#include #include "shared.h" #define S_MP_RAND_JENKINS_C #include "s_mp_rand_jenkins.c" static long rand_long(void) { long x; if (s_mp_rand_jenkins(&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_jenkins(&x, sizeof(x)) != MP_OKAY) { fprintf(stderr, "s_mp_rand_source failed\n"); exit(EXIT_FAILURE); } return x; } static int32_t rand_int32(void) { int32_t x; if (s_mp_rand_jenkins(&x, sizeof(x)) != MP_OKAY) { fprintf(stderr, "s_mp_rand_source failed\n"); exit(EXIT_FAILURE); } return x; } static int64_t rand_int64(void) { int64_t x; if (s_mp_rand_jenkins(&x, sizeof(x)) != MP_OKAY) { fprintf(stderr, "s_mp_rand_source failed\n"); exit(EXIT_FAILURE); } return x; } static uint32_t uabs32(int32_t x) { return (x > 0) ? (uint32_t)x : -(uint32_t)x; } static uint64_t uabs64(int64_t x) { return (x > 0) ? (uint64_t)x : -(uint64_t)x; } /* This function prototype is needed * to test dead code elimination * which is used for feature detection. * * If the feature detection does not * work as desired we will get a linker error. */ void does_not_exist(void); static int test_feature_detection(void) { #define TEST_FEATURE1_C if (!MP_HAS(TEST_FEATURE1)) { does_not_exist(); return EXIT_FAILURE; } #define TEST_FEATURE2_C 1 if (MP_HAS(TEST_FEATURE2)) { does_not_exist(); return EXIT_FAILURE; } #define TEST_FEATURE3_C 0 if (MP_HAS(TEST_FEATURE3)) { does_not_exist(); return EXIT_FAILURE; } #define TEST_FEATURE4_C something if (MP_HAS(TEST_FEATURE4)) { does_not_exist(); return EXIT_FAILURE; } if (MP_HAS(TEST_FEATURE5)) { does_not_exist(); return EXIT_FAILURE; } return EXIT_SUCCESS; } static int test_trivial_stuff(void) { mp_int a, b, c, d; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); EXPECT(mp_error_to_string(MP_OKAY) != NULL); /* a: 0->5 */ mp_set(&a, 5u); /* a: 5-> b: -5 */ DO(mp_neg(&a, &b)); EXPECT(mp_cmp(&a, &b) == MP_GT); EXPECT(mp_cmp(&b, &a) == MP_LT); EXPECT(mp_isneg(&b)); /* a: 5-> a: -5 */ DO(mp_neg(&a, &a)); EXPECT(mp_cmp(&b, &a) == MP_EQ); EXPECT(mp_isneg(&a)); /* a: -5-> b: 5 */ DO(mp_abs(&a, &b)); EXPECT(!mp_isneg(&b)); /* a: -5-> b: -4 */ DO(mp_add_d(&a, 1u, &b)); EXPECT(mp_isneg(&b)); EXPECT(mp_get_i32(&b) == -4); EXPECT(mp_get_u32(&b) == (uint32_t)-4); EXPECT(mp_get_mag_u32(&b) == 4); /* a: -5-> b: 1 */ DO(mp_add_d(&a, 6u, &b)); EXPECT(mp_get_u32(&b) == 1); /* a: -5-> a: 1 */ DO(mp_add_d(&a, 6u, &a)); EXPECT(mp_get_u32(&a) == 1); mp_zero(&a); /* a: 0-> a: 6 */ DO(mp_add_d(&a, 6u, &a)); EXPECT(mp_get_u32(&a) == 6); mp_set(&a, 42u); mp_set(&b, 1u); DO(mp_neg(&b, &b)); mp_set(&c, 1u); DO(mp_exptmod(&a, &b, &c, &d)); mp_set(&c, 7u); /* same here */ EXPECT(mp_exptmod(&a, &b, &c, &d) != MP_OKAY); EXPECT(mp_iseven(&a) != mp_isodd(&a)); 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_hash(void) { mp_int a; mp_hval hash; int i; int len = 5; const char *input[] = { "0", "///////////////////////////////////////////////////////////////////", "4n9cbk886QtLQmofprid3l2Q0GD8Yv979Lh8BdZkFE8g2pDUUSMBET/+M/YFyVZ3mBp", "5NlgzHhmIX05O5YoW5yW5reAlVNtRAlIcN2dfoATnNdc1Cw5lHZUTwNthmK6/ZLKfY6", "3gweiHDX+ji5utraSe46IJX+uuh7iggs63xIpMP5MriU4Np+LpHI5are8RzS9pKh9xP" }; const mp_hval hvals[] = { #if (MP_DIGIT_BIT == 15) 0x50c5d1f, 0x51b3ba04, 0xf83febd7, 0x2dc8624c, 0xf5c2996b #elif (MP_DIGIT_BIT == 60) 0xaf63bd4c8601b7df, 0xdb090f8a5cd75210, 0xabae35c7872c107d, 0xfec74888bcef5fcd, 0x27ba96030abceda5 #elif (MP_DIGIT_BIT == 31) 0xaf63bd4c8601b7df, 0xec1be1c4749a7b86, 0x138ac13639116f2e, 0xdd317b32ac9dd90f, 0x6f87eaac03140738 #else 0xaf63bd4c8601b7df, 0x7e868fbf541faf44, 0x420cca3a4cb623bb, 0x16636d996304ee7f, 0x33afc9f1b274fa67 #endif }; DOR(mp_init(&a)); for (i = 0; i < len; ++i) { DO(mp_read_radix(&a, input[i], 64)); DO(mp_hash(&a, &hash)); EXPECT(hash == hvals[i]); } mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } static int check_get_set_i32(mp_int *a, int32_t b) { mp_clear(a); DO(mp_shrink(a)); mp_set_i32(a, b); DO(mp_shrink(a)); EXPECT(mp_get_i32(a) == b); EXPECT(mp_get_u32(a) == (uint32_t)b); EXPECT(mp_get_mag_u32(a) == uabs32(b)); mp_set_u32(a, (uint32_t)b); EXPECT(mp_get_u32(a) == (uint32_t)b); EXPECT(mp_get_i32(a) == (int32_t)(uint32_t)b); return EXIT_SUCCESS; LBL_ERR: return EXIT_FAILURE; } static int test_mp_get_set_i32(void) { int i; mp_int a; DOR(mp_init(&a)); check_get_set_i32(&a, 0); check_get_set_i32(&a, -1); check_get_set_i32(&a, 1); check_get_set_i32(&a, INT32_MIN); check_get_set_i32(&a, INT32_MAX); for (i = 0; i < 1000; ++i) { int32_t b = rand_int32(); EXPECT(check_get_set_i32(&a, b) == EXIT_SUCCESS); } mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } static int check_get_set_i64(mp_int *a, int64_t b) { mp_clear(a); if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE; mp_set_i64(a, b); if (mp_shrink(a) != MP_OKAY) return EXIT_FAILURE; if (mp_get_i64(a) != b) return EXIT_FAILURE; if (mp_get_u64(a) != (uint64_t)b) return EXIT_FAILURE; if (mp_get_mag_u64(a) != uabs64(b)) return EXIT_FAILURE; mp_set_u64(a, (uint64_t)b); if (mp_get_u64(a) != (uint64_t)b) return EXIT_FAILURE; if (mp_get_i64(a) != (int64_t)(uint64_t)b) return EXIT_FAILURE; return EXIT_SUCCESS; } static int test_mp_get_set_i64(void) { int i; mp_int a; DOR(mp_init(&a)); check_get_set_i64(&a, 0); check_get_set_i64(&a, -1); check_get_set_i64(&a, 1); check_get_set_i64(&a, INT64_MIN); check_get_set_i64(&a, INT64_MAX); for (i = 0; i < 1000; ++i) { int64_t b = rand_int64(); if (check_get_set_i64(&a, b) != EXIT_SUCCESS) { goto LBL_ERR; } } mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } static int test_mp_fread_fwrite(void) { mp_int a, b; FILE *tmp = NULL; DOR(mp_init_multi(&a, &b, NULL)); mp_set_ul(&a, 123456uL); tmp = tmpfile(); DO(mp_fwrite(&a, 64, tmp)); rewind(tmp); DO(mp_fread(&b, 64, tmp)); EXPECT(mp_get_u32(&b) == 123456uL); 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 e = MP_OKAY; DOR(mp_init_multi(&a, &b, NULL)); mp_rand_source(very_random_source); for (n = 1; n < 1024; ++n) { DO(mp_rand(&a, n)); DO(mp_incr(&a)); DO(mp_div_2d(&a, n * MP_DIGIT_BIT, &b, NULL)); if (mp_cmp_d(&b, 1u) != MP_EQ) { ndraw(&a, "mp_rand() a"); ndraw(&b, "mp_rand() b"); e = MP_ERR; break; } } LBL_ERR: mp_rand_source(s_mp_rand_jenkins); mp_clear_multi(&a, &b, NULL); return (e == MP_OKAY) ? EXIT_SUCCESS : 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_int a, b; DOR(mp_init_multi(&a, &b, NULL)); mp_set_ul(&a, 0uL); mp_set_ul(&b, 1uL); DO(mp_kronecker(&a, &b, &i)); EXPECT(i == 1); for (cnt = 0; cnt < (int)(sizeof(kronecker)/sizeof(kronecker[0])); ++cnt) { k = kronecker[cnt].n; mp_set_l(&a, k); /* only test positive values of a */ for (m = -10; m <= 10; m++) { mp_set_l(&b, m); DO(mp_kronecker(&a, &b, &i)); EXPECT(i == kronecker[cnt].c[m + 10]); } } 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; DOR(mp_init_multi(&a, &b, &c, NULL)); for (i = 0; i < 1000; ++i) { long l = rand_long(); mp_set_l(&a, l); DO(mp_complement(&a, &b)); l = ~l; mp_set_l(&c, l); EXPECT(mp_cmp(&b, &c) == MP_EQ); } 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_signed_rsh(void) { int i; mp_int a, b, d; DOR(mp_init_multi(&a, &b, &d, NULL)); for (i = 0; i < 1000; ++i) { long l; int em; l = rand_long(); mp_set_l(&a, l); em = abs(rand_int()) % 32; mp_set_l(&d, l >> em); DO(mp_signed_rsh(&a, em, &b)); EXPECT(mp_cmp(&b, &d) == MP_EQ); } 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_xor(void) { int i; mp_int a, b, c, d; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); for (i = 0; i < 1000; ++i) { long l, em; l = rand_long(); mp_set_l(&a,l); em = rand_long(); mp_set_l(&b, em); mp_set_l(&d, l ^ em); DO(mp_xor(&a, &b, &c)); EXPECT(mp_cmp(&c, &d) == MP_EQ); } 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_or(void) { int i; mp_int a, b, c, d; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); for (i = 0; i < 1000; ++i) { long l, em; l = rand_long(); mp_set_l(&a, l); em = rand_long(); mp_set_l(&b, em); mp_set_l(&d, l | em); DO(mp_or(&a, &b, &c)); EXPECT(mp_cmp(&c, &d) == MP_EQ); } 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_and(void) { int i; mp_int a, b, c, d; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); for (i = 0; i < 1000; ++i) { long l, em; l = rand_long(); mp_set_l(&a, l); em = rand_long(); mp_set_l(&b, em); mp_set_l(&d, l & em); DO(mp_and(&a, &b, &c)); EXPECT(mp_cmp(&c, &d) == MP_EQ); } 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; int i, j, k; int e; int results[21][21] = /* Table generated with Pari/GP for(i=-10,10, k=0; d=0; printf(" {"); for(j=-10,10, iferr( printf(lift(Mod(1/i, j)) ", "), k, printf("-1, ")) ); print("},") ) Changes to the output: replaced j < 1 with -1 for now and added the result of 0^(-1) mod (1) j = -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 */ { {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 8, -1 }, /* i = -10 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 3, 1, -1, 3, 7, -1, 1 }, /* -9 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 3, -1, 6, -1, 1, -1 }, /* -8 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 1, 2, 5, -1, 1, 5, 7 }, /* -7 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, -1, 1, -1, -1, -1 }, /* -6 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 3, -1, 1, 4, 3, 7, -1 }, /* -5 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 1, -1, 5, -1, 2, -1 }, /* -4 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 3, -1, 2, 5, -1, 3 }, /* -3 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 2, -1, 3, -1, 4, -1 }, /* -2 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9 }, /* -1 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1 }, /* 0 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 }, /* 1 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 2, -1, 3, -1, 4, -1, 5, -1 }, /* 2 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, -1, 3, 2, -1, 5, 3, -1, 7 }, /* 3 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 1, -1, 4, -1, 2, -1, 7, -1 }, /* 4 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 2, 1, -1, 5, 3, 5, 2, -1 }, /* 5 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, 1, -1, 6, -1, -1, -1 }, /* 6 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 3, 3, 1, -1, 7, 4, 3 }, /* 7 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 2, -1, 2, -1, 1, -1, 8, -1 }, /* 8 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, -1, 1, 4, -1, 4, 1, -1, 9 }, /* 9 */ {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 1, -1, -1, -1, 5, -1, 1, -1 } /* 10 */ }; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); /* mp_invmod corner-case of https://github.com/libtom/libtommath/issues/118 */ { const char *a_ = "47182BB8DF0FFE9F61B1F269BACC066B48BA145D35137D426328DC3F88A5EA44"; const char *b_ = "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF"; const char *should_ = "0521A82E10376F8E4FDEF9A32A427AC2A0FFF686E00290D39E3E4B5522409596"; DO(mp_read_radix(&a, a_, 16)); DO(mp_read_radix(&b, b_, 16)); DO(mp_read_radix(&c, should_, 16)); DO(mp_invmod(&a, &b, &d)); EXPECT(mp_cmp(&c, &d) == MP_EQ); } /* Some small general tests https://github.com/libtom/libtommath/issues/534 */ for (i = -10; i < 11; i++) { for (j = -10; j < 11; j++) { mp_set_i32(&a, i); mp_set_i32(&b, j); e = mp_invmod(&a, &b, &c); if (e != MP_OKAY) { if (results[i+10][j+10] != -1) { printf("error = %s from ", mp_error_to_string(e)); printf("error at i = %d, j =%d should be an error but gave ",i,j); e = mp_fwrite(&c,10,stdout); printf("\n"); goto LBL_ERR; } } else { k = mp_get_i32(&c); if (k != results[i+10][j+10]) { printf("result at i = %d, j =%d is %d but should be %d \n", i,j,k,results[i+10][j+10]); 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; } #if defined(MP_HAS_SET_DOUBLE) #ifdef _MSC_VER #pragma warning(push) #pragma warning(disable: 