/* Tests the time required for a point multiplication */ mp_err testPointMulTime(ECGroup *ecgroup) { mp_err res = MP_OKAY; mp_int rx, ry, n; int size; MP_DIGITS(&rx) = 0; MP_DIGITS(&ry) = 0; MP_DIGITS(&n) = 0; MP_CHECKOK(mp_init(&rx)); MP_CHECKOK(mp_init(&ry)); MP_CHECKOK(mp_init(&n)); /* compute random scalar */ size = mpl_significant_bits(&ecgroup->meth->irr); if (size < MP_OKAY) { res = MP_NO; goto CLEANUP; } MP_CHECKOK(mpp_random_size(&n, (size + ECL_BITS - 1) / ECL_BITS)); MP_CHECKOK(ecgroup->meth->field_mod(&n, &n, ecgroup->meth)); M_TimeOperation(ec_GFp_pt_mul_jac_fp (&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup), 1000); M_TimeOperation(ec_GFp_point_mul_jac_4w_fp (&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup), 1000); M_TimeOperation(ec_GFp_point_mul_wNAF_fp (&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup), 1000); M_TimeOperation(ec_GFp_pt_mul_jac (&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup), 100); CLEANUP: if (res == MP_OKAY) printf(" Test Passed - Point Multiplication Timing\n"); else printf("TEST FAILED - Point Multiplication Timing\n"); mp_clear(&rx); mp_clear(&ry); mp_clear(&n); return res; }
/* Tests point multiplication with a random scalar repeatedly, comparing * for consistency within different algorithms. */ mp_err testPointMulRandom(ECGroup *ecgroup) { mp_err res; mp_int rx, ry, rx2, ry2, n; int i, size; EC_group_fp *group = (EC_group_fp *) ecgroup->extra1; MP_DIGITS(&rx) = 0; MP_DIGITS(&ry) = 0; MP_DIGITS(&rx2) = 0; MP_DIGITS(&ry2) = 0; MP_DIGITS(&n) = 0; MP_CHECKOK(mp_init(&rx)); MP_CHECKOK(mp_init(&ry)); MP_CHECKOK(mp_init(&rx2)); MP_CHECKOK(mp_init(&ry2)); MP_CHECKOK(mp_init(&n)); for (i = 0; i < 100; i++) { /* compute random scalar */ size = mpl_significant_bits(&ecgroup->meth->irr); if (size < MP_OKAY) { res = MP_NO; goto CLEANUP; } MP_CHECKOK(mpp_random_size(&n, group->orderBitSize)); MP_CHECKOK(mp_mod(&n, &ecgroup->order, &n)); ec_GFp_pt_mul_jac(&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup); ec_GFp_pt_mul_jac_fp(&n, &ecgroup->genx, &ecgroup->geny, &rx2, &ry2, ecgroup); if ((mp_cmp(&rx, &rx2) != 0) || (mp_cmp(&ry, &ry2) != 0)) { printf (" Error: different results for Point Multiplication - Double & Add.\n"); res = MP_NO; goto CLEANUP; } ec_GFp_point_mul_wNAF_fp(&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup); if ((mp_cmp(&rx, &rx2) != 0) || (mp_cmp(&ry, &ry2) != 0)) { printf (" Error: different results for Point Multiplication - wNAF.\n"); res = MP_NO; goto CLEANUP; } ec_GFp_point_mul_jac_4w_fp(&n, &ecgroup->genx, &ecgroup->geny, &rx, &ry, ecgroup); if ((mp_cmp(&rx, &rx2) != 0) || (mp_cmp(&ry, &ry2) != 0)) { printf (" Error: different results for Point Multiplication - 4 bit window.\n"); res = MP_NO; goto CLEANUP; } } CLEANUP: if (res == MP_OKAY) printf(" Test Passed - Point Random Multiplication\n"); else printf("TEST FAILED - Point Random Multiplication\n"); mp_clear(&rx); mp_clear(&ry); mp_clear(&rx2); mp_clear(&ry2); mp_clear(&n); return res; }
