int main(int argc, char *argv[])
{
int ntests, prec