4723) /* potential divide by 0 */ #endif static int test_mp_set_double(void) { int i; double dbl_zero = 0.0; mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); /* test mp_get_double/mp_set_double */ EXPECT(mp_set_double(&a, +1.0/dbl_zero) == MP_VAL); EXPECT(mp_set_double(&a, -1.0/dbl_zero) == MP_VAL); EXPECT(mp_set_double(&a, +0.0/dbl_zero) == MP_VAL); EXPECT(mp_set_double(&a, -0.0/dbl_zero) == MP_VAL); for (i = 0; i < 1000; ++i) { int tmp = rand_int(); double dbl = (double)tmp * rand_int() + 1; DO(mp_set_double(&a, dbl)); EXPECT(dbl == mp_get_double(&a)); DO(mp_set_double(&a, -dbl)); EXPECT(-dbl == mp_get_double(&a)); } mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } #ifdef _MSC_VER #pragma warning(pop) #endif #endif static int test_mp_get_u32(void) { uint32_t t; int i; mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); for (i = 0; i < 1000; ++i) { t = (uint32_t)rand_long(); mp_set_ul(&a, t); EXPECT(t == mp_get_u32(&a)); } mp_set_ul(&a, 0uL); EXPECT(mp_get_u32(&a) == 0); mp_set_ul(&a, UINT32_MAX); EXPECT(mp_get_u32(&a) == UINT32_MAX); 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_ul(void) { unsigned long s, t; int i; mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); for (i = 0; i < ((int)MP_SIZEOF_BITS(unsigned long) - 1); ++i) { t = (1UL << (i+1)) - 1; if (!t) t = ~0UL; printf(" t = 0x%lx i = %d\r", t, i); do { mp_set_ul(&a, t); s = mp_get_ul(&a); EXPECT(s == t); 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_u64(void) { uint64_t q, r; int i; mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); for (i = 0; i < (int)(MP_SIZEOF_BITS(uint64_t) - 1); ++i) { r = ((uint64_t)1 << (i+1)) - 1; if (!r) r = UINT64_MAX; printf(" r = 0x%" PRIx64 " i = %d\r", r, i); do { mp_set_u64(&a, r); q = mp_get_u64(&a); EXPECT(q == r); r <<= 1; } while (r != 0u); } 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; DOR(mp_init_multi(&a, &b, &c, NULL)); for (i = 0; i < 1000; ++i) { printf("%6d\r", i); fflush(stdout); n = (rand_int() & 15) + 1; DO(mp_rand(&a, n)); DO(mp_sqrt(&a, &b)); DO(mp_root_n(&a, 2, &c)); EXPECT(mp_cmp_mag(&b, &c) == MP_EQ); } 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_is_square(void) { int i, n; mp_int a, b; bool res; DOR(mp_init_multi(&a, &b, NULL)); /* Domain is {x \in \mathbb{Z} : x \le 0} */ mp_set_l(&a, -1); EXPECT(mp_is_square(&a, &res) == MP_VAL); EXPECT(!res); /* Zero is a perfect square, too */ mp_zero(&a); DO(mp_is_square(&a, &res)); EXPECT(res); for (i = 0; i < 1000; ++i) { printf("%6d\r", i); fflush(stdout); /* test mp_is_square false negatives */ n = (rand_int() & 7) + 1; DO(mp_rand(&a, n)); DO(mp_sqr(&a, &a)); DO(mp_is_square(&a, &res)); EXPECT(res); /* test for false positives */ DO(mp_add_d(&a, 1u, &a)); DO(mp_is_square(&a, &res)); EXPECT(!res); } 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 }, /* 5 \cong 1 (mod 4) */ { 7, 9, 4 }, /* 7 \cong 3 (mod 4) */ { 113, 2, 62 } /* 113 \cong 1 (mod 4) */ }; int i; mp_int a, b, c; DOR(mp_init_multi(&a, &b, &c, NULL)); /* r^2 = n (mod p) */ for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) { mp_set_ul(&a, sqrtmod_prime[i].p); mp_set_ul(&b, sqrtmod_prime[i].n); DO(mp_sqrtmod_prime(&b, &a, &c)); EXPECT(mp_cmp_d(&c, sqrtmod_prime[i].r) == MP_EQ); } /* Check handling of wrong input (here: modulus is square and cong. 1 mod 4,24 ) */ mp_set_ul(&a, 25); mp_set_ul(&b, 2); EXPECT(mp_sqrtmod_prime(&b, &a, &c) == MP_VAL); /* b \cong 0 (mod a) */ mp_set_ul(&a, 45); mp_set_ul(&b, 3); EXPECT(mp_sqrtmod_prime(&b, &a, &c) == MP_VAL); 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_int a, b; DOR(mp_init_multi(&a, &b, NULL)); /* test for size */ for (ix = 10; ix < 128; ix++) { printf("Testing (not safe-prime): %9d bits \n", ix); fflush(stdout); DO(mp_prime_rand(&a, 8, ix, (rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON)); EXPECT(mp_count_bits(&a) == ix); } 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 e; bool cnt, fu; mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); /* strong Miller-Rabin pseudoprime to the first 200 primes (F. Arnault) */ printf("Testing mp_prime_is_prime() with Arnault's pseudoprime 803...901"); DO(mp_read_radix(&a, "91xLNF3roobhzgTzoFIG6P13ZqhOVYSN60Fa7Cj2jVR1g0k89zdahO9/kAiRprpfO1VAp1aBHucLFV/qLKLFb+zonV7R2Vxp1K13ClwUXStpV0oxTNQVjwybmFb5NBEHImZ6V7P6+udRJuH8VbMEnS0H8/pSqQrg82OoQQ2fPpAk6G1hkjqoCv5s/Yr", 64)); DO(mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt)); if (cnt) { 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 */ printf("\rTesting mp_prime_is_prime() with certified prime 2^1119 + 53 "); mp_set(&a, 1u); DO(mp_mul_2d(&a,1119,&a)); DO(mp_add_d(&a, 53u, &a)); e = mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt); /* small problem */ if (e != MP_OKAY) { printf("\nfailed with error: %s\n", mp_error_to_string(e)); } /* large problem */ if (!cnt) { printf("A certified prime is a prime but mp_prime_is_prime says it is not.\n"); } if ((e != MP_OKAY) || !cnt) { printf("prime tested was: 0x"); DO(mp_fwrite(&a,16,stdout)); putchar('\n'); goto LBL_ERR; } printf("\r "); for (ix = 16; ix < 128; ix++) { printf("\rTesting ( safe-prime): %9d bits ", ix); fflush(stdout); DO(mp_prime_rand(&a, 8, ix, ((rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON) | MP_PRIME_SAFE)); EXPECT(mp_count_bits(&a) == ix); /* let's see if it's really a safe prime */ DO(mp_sub_d(&a, 1u, &b)); DO(mp_div_2(&b, &b)); DO(mp_prime_is_prime(&b, mp_prime_rabin_miller_trials(mp_count_bits(&b)), &cnt)); /* large problem */ EXPECT(cnt); DO(mp_prime_frobenius_underwood(&b, &fu)); EXPECT(fu); if ((e != MP_OKAY) || !cnt) { printf("prime tested was: 0x"); DO(mp_fwrite(&a,16,stdout)); putchar('\n'); printf("sub tested was: 0x"); DO(mp_fwrite(&b,16,stdout)); putchar('\n'); goto LBL_ERR; } } /* Check regarding problem #143 */ DO(mp_read_radix(&a, "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF", 