/* Performs basic tests of elliptic curve cryptography over prime fields. * If tests fail, then it prints an error message, aborts, and returns an * error code. Otherwise, returns 0. */ int ectest_curve_GFp(ECGroup *group, int ectestPrint, int ectestTime, int generic) { mp_int one, order_1, gx, gy, rx, ry, n; int size; mp_err res; char s[1000]; /* initialize values */ MP_CHECKOK(mp_init(&one)); MP_CHECKOK(mp_init(&order_1)); MP_CHECKOK(mp_init(&gx)); MP_CHECKOK(mp_init(&gy)); MP_CHECKOK(mp_init(&rx)); MP_CHECKOK(mp_init(&ry)); MP_CHECKOK(mp_init(&n)); MP_CHECKOK(mp_set_int(&one, 1)); MP_CHECKOK(mp_sub(&group->order, &one, &order_1)); /* encode base point */ if (group->meth->field_dec) { MP_CHECKOK(group->meth->field_dec(&group->genx, &gx, group->meth)); MP_CHECKOK(group->meth->field_dec(&group->geny, &gy, group->meth)); } else { MP_CHECKOK(mp_copy(&group->genx, &gx)); MP_CHECKOK(mp_copy(&group->geny, &gy)); } if (ectestPrint) { /* output base point */ printf(" base point P:\n"); MP_CHECKOK(mp_toradix(&gx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&gy, s, 16)); printf(" %s\n", s); if (group->meth->field_enc) { printf(" base point P (encoded):\n"); MP_CHECKOK(mp_toradix(&group->genx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&group->geny, s, 16)); printf(" %s\n", s); } } #ifdef ECL_ENABLE_GFP_PT_MUL_AFF /* multiply base point by order - 1 and check for negative of base * point */ MP_CHECKOK(ec_GFp_pt_mul_aff(&order_1, &group->genx, &group->geny, &rx, &ry, group)); if (ectestPrint) { printf(" (order-1)*P (affine):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } MP_CHECKOK(group->meth->field_neg(&ry, &ry, group->meth)); if ((mp_cmp(&rx, &group->genx) != 0) || (mp_cmp(&ry, &group->geny) != 0)) { printf(" Error: invalid result (expected (- base point)).\n"); res = MP_NO; goto CLEANUP; } #endif #ifdef ECL_ENABLE_GFP_PT_MUL_AFF /* multiply base point by order - 1 and check for negative of base * point */ MP_CHECKOK(ec_GFp_pt_mul_jac(&order_1, &group->genx, &group->geny, &rx, &ry, group)); if (ectestPrint) { printf(" (order-1)*P (jacobian):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } MP_CHECKOK(group->meth->field_neg(&ry, &ry, group->meth)); if ((mp_cmp(&rx, &group->genx) != 0) || (mp_cmp(&ry, &group->geny) != 0)) { printf(" Error: invalid result (expected (- base point)).\n"); res = MP_NO; goto CLEANUP; } #endif /* multiply base point by order - 1 and check for negative of base * point */ MP_CHECKOK(ECPoint_mul(group, &order_1, NULL, NULL, &rx, &ry)); if (ectestPrint) { printf(" (order-1)*P (ECPoint_mul):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } MP_CHECKOK(mp_submod(&group->meth->irr, &ry, &group->meth->irr, &ry)); if ((mp_cmp(&rx, &gx) != 0) || (mp_cmp(&ry, &gy) != 0)) { printf(" Error: invalid result (expected (- base point)).\n"); res = MP_NO; goto CLEANUP; } /* multiply base point by order - 1 and check for negative of base * point */ MP_CHECKOK(ECPoint_mul(group, &order_1, &gx, &gy, &rx, &ry)); if (ectestPrint) { printf(" (order-1)*P (ECPoint_mul):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } MP_CHECKOK(mp_submod(&group->meth->irr, &ry, &group->meth->irr, &ry)); if ((mp_cmp(&rx, &gx) != 0) || (mp_cmp(&ry, &gy) != 0)) { printf(" Error: invalid result (expected (- base point)).\n"); res = MP_NO; goto CLEANUP; } #ifdef ECL_ENABLE_GFP_PT_MUL_AFF /* multiply base point by order and check for point at infinity */ MP_CHECKOK(ec_GFp_pt_mul_aff(&group->order, &group->genx, &group->geny, &rx, &ry, group)); if (ectestPrint) { printf(" (order)*P (affine):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) { printf(" Error: invalid result (expected point at infinity).