if (strcmp(cmd, "div2d") == 0) { ++div2d_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); sscanf(buf, "%u", &rr); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_div_2d(&a, rr, &a, &e); a.sign = b.sign; if ((a.used == b.used) && (a.used == 0)) { a.sign = b.sign = MP_ZPOS; } if (mp_cmp(&a, &b) != MP_EQ) { printf("div2d failed, rr == %u\n", rr); draw(&a); draw(&b); return EXIT_FAILURE; } } else if (strcmp(cmd, "add") == 0) { ++add_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); mp_copy(&a, &d); mp_add(&d, &b, &d); if (mp_cmp(&c, &d) != MP_EQ) { printf("add %lu failure!\n", add_n); draw(&a); draw(&b); draw(&c); draw(&d); return EXIT_FAILURE; } /* test the sign/unsigned storage functions */ rr = mp_signed_bin_size(&c); mp_to_signed_bin(&c, (unsigned char *) cmd); memset(cmd + rr, rand() & 0xFFu, sizeof(cmd) - rr); mp_read_signed_bin(&d, (unsigned char *) cmd, rr); if (mp_cmp(&c, &d) != MP_EQ) { printf("mp_signed_bin failure!\n"); draw(&c); draw(&d); return EXIT_FAILURE; } rr = mp_unsigned_bin_size(&c); mp_to_unsigned_bin(&c, (unsigned char *) cmd); memset(cmd + rr, rand() & 0xFFu, sizeof(cmd) - rr); mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr); if (mp_cmp_mag(&c, &d) != MP_EQ) { printf("mp_unsigned_bin failure!\n"); draw(&c); draw(&d); return EXIT_FAILURE; } } else if (strcmp(cmd, "sub") == 0) { ++sub_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); mp_copy(&a, &d); mp_sub(&d, &b, &d); if (mp_cmp(&c, &d) != MP_EQ) { printf("sub %lu failure!\n", sub_n); draw(&a); draw(&b); draw(&c); draw(&d); return EXIT_FAILURE; } } else if (strcmp(cmd, "mul") == 0) { ++mul_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); mp_copy(&a, &d); mp_mul(&d, &b, &d); if (mp_cmp(&c, &d) != MP_EQ) { printf("mul %lu failure!\n", mul_n); draw(&a); draw(&b); draw(&c); draw(&d); return EXIT_FAILURE; } } else if (strcmp(cmd, "div") == 0) { ++div_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&d, buf, 64); mp_div(&a, &b, &e, &f); if ((mp_cmp(&c, &e) != MP_EQ) || (mp_cmp(&d, &f) != MP_EQ)) { printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e), mp_cmp(&d, &f)); draw(&a); draw(&b); draw(&c); draw(&d); draw(&e); draw(&f); return EXIT_FAILURE; } } else if (strcmp(cmd, "sqr") == 0) { ++sqr_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_copy(&a, &c); mp_sqr(&c, &c); if (mp_cmp(&b, &c) != MP_EQ) { printf("sqr %lu failure!\n", sqr_n); draw(&a); draw(&b); draw(&c); return EXIT_FAILURE; } } else if (strcmp(cmd, "gcd") == 0) { ++gcd_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); mp_copy(&a, &d); mp_gcd(&d, &b, &d); d.sign = c.sign; if (mp_cmp(&c, &d) != MP_EQ) { printf("gcd %lu failure!\n", gcd_n); draw(&a); draw(&b); draw(&c); draw(&d); return EXIT_FAILURE; } } else if (strcmp(cmd, "lcm") == 0) { ++lcm_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); mp_copy(&a, &d); mp_lcm(&d, &b, &d); d.sign = c.sign; if (mp_cmp(&c, &d) != MP_EQ) { printf("lcm %lu failure!\n", lcm_n); draw(&a); draw(&b); draw(&c); draw(&d); return EXIT_FAILURE; } } else if (strcmp(cmd, "expt") == 0) { ++expt_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&d, buf, 64); mp_copy(&a, &e); mp_exptmod(&e, &b, &c, &e); if (mp_cmp(&d, &e) != MP_EQ) { printf("expt %lu failure!\n", expt_n); draw(&a); draw(&b); draw(&c); draw(&d); draw(&e); return EXIT_FAILURE; } } else if (strcmp(cmd, "invmod") == 0) { ++inv_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&c, buf, 64); mp_invmod(&a, &b, &d); mp_mulmod(&d, &a, &b, &e); if (mp_cmp_d(&e, 1uL) != MP_EQ) { printf("inv [wrong value from MPI?!] failure\n"); draw(&a); draw(&b); draw(&c); draw(&d); draw(&e); mp_gcd(&a, &b, &e); draw(&e); return EXIT_FAILURE; } } else if (strcmp(cmd, "div2") == 0) { ++div2_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_div_2(&a, &c); if (mp_cmp(&c, &b) != MP_EQ) { printf("div_2 %lu failure\n", div2_n); draw(&a); draw(&b); draw(&c); return EXIT_FAILURE; } } else if (strcmp(cmd, "mul2") == 0) { ++mul2_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_mul_2(&a, &c); if (mp_cmp(&c, &b) != MP_EQ) { printf("mul_2 %lu failure\n", mul2_n); draw(&a); draw(&b); draw(&c); return EXIT_FAILURE; } } else if (strcmp(cmd, "add_d") == 0) { ++add_d_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); sscanf(buf, "%d", &ix); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_add_d(&a, ix, &c); if (mp_cmp(&b, &c) != MP_EQ) { printf("add_d %lu failure\n", add_d_n); draw(&a); draw(&b); draw(&c); printf("d == %d\n", ix); return EXIT_FAILURE; } } else if (strcmp(cmd, "sub_d") == 0) { ++sub_d_n; FGETS(buf, 4095, stdin); mp_read_radix(&a, buf, 64); FGETS(buf, 4095, stdin); sscanf(buf, "%d", &ix); FGETS(buf, 4095, stdin); mp_read_radix(&b, buf, 64); mp_sub_d(&a, ix, &c); if (mp_cmp(&b, &c) != MP_EQ) { printf("sub_d %lu failure\n", sub_d_n); draw(&a); draw(&b); draw(&c); printf("d == %d\n", ix); return EXIT_FAILURE; } } else if (strcmp(cmd, "exit") == 0) { printf("\nokay, exiting now\n"); break; } } #endif return 0; } /* ref: $Format:%D$ */ /* git commit: $Format:%H$ */ /* commit time: $Format:%ai$ */