16)); DO(mp_prime_strong_lucas_selfridge(&a, &cnt)); /* large problem */ EXPECT(cnt); if ((e != MP_OKAY) || !cnt) { printf("prime tested was: 0x"); DO(mp_fwrite(&a,16,stdout)); putchar('\n'); 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_prime_next_prime(void) { mp_int a, b, c; DOR(mp_init_multi(&a, &b, &c, NULL)); /* edge cases */ mp_set(&a, 0u); DO(mp_prime_next_prime(&a, 5, false)); if (mp_cmp_d(&a, 2u) != MP_EQ) { printf("mp_prime_next_prime: output should have been 2 but was: "); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); goto LBL_ERR; } mp_set(&a, 0u); DO(mp_prime_next_prime(&a, 5, true)); if (mp_cmp_d(&a, 3u) != MP_EQ) { printf("mp_prime_next_prime: output should have been 3 but was: "); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); goto LBL_ERR; } mp_set(&a, 2u); DO(mp_prime_next_prime(&a, 5, false)); if (mp_cmp_d(&a, 3u) != MP_EQ) { printf("mp_prime_next_prime: output should have been 3 but was: "); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); goto LBL_ERR; } mp_set(&a, 2u); DO(mp_prime_next_prime(&a, 5, true)); if (mp_cmp_d(&a, 3u) != MP_EQ) { printf("mp_prime_next_prime: output should have been 3 but was: "); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); goto LBL_ERR; } mp_set(&a, 8u); DO(mp_prime_next_prime(&a, 5, true)); if (mp_cmp_d(&a, 11u) != MP_EQ) { printf("mp_prime_next_prime: output should have been 11 but was: "); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); goto LBL_ERR; } /* 2^300 + 157 is a 300 bit large prime to guarantee a multi-limb bigint */ DO(mp_2expt(&a, 300)); mp_set_u32(&b, 157); DO(mp_add(&a, &b, &a)); DO(mp_copy(&a, &b)); /* 2^300 + 385 is the next prime */ mp_set_u32(&c, 228); DO(mp_add(&b, &c, &b)); DO(mp_prime_next_prime(&a, 5, false)); if (mp_cmp(&a, &b) != MP_EQ) { printf("mp_prime_next_prime: output should have been\n"); DO(mp_fwrite(&b,10,stdout)); putchar('\n'); printf("but was:\n"); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); goto LBL_ERR; } /* Use another temporary variable or recompute? Mmh... */ DO(mp_2expt(&a, 300)); mp_set_u32(&b, 157); DO(mp_add(&a, &b, &a)); DO(mp_copy(&a, &b)); /* 2^300 + 631 is the next prime congruent to 3 mod 4*/ mp_set_u32(&c, 474); DO(mp_add(&b, &c, &b)); DO(mp_prime_next_prime(&a, 5, true)); if (mp_cmp(&a, &b) != MP_EQ) { printf("mp_prime_next_prime (bbs): output should have been\n"); DO(mp_fwrite(&b,10,stdout)); putchar('\n'); printf("but was:\n"); DO(mp_fwrite(&a,10,stdout)); putchar('\n'); 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_montgomery_reduce(void) { mp_digit mp; int ix, i, n; char buf[4096]; /* size_t written; */ mp_int a, b, c, d, e; DOR(mp_init_multi(&a, &b, &c, &d, &e, NULL)); /* 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++) { DO(mp_rand(&a, i)); a.dp[0] |= 1; /* let's see if R is right */ DO(mp_montgomery_calc_normalization(&b, &a)); DO(mp_montgomery_setup(&a, &mp)); /* now test a random reduction */ for (ix = 0; ix < 100; ix++) { DO(mp_rand(&c, 1 + (abs(rand_int()) % (2*i)))); DO(mp_copy(&c, &d)); DO(mp_copy(&c, &e)); DO(mp_mod(&d, &a, &d)); DO(mp_montgomery_reduce(&c, &a, mp)); DO(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"); DO(mp_to_decimal(&a, buf, sizeof(buf))); printf("a = %s\n", buf); DO(mp_to_decimal(&e, buf, sizeof(buf))); printf("e = %s\n", buf); DO(mp_to_decimal(&d, buf, sizeof(buf))); printf("d = %s\n", buf); DO(mp_to_decimal(&c, buf, sizeof(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; } } } } 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]; size_t written; mp_int a; DOR(mp_init_multi(&a, NULL)); DO(mp_read_radix(&a, "123456", 10)); DO(mp_to_radix(&a, buf, sizeof(buf), &written, 10)); printf(" '123456' a == %s, length = %zu", buf, written); /* See comment in mp_to_radix.c */ /* if( (err = mp_to_radix(&a, buf, 3u, &written, 10) ) != MP_OKAY) goto LBL_ERR; printf(" '56' a == %s, length = %zu\n", buf, written); if( (err = mp_to_radix(&a, buf, 4u, &written, 10) ) != MP_OKAY) goto LBL_ERR; printf(" '456' a == %s, length = %zu\n", buf, written); if( (err = mp_to_radix(&a, buf, 30u, &written, 10) ) != MP_OKAY) goto LBL_ERR; printf(" '123456' a == %s, length = %zu, error = %s\n", buf, written, mp_error_to_string(err)); */ DO(mp_read_radix(&a, "-123456", 10)); DO(mp_to_radix(&a, buf, sizeof(buf), &written, 10)); printf("\r '-123456' a == %s, length = %zu", buf, written); DO(mp_read_radix(&a, "0", 10)); DO(mp_to_radix(&a, buf, sizeof(buf), &written, 10)); printf("\r '0' a == %s, length = %zu", buf, written); while (0) { char *s = fgets(buf, sizeof(buf), stdin); if (s != buf) break; DO(mp_read_radix(&a, buf, 10)); DO(mp_prime_next_prime(&a, 5, true)); DO(mp_to_radix(&a, buf, sizeof(buf), NULL, 10)); printf("%s, %lu\n", buf, (unsigned long)a.dp[0] & 3uL); } mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } static int test_mp_cnt_lsb(void) { int ix; mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); mp_set(&a, 1u); for (ix = 0; ix < 1024; ix++) { EXPECT(mp_cnt_lsb(&a) == ix); DO(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; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); /* test mp_reduce_2k */ for (cnt = 3; cnt <= 128; ++cnt) { mp_digit tmp; DO(mp_2expt(&a, cnt)); DO(mp_sub_d(&a, 2u, &a)); /* a = 2**cnt - 2 */ printf("\r %4d bits", cnt); printf("(%d)", mp_reduce_is_2k(&a)); DO(mp_reduce_2k_setup(&a, &tmp)); printf("(%lu)", (unsigned long) tmp); for (ix = 0; ix < 1000; ix++) { if (!(ix & 127)) { printf("."); fflush(stdout); } DO(mp_rand(&b, ((cnt / MP_DIGIT_BIT) + 1) * 2)); DO(mp_copy(&c, &b)); DO(mp_mod(&c, &a, &c)); DO(mp_reduce_2k(&b, &a, 2u)); EXPECT(mp_cmp(&c, &b) == MP_EQ); } } 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_s_mp_div_3(void) { int cnt; mp_int a, b, c, d, e; DOR(mp_init_multi(&a, &b, &c, &d, &e, NULL)); /* test s_mp_div_3 */ mp_set(&d, 3u); for (cnt = 0; cnt < 10000;) { mp_digit r2; if (!