\n"); res = MP_NO; goto CLEANUP; } #endif #ifdef ECL_ENABLE_GFP_PT_MUL_JAC /* multiply base point by order and check for point at infinity */ MP_CHECKOK(ec_GFp_pt_mul_jac(&group->order, &group->genx, &group->geny, &rx, &ry, group)); if (ectestPrint) { printf(" (order)*P (jacobian):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) { printf(" Error: invalid result (expected point at infinity).\n"); res = MP_NO; goto CLEANUP; } #endif /* multiply base point by order and check for point at infinity */ MP_CHECKOK(ECPoint_mul(group, &group->order, NULL, NULL, &rx, &ry)); if (ectestPrint) { printf(" (order)*P (ECPoint_mul):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) { printf(" Error: invalid result (expected point at infinity).\n"); res = MP_NO; goto CLEANUP; } /* multiply base point by order and check for point at infinity */ MP_CHECKOK(ECPoint_mul(group, &group->order, &gx, &gy, &rx, &ry)); if (ectestPrint) { printf(" (order)*P (ECPoint_mul):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } if (ec_GFp_pt_is_inf_aff(&rx, &ry) != MP_YES) { printf(" Error: invalid result (expected point at infinity).\n"); res = MP_NO; goto CLEANUP; } /* check that (order-1)P + (order-1)P + P == (order-1)P */ MP_CHECKOK(ECPoints_mul(group, &order_1, &order_1, &gx, &gy, &rx, &ry)); MP_CHECKOK(ECPoints_mul(group, &one, &one, &rx, &ry, &rx, &ry)); if (ectestPrint) { printf(" (order-1)*P + (order-1)*P + P == (order-1)*P (ECPoints_mul):\n"); MP_CHECKOK(mp_toradix(&rx, s, 16)); printf(" %s\n", s); MP_CHECKOK(mp_toradix(&ry, s, 16)); printf(" %s\n", s); } MP_CHECKOK(mp_submod(&group->meth->irr, &ry, &group->meth->irr, &ry)); if ((mp_cmp(&rx, &gx) != 0) || (mp_cmp(&ry, &gy) != 0)) { printf(" Error: invalid result (expected (- base point)).\n"); res = MP_NO; goto CLEANUP; } /* test validate_point function */ if (ECPoint_validate(group, &gx, &gy) != MP_YES) { printf(" Error: validate point on base point failed.\n"); res = MP_NO; goto CLEANUP; } MP_CHECKOK(mp_add_d(&gy, 1, &ry)); if (ECPoint_validate(group, &gx, &ry) != MP_NO) { printf(" Error: validate point on invalid point passed.\n"); res = MP_NO; goto CLEANUP; } if (ectestTime) { /* compute random scalar */ size = mpl_significant_bits(&group->meth->irr); if (size < MP_OKAY) { goto CLEANUP; } MP_CHECKOK(mpp_random_size(&n, (size + ECL_BITS - 1) / ECL_BITS)); MP_CHECKOK(group->meth->field_mod(&n, &n, group->meth)); /* timed test */ if (generic) { #ifdef ECL_ENABLE_GFP_PT_MUL_AFF M_TimeOperation(MP_CHECKOK(ec_GFp_pt_mul_aff(&n, &group->genx, &group->geny, &rx, &ry, group)), 100); #endif M_TimeOperation(MP_CHECKOK(ECPoint_mul(group, &n, NULL, NULL, &rx, &ry)), 100); M_TimeOperation(MP_CHECKOK(ECPoints_mul(group, &n, &n, &gx, &gy, &rx, &ry)), 100); } else { M_TimeOperation(MP_CHECKOK(ECPoint_mul(group, &n, NULL, NULL, &rx, &ry)), 100); M_TimeOperation(MP_CHECKOK(ECPoint_mul(group, &n, &gx, &gy, &rx, &ry)), 100); M_TimeOperation(MP_CHECKOK(ECPoints_mul(group, &n, &n, &gx, &gy, &rx, &ry)), 100); } } CLEANUP: mp_clear(&one); mp_clear(&order_1); mp_clear(&gx); mp_clear(&gy); mp_clear(&rx); mp_clear(&ry); mp_clear(&n); if (res != MP_OKAY) { printf(" Error: exiting with error value %i\n", res); } return res; }