(++cnt & 127)) { printf("\r %9d", cnt); fflush(stdout); } DO(mp_rand(&a, (abs(rand_int()) % 128) + 1)); DO(mp_div(&a, &d, &b, &e)); DO(s_mp_div_3(&a, &c, &r2)); EXPECT(!mp_cmp(&b, &c) && !mp_cmp_d(&e, r2)); } printf("... passed!"); 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; DOR(mp_init_multi(&a, &b, &c, NULL)); /* test the DR reduction */ for (cnt = 2; cnt < 32; cnt++) { printf("\r%d digit modulus", cnt); DO(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; DO(mp_rand(&b, cnt - 1)); DO(mp_copy(&b, &c)); rr = 0; do { if (!(rr & 127)) { printf("."); fflush(stdout); } DO(mp_sqr(&b, &b)); DO(mp_add_d(&b, 1u, &b)); DO(mp_copy(&b, &c)); DO(mp_mod(&b, &a, &b)); mp_dr_setup(&a, &mp); DO(mp_dr_reduce(&c, &a, mp)); EXPECT(mp_cmp(&b, &c) == MP_EQ); } 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, c, d; int cnt; char buf[4096]; size_t length; DOR(mp_init_multi(&a, &b, NULL)); /* 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 */ DO(mp_2expt(&a, 1024)); DO(mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16)); DO(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 */ DO(mp_2expt(&a, 2048)); DO(mp_read_radix(&b, "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F", 16)); DO(mp_sub(&a, &b, &a)); # else # error oops # endif DO(mp_to_radix(&a, buf, sizeof(buf), &length, 10)); printf("\n\np==%s, length = %zu\n", buf, length); /* now mp_reduce_is_2k_l() should return */ EXPECT(mp_reduce_is_2k_l(&a) == 1); DO(mp_reduce_2k_setup_l(&a, &d)); /* now do a million square+1 to see if it varies */ DO(mp_rand(&b, 64)); DO(mp_mod(&b, &a, &b)); DO(mp_copy(&b, &c)); printf("Testing: mp_reduce_2k_l..."); fflush(stdout); for (cnt = 0; cnt < (int)(1uL << 20); cnt++) { DO(mp_sqr(&b, &b)); DO(mp_add_d(&b, 1u, &b)); DO(mp_reduce_2k_l(&b, &a, &d)); DO(mp_sqr(&c, &c)); DO(mp_add_d(&c, 1u, &c)); DO(mp_mod(&c, &a, &c)); if (mp_cmp(&b, &c) != MP_EQ) { printf("mp_reduce_2k_l() failed at step %d\n", cnt); DO(mp_to_hex(&b, buf, sizeof(buf))); printf("b == %s\n", buf); DO(mp_to_hex(&c, buf, sizeof(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 to +3 */ static mp_err s_rs(const mp_int *a, int radix, int *size) { mp_err res; int digs = 0u; mp_int t; mp_digit d; *size = 0u; if (mp_iszero(a)) { *size = 2u; return MP_OKAY; } if (radix == 2) { *size = mp_count_bits(a) + 1; return MP_OKAY; } DO_WHAT(mp_init_copy(&t, a), return MP_ERR); t.sign = MP_ZPOS; while (!mp_iszero(&t)) { 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_log_n(void) { mp_int a; mp_digit d; int base, lb, size, i; const int max_base = MP_MIN(INT_MAX, MP_DIGIT_MAX); if (MP_HAS(S_MP_WORD_TOO_SMALL)) { fprintf(stderr, "Testing mp_log_n with restricted size of mp_word.\n"); } else { fprintf(stderr, "Testing mp_log_n with normal size of mp_word.\n"); } DOR(mp_init(&a)); /* base a result 0 x MP_VAL 1 x MP_VAL */ mp_set(&a, 42u); base = 0u; EXPECT(mp_log_n(&a, base, &lb) == MP_VAL); base = 1u; EXPECT(mp_log_n(&a, base, &lb) == MP_VAL); /* base a result 2 0 MP_VAL 2 1 0 2 2 1 2 3 1 */ base = 2u; mp_zero(&a); EXPECT(mp_log_n(&a, base, &lb) == MP_VAL); for (d = 1; d < 4; d++) { mp_set(&a, d); DO(mp_log_n(&a, base, &lb)); EXPECT(lb == ((d == 1)?0:1)); } /* base a result 3 0 MP_VAL 3 1 0 3 2 0 3 3 1 */ base = 3u; mp_zero(&a); EXPECT(mp_log_n(&a, base, &lb) == MP_VAL); for (d = 1; d < 4; d++) { mp_set(&a, d); DO(mp_log_n(&a, base, &lb)); EXPECT(lb == (((int)d < base)?0:1)); } /* bases 2..64 with "a" a random large constant. The range of bases tested allows to check with radix_size. */ DO(mp_rand(&a, 10)); for (base = 2; base < 65; base++) { DO(mp_log_n(&a, base, &lb)); DO(s_rs(&a,base, &size)); /* radix_size includes the memory needed for '\0', too*/ size -= 2; EXPECT(lb == size); } /* bases 2..64 with "a" a small constant and a small exponent "n" to test in the range a^n - 10 .. a^n + 10. That will check the correction loops and the test for perfect power. For simplicity a = base and n = 23 (64^23 == 2^138 > 2^128) */ for (base = 2; base < 65; base++) { mp_set(&a,(mp_digit)base); DO(mp_expt_n(&a, 23, &a)); DO(mp_sub_d(&a, 10u, &a)); for (i = 0; i < 20; i++) { DO(mp_log_n(&a, base, &lb)); DO(s_rs(&a, base, &size)); size -= 2; EXPECT(lb == size); DO(mp_add_d(&a, 1u, &a)); } } /*Test base upper edgecase with base = UINT32_MAX and number = (UINT32_MAX/2)*UINT32_MAX^10 */ mp_set(&a, max_base); DO(mp_expt_n(&a, 10uL, &a)); DO(mp_add_d(&a, max_base / 2, &a)); DO(mp_log_n(&a, max_base, &lb)); EXPECT(lb == 10u); mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } static int test_mp_log(void) { mp_int a, base, bn, t; int lb, lb2, i, j; if (MP_HAS(S_MP_WORD_TOO_SMALL)) { fprintf(stdout, "Testing mp_log with restricted size of mp_word.\n"); } else { fprintf(stdout, "Testing mp_log with normal size of mp_word.\n"); } DOR(mp_init_multi(&a, &base, &bn, &t, NULL)); /* The small values got tested above for mp_log_n already, leaving the big stuff with bases larger than INT_MAX. */ /* Edgecases a^b and -1+a^b (floor(log_2(256^129)) = 1032) */ for (i = 2; i < 256; i++) { mp_set_i32(&a,i); for (j = 2; j < ((i/2)+1); j++) { DO(mp_expt_n(&a, j, &bn)); mp_set_i32(&base,j); /* i^j a perfect power */ DO(mp_log(&bn, &a, &lb)); DO(mp_expt_n(&a, lb, &t)); if (mp_cmp(&t, &bn) != MP_EQ) { fprintf(stderr,"FAILURE mp_log for perf. power at i = %d, j = %d\n", i, j); goto LBL_ERR; } /* -1 + i^j */ DO(mp_decr(&bn)); DO(mp_log(&bn, &a, &lb2)); if (lb != (lb2+1)) { fprintf(stderr,"FAILURE mp_log for -1 + i^j at i = %d, j = %d\n", i, j); goto LBL_ERR; } } } /* Random a, base */ for (i = 1; i < 256; i++) { do { DO(mp_rand(&a, i)); } while (mp_cmp_d(&a,2u) == MP_LT); for (j = 1; j < ((i/2)+1); j++) { do { DO(mp_rand(&base, j)); } while (mp_cmp_d(&base,2u) == MP_LT); DO(mp_log(&a, &base, &lb)); DO(mp_expt_n(&base, lb, &bn)); /* "bn" must be smaller than or equal to "a" at this point. */ if (mp_cmp(&bn, &a) == MP_GT) { fprintf(stderr,"FAILURE mp_log random in GT check"); goto LBL_ERR; } DO(mp_mul(&bn, &base, &bn)); /* "bn" must be bigger than "a" at this point. */ if (mp_cmp(&bn, &a) != MP_GT) { fprintf(stderr,"FAILURE mp_log random in NOT GT check"); goto LBL_ERR; } } } mp_clear_multi(&a, &base, &bn, &t, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &base, &bn, &t, NULL); return EXIT_FAILURE; } static int test_mp_incr(void) { mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); /* Does it increment inside the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK/2); DO(mp_incr(&a)); EXPECT(mp_cmp_d(&a, (MP_MASK/2u) + 1u) == MP_EQ); /* Does it increment outside of the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK); mp_set(&b, MP_MASK); DO(mp_incr(&a)); DO(mp_add_d(&b, 1u, &b)); EXPECT(mp_cmp(&a, &b) == MP_EQ); /* Does it increment from -1 to 0? */ mp_set(&a, 1u); a.sign = MP_NEG; DO(mp_incr(&a)); EXPECT(mp_cmp_d(&a, 0u) == MP_EQ); /* Does it increment from -(MP_MASK + 1) to -MP_MASK? */ mp_set(&a, MP_MASK); DO(mp_add_d(&a, 1u, &a)); a.sign = MP_NEG; DO(mp_incr(&a)); EXPECT(a.sign == MP_NEG); a.sign = MP_ZPOS; EXPECT(mp_cmp_d(&a, MP_MASK) == MP_EQ); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } static int test_mp_decr(void) { mp_int a, b; DOR(mp_init_multi(&a, &b, NULL)); /* Does it decrement inside the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK/2); DO(mp_decr(&a)); EXPECT(mp_cmp_d(&a, (MP_MASK/2u) - 1u) == MP_EQ); /* Does it decrement outside of the limits of a MP_xBIT limb? */ mp_set(&a, MP_MASK); DO(mp_add_d(&a, 1u, &a)); DO(mp_decr(&a)); EXPECT(mp_cmp_d(&a, MP_MASK) == MP_EQ); /* Does it decrement from 0 to -1? */ mp_zero(&a); DO(mp_decr(&a)); if (a.sign == MP_NEG) { a.sign = MP_ZPOS; EXPECT(mp_cmp_d(&a, 1u) == MP_EQ); } else { goto LBL_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; DO(mp_sub_d(&b, 1u, &b)); DO(mp_decr(&a)); EXPECT(mp_cmp(&a, &b) == MP_EQ); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } /* Cannot test mp_exp(_d) without mp_root_n 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 simplify things, especially for the low-mp branch. */ static int test_mp_root_n(void) { mp_int a, c, r; 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" } }; DOR(mp_init_multi(&a, &c, &r, NULL)); for (i = 0; i < 10; i++) { DO(mp_read_radix(&a, input[i], 64)); for (j = 3; j < 100; j++) { DO(mp_root_n(&a, j, &c)); DO(mp_read_radix(&r, root[i][j-3], 10)); EXPECT(mp_cmp(&r, &c) == MP_EQ); } } mp_clear_multi(&a, &c, &r, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &c, &r, NULL); return EXIT_FAILURE; } /* Less error-prone than -1 + 2^n with mp_2expt */ static mp_err s_fill_with_ones(mp_int *a, int size) { int i; mp_err err = MP_OKAY; mp_zero(a); if ((err = mp_grow(a, size)) != MP_OKAY) goto LTM_ERR; for (i = 0; i < size; i++) { a->dp[i] = (mp_digit)MP_MASK; a->used++; } LTM_ERR: return err; } static int test_s_mp_sqr(void) { mp_int a, b, c; int i; DOR(mp_init_multi(&a, &b, &c, NULL)); /* s_mp_mul() has a hardcoded branch to s_mul_comba if s_mul_comba is available, so test another 10 just in case. */ for (i = 1; i < MP_MAX_COMBA + 10; i++) { DO(s_fill_with_ones(&a, i)); DO(s_mp_sqr(&a, &b)); DO(s_mp_mul(&a, &a, &c, 2*i + 1)); EXPECT(mp_cmp(&b, &c) == MP_EQ); DO(mp_rand(&a, i)); DO(s_mp_sqr(&a, &b)); DO(s_mp_mul(&a, &a, &c, 2*i + 1)); EXPECT(mp_cmp(&b, &c) == MP_EQ); } 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_s_mp_sqr_comba(void) { mp_int a, r1, r2; int i, j; DOR(mp_init_multi(&a, &r1, &r2, NULL)); for (i = 1; i <= MP_MAX_COMBA; i++) { DO(s_fill_with_ones(&a, i)); DO(s_mp_sqr_comba(&a, &r1)); DO(s_mp_sqr(&a, &r2)); EXPECT(mp_cmp(&r1, &r2) == MP_EQ); for (j = 0; j < 20; j++) { DO(mp_rand(&a, i)); DO(s_mp_sqr_comba(&a, &r1)); DO(s_mp_sqr(&a, &r2)); EXPECT(mp_cmp(&r1, &r2) == MP_EQ); } } mp_clear_multi(&a, &r1, &r2, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &r1, &r2, NULL); return EXIT_FAILURE; } static int test_s_mp_mul_balance(void) { mp_int a, b, c; const char *na = "4b0I5uMTujCysw+1OOuOyH2FX2WymrHUqi8BBDb7XpkV/4i7vXTbEYUy/kdIfCKu5jT5JEqYkdmnn3jAYo8XShPzNLxZx9yoLjxYRyptSuOI2B1DspvbIVYXY12sxPZ4/HCJ4Usm2MU5lO/006KnDMxuxiv1rm6YZJZ0eZU"; const char *nb = "3x9vs0yVi4hIq7poAeVcggC3WoRt0zRLKO"; const char *nc = "HzrSq9WVt1jDTVlwUxSKqxctu2GVD+N8+SVGaPFRqdxyld6IxDBbj27BPJzYUdR96k3sWpkO8XnDBvupGPnehpQe4KlO/KmN1PjFov/UTZYM+LYzkFcBPyV6hkkL8ePC1rlFLAHzgJMBCXVp4mRqtkQrDsZXXlcqlbTFu69wF6zDEysiX2cAtn/kP9ldblJiwYPCD8hG"; DOR(mp_init_multi(&a, &b, &c, NULL)); DO(mp_read_radix(&a, na, 64)); DO(mp_read_radix(&b, nb, 64)); DO(s_mp_mul_balance(&a, &b, &c)); DO(mp_read_radix(&b, nc, 64)); EXPECT(mp_cmp(&b, &c) == MP_EQ); mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } #define s_mp_mul_full(a, b, c) s_mp_mul(a, b, c, (a)->used + (b)->used + 1) static int test_s_mp_mul_karatsuba(void) { mp_int a, b, c, d; int size; DOR(mp_init_multi(&a, &b, &c, &d, NULL)); for (size = MP_MUL_KARATSUBA_CUTOFF; size < (MP_MUL_KARATSUBA_CUTOFF + 20); size++) { DO(mp_rand(&a, size)); DO(mp_rand(&b, size)); DO(s_mp_mul_karatsuba(&a, &b, &c)); DO(s_mp_mul_full(&a,&b,&d)); EXPECT(mp_cmp(&c, &d) == MP_EQ); } 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_s_mp_sqr_karatsuba(void) { mp_int a, b, c; int size; DOR(mp_init_multi(&a, &b, &c, NULL)); for (size = MP_SQR_KARATSUBA_CUTOFF; size < (MP_SQR_KARATSUBA_CUTOFF + 20); size++) { DO(mp_rand(&a, size)); DO(s_mp_sqr_karatsuba(&a, &b)); DO(s_mp_sqr(&a, &c)); EXPECT(mp_cmp(&b, &c) == MP_EQ); } 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_s_mp_mul_toom(void) { mp_int a, b, c, d; int size; #if (MP_DIGIT_BIT == 60) int tc_cutoff; #endif DOR(mp_init_multi(&a, &b, &c, &d, NULL)); /* This number construction is limb-size specific */ #if (MP_DIGIT_BIT == 60) DO(mp_rand(&a, 1196)); DO(mp_mul_2d(&a,71787 - mp_count_bits(&a), &a)); DO(mp_rand(&b, 1338)); DO(mp_mul_2d(&b, 80318 - mp_count_bits(&b), &b)); DO(mp_mul_2d(&b, 6310, &b)); DO(mp_2expt(&c, 99000 - 1000)); DO(mp_add(&b, &c, &b)); tc_cutoff = MP_MUL_TOOM_CUTOFF; MP_MUL_TOOM_CUTOFF = INT_MAX; DO(mp_mul(&a, &b, &c)); MP_MUL_TOOM_CUTOFF = tc_cutoff; DO(mp_mul(&a, &b, &d)); EXPECT(mp_cmp(&c, &d) == MP_EQ); #endif for (size = MP_MUL_TOOM_CUTOFF; size < (MP_MUL_TOOM_CUTOFF + 20); size++) { DO(mp_rand(&a, size)); DO(mp_rand(&b, size)); DO(s_mp_mul_toom(&a, &b, &c)); DO(s_mp_mul_full(&a,&b,&d)); EXPECT(mp_cmp(&c, &d) == MP_EQ); } 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_s_mp_sqr_toom(void) { mp_int a, b, c; int size; DOR(mp_init_multi(&a, &b, &c, NULL)); for (size = MP_SQR_TOOM_CUTOFF; size < (MP_SQR_TOOM_CUTOFF + 20); size++) { DO(mp_rand(&a, size)); DO(s_mp_sqr_toom(&a, &b)); DO(s_mp_sqr(&a, &c)); EXPECT(mp_cmp(&b, &c) == MP_EQ); } 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_radix_size(void) { mp_int a; int radix; size_t size; /* *INDENT-OFF* */ size_t results[65] = { 0, 0, 1627, 1027, 814, 702, 630, 581, 543, 514, 491, 471, 455, 441, 428, 418, 408, 399, 391, 384, 378, 372, 366, 361, 356, 352, 347, 343, 340, 336, 333, 330, 327, 324, 321, 318, 316, 314, 311, 309, 307, 305, 303, 301, 299, 298, 296, 294, 293, 291, 290, 288, 287, 285, 284, 283, 281, 280, 279, 278, 277, 276, 275, 273, 272 }; /* *INDENT-ON* */ DOR(mp_init(&a)); /* number to result in a different size for every base: 67^(4 * 67) */ mp_set(&a, 67); DO(mp_expt_n(&a, 268, &a)); for (radix = 2; radix < 65; radix++) { DO(mp_radix_size(&a, radix, &size)); EXPECT(size == results[radix]); a.sign = MP_NEG; DO(mp_radix_size(&a, radix, &size)); EXPECT(size == (results[radix] + 1)); a.sign = MP_ZPOS; } mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } #define PRINTERR_V(...) /* Some larger values to test the fast division algorithm */ static int test_s_mp_div_recursive(void) { mp_int a, b, c_q, c_r, d_q, d_r; int size; DOR(mp_init_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL)); for (size = MP_MUL_KARATSUBA_CUTOFF; size < (3 * MP_MUL_KARATSUBA_CUTOFF); size += 10) { printf("\rsizes = %d / %d", 10 * size, size); /* Relation 10:1 */ DO(mp_rand(&a, 10 * size)); DO(mp_rand(&b, size)); DO(s_mp_div_recursive(&a, &b, &c_q, &c_r)); DO(s_mp_div_school(&a, &b, &d_q, &d_r)); EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ); EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ); printf("\rsizes = %d / %d", 2 * size, size); /* Relation 10:1 negative numerator*/ DO(mp_rand(&a, 10 * size)); DO(mp_neg(&a, &a)); DO(mp_rand(&b, size)); DO(s_mp_div_recursive(&a, &b, &c_q, &c_r)); DO(s_mp_div_school(&a, &b, &d_q, &d_r)); EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ); EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ); printf("\rsizes = %d / %d, negative numerator", 2 * size, size); /* Relation 10:1 negative denominator*/ DO(mp_rand(&a, 10 * size)); DO(mp_rand(&b, size)); DO(mp_neg(&b, &b)); DO(s_mp_div_recursive(&a, &b, &c_q, &c_r)); DO(s_mp_div_school(&a, &b, &d_q, &d_r)); EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ); EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ); printf("\rsizes = %d / %d, negative denominator", 2 * size, size); /* Relation 2:1 */ DO(mp_rand(&a, 2 * size)); DO(mp_rand(&b, size)); DO(s_mp_div_recursive(&a, &b, &c_q, &c_r)); DO(s_mp_div_school(&a, &b, &d_q, &d_r)); EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ); EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ); printf("\rsizes = %d / %d", 3 * size, 2 * size); /* Upper limit 3:2 */ DO(mp_rand(&a, 3 * size)); DO(mp_rand(&b, 2 * size)); DO(s_mp_div_recursive(&a, &b, &c_q, &c_r)); DO(s_mp_div_school(&a, &b, &d_q, &d_r)); EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ); EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ); } mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL); return EXIT_FAILURE; } static int test_s_mp_div_small(void) { mp_int a, b, c_q, c_r, d_q, d_r; int size; DOR(mp_init_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL)); for (size = 1; size < MP_MUL_KARATSUBA_CUTOFF; size += 10) { printf("\rsizes = %d / %d", 2 * size, size); /* Relation 10:1 */ DO(mp_rand(&a, 2 * size)); DO(mp_rand(&b, size)); DO(s_mp_div_small(&a, &b, &c_q, &c_r)); DO(s_mp_div_school(&a, &b, &d_q, &d_r)); EXPECT(mp_cmp(&c_q, &d_q) == MP_EQ); EXPECT(mp_cmp(&c_r, &d_r) == MP_EQ); } mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL); return EXIT_SUCCESS; LBL_ERR: mp_clear_multi(&a, &b, &c_q, &c_r, &d_q, &d_r, NULL); return EXIT_FAILURE; } static int test_s_mp_radix_size_overestimate(void) { mp_int a; int radix, n; size_t size, size2; /* *INDENT-OFF* */ size_t results[65] = { 0u, 0u, 1627u, 1027u, 814u, 702u, 630u, 581u, 543u, 514u, 491u, 471u, 455u, 441u, 428u, 418u, 408u, 399u, 391u, 384u, 378u, 372u, 366u, 361u, 356u, 352u, 347u, 343u, 340u, 336u, 333u, 330u, 327u, 324u, 321u, 318u, 316u, 314u, 311u, 309u, 307u, 305u, 303u, 301u, 299u, 298u, 296u, 294u, 293u, 291u, 290u, 288u, 287u, 285u, 284u, 283u, 281u, 280u, 279u, 278u, 277u, 276u, 275u, 273u, 272u }; /* *INDENT-ON* */ DO(mp_init(&a)); /* number to result in a different size for every base: 67^(4 * 67) */ mp_set(&a, 67); DO(mp_expt_n(&a, 268, &a)); for (radix = 2; radix < 65; radix++) { DO(s_mp_radix_size_overestimate(&a, radix, &size)); EXPECT(size >= results[radix]); EXPECT(size < results[radix] + 20); /* some error bound */ a.sign = MP_NEG; DO(s_mp_radix_size_overestimate(&a, radix, &size)); EXPECT(size >= results[radix]); EXPECT(size < results[radix] + 20); /* some error bound */ a.sign = MP_ZPOS; } /* randomized test */ for (n = 1; n < 1024; n += 1234) { DO(mp_rand(&a, n)); for (radix = 2; radix < 65; radix++) { DO(s_mp_radix_size_overestimate(&a, radix, &size)); DO(mp_radix_size(&a, radix, &size2)); EXPECT(size >= size2); EXPECT(size < size2 + 20); /* some error bound */ a.sign = MP_NEG; DO(s_mp_radix_size_overestimate(&a, radix, &size)); DO(mp_radix_size(&a, radix, &size2)); EXPECT(size >= size2); EXPECT(size < size2 + 20); /* some error bound */ a.sign = MP_ZPOS; } } mp_clear(&a); return EXIT_SUCCESS; LBL_ERR: mp_clear(&a); return EXIT_FAILURE; } static int test_mp_read_write_ubin(void) { mp_int a, b, c; size_t size, len; uint8_t *buf = NULL; DOR(mp_init_multi(&a, &b, &c, NULL)); DO(mp_rand(&a, 15)); DO(mp_neg(&a, &b)); size = mp_ubin_size(&a); printf("mp_to_ubin_size %zu - ", size); buf = (uint8_t *)malloc(sizeof(*buf) * size); if (buf == NULL) { fprintf(stderr, "test_read_write_binaries (u) failed to allocate %zu bytes\n", sizeof(*buf) * size); goto LBL_ERR; } DO(mp_to_ubin(&a, buf, size, &len)); printf("mp_to_ubin len = %zu", len); DO(mp_from_ubin(&c, buf, len)); if (mp_cmp(&a, &c) != MP_EQ) { fprintf(stderr, "to/from ubin cycle failed\n"); goto LBL_ERR; } free(buf); mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LBL_ERR: free(buf); mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } static int test_mp_read_write_sbin(void) { mp_int a, b, c; size_t size, len; uint8_t *buf = NULL; DOR(mp_init_multi(&a, &b, &c, NULL)); DO(mp_rand(&a, 15)); DO(mp_neg(&a, &b)); size = mp_sbin_size(&a); printf("mp_to_sbin_size %zu - ", size); buf = (uint8_t *)malloc(sizeof(*buf) * size); if (buf == NULL) { fprintf(stderr, "test_read_write_binaries (s) failed to allocate %zu bytes\n", sizeof(*buf) * size); goto LBL_ERR; } DO(mp_to_sbin(&b, buf, size, &len)); printf("mp_to_sbin len = %zu", len); DO(mp_from_sbin(&c, buf, len)); if (mp_cmp(&b, &c) != MP_EQ) { fprintf(stderr, "to/from ubin cycle failed\n"); goto LBL_ERR; } free(buf); mp_clear_multi(&a, &b, &c, NULL); return EXIT_SUCCESS; LBL_ERR: free(buf); mp_clear_multi(&a, &b, &c, NULL); return EXIT_FAILURE; } static int test_mp_pack_unpack(void) { mp_int a, b; size_t written, count; uint8_t *buf = NULL; mp_order order = MP_LSB_FIRST; mp_endian endianness = MP_NATIVE_ENDIAN; DOR(mp_init_multi(&a, &b, NULL)); DO(mp_rand(&a, 15)); count = mp_pack_count(&a, 0uL, 1uL); buf = (uint8_t *)malloc(count); if (buf == NULL) { fprintf(stderr, "test_pack_unpack failed to allocate\n"); goto LBL_ERR; } DO(mp_pack((void *)buf, count, &written, order, 1uL, endianness, 0uL, &a)); DO(mp_unpack(&b, count, order, 1uL, endianness, 0uL, (const void *)buf)); if (mp_cmp(&a, &b) != MP_EQ) { fprintf(stderr, "pack/unpack cycle failed\n"); goto LBL_ERR; } free(buf); mp_clear_multi(&a, &b, NULL); return EXIT_SUCCESS; LBL_ERR: free(buf); mp_clear_multi(&a, &b, NULL); return EXIT_FAILURE; } #ifndef LTM_TEST_DYNAMIC #define ONLY_PUBLIC_API_C #endif static int unit_tests(int argc, char **argv) { static const struct { const char *name; int (*fn)(void); } test[] = { #define T0(n) { #n, test_##n } #define T1(n, o) { #n, MP_HAS(o) ? test_##n : NULL } #define T2(n, o1, o2) { #n, (MP_HAS(o1) && MP_HAS(o2)) ? test_##n : NULL } #define T3(n, o1, o2, o3) { #n, (MP_HAS(o1) && MP_HAS(o2) && MP_HAS(o3)) ? test_##n : NULL } T0(feature_detection), T0(trivial_stuff), T1(mp_hash, MP_HASH), T2(mp_get_set_i32, MP_GET_I32, MP_GET_MAG_U32), T2(mp_get_set_i64, MP_GET_I64, MP_GET_MAG_U64), T1(mp_and, MP_AND), T1(mp_cnt_lsb, MP_CNT_LSB), T1(mp_complement, MP_COMPLEMENT), T1(mp_decr, MP_SUB_D), T2(s_mp_div_3, ONLY_PUBLIC_API, S_MP_DIV_3), T1(mp_dr_reduce, MP_DR_REDUCE), T2(mp_pack_unpack,MP_PACK, MP_UNPACK), T2(mp_fread_fwrite, MP_FREAD, MP_FWRITE), T1(mp_get_u32, MP_GET_I32), T1(mp_get_u64, MP_GET_I64), T1(mp_get_ul, MP_GET_L), T1(mp_log_n, MP_LOG_N), T1(mp_log, MP_LOG), T1(mp_incr, MP_ADD_D), T1(mp_invmod, MP_INVMOD), T1(mp_is_square, MP_IS_SQUARE), T1(mp_kronecker, MP_KRONECKER), T1(mp_montgomery_reduce, MP_MONTGOMERY_REDUCE), T1(mp_root_n, MP_ROOT_N), T1(mp_or, MP_OR), T1(mp_prime_is_prime, MP_PRIME_IS_PRIME), T1(mp_prime_next_prime, MP_PRIME_NEXT_PRIME), T1(mp_prime_rand, MP_PRIME_RAND), T1(mp_rand, MP_RAND), T1(mp_read_radix, MP_READ_RADIX), T1(mp_read_write_ubin, MP_TO_UBIN), T1(mp_read_write_sbin, MP_TO_SBIN), T1(mp_reduce_2k, MP_REDUCE_2K), T1(mp_reduce_2k_l, MP_REDUCE_2K_L), T1(mp_radix_size, MP_RADIX_SIZE), T2(s_mp_radix_size_overestimate, ONLY_PUBLIC_API, S_MP_RADIX_SIZE_OVERESTIMATE), #if defined(MP_HAS_SET_DOUBLE) T1(mp_set_double, MP_SET_DOUBLE), #endif T1(mp_signed_rsh, MP_SIGNED_RSH), T2(mp_sqrt, MP_SQRT, MP_ROOT_N), T1(mp_sqrtmod_prime, MP_SQRTMOD_PRIME), T1(mp_xor, MP_XOR), T3(s_mp_div_recursive, ONLY_PUBLIC_API, S_MP_DIV_RECURSIVE, S_MP_DIV_SCHOOL), T3(s_mp_div_small, ONLY_PUBLIC_API, S_MP_DIV_SMALL, S_MP_DIV_SCHOOL), T2(s_mp_sqr, ONLY_PUBLIC_API, S_MP_SQR), /* s_mp_mul_comba not (yet) testable because s_mp_mul branches to s_mp_mul_comba automatically */ T2(s_mp_sqr_comba, ONLY_PUBLIC_API, S_MP_SQR_COMBA), T2(s_mp_mul_balance, ONLY_PUBLIC_API, S_MP_MUL_BALANCE), T2(s_mp_mul_karatsuba, ONLY_PUBLIC_API, S_MP_MUL_KARATSUBA), T2(s_mp_sqr_karatsuba, ONLY_PUBLIC_API, S_MP_SQR_KARATSUBA), T2(s_mp_mul_toom, ONLY_PUBLIC_API, S_MP_MUL_TOOM), T2(s_mp_sqr_toom, ONLY_PUBLIC_API, S_MP_SQR_TOOM) #undef T3 #undef T2 #undef T1 }; unsigned long i, ok, fail, nop; uint64_t t; int j; ok = fail = nop = 0; t = (uint64_t)time(NULL); printf("SEED: 0x%" PRIx64 "\n\n", t); s_mp_rand_jenkins_init(t); 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", test[i].name); if (test[i].fn == NULL) { nop++; printf("NOP %s\n\n", test[i].name); } else if (test[i].fn() == EXIT_SUCCESS) { ok++; printf("\n"); } else { fail++; printf("\n\nFAIL %s\n\n", test[i].name); } } fprintf(fail?stderr:stdout, "Tests OK/NOP/FAIL: %lu/%lu/%lu\n", ok, nop, fail); if (fail != 0) return EXIT_FAILURE; else return EXIT_SUCCESS; } int main(int argc, char **argv) { print_header(); return unit_tests(argc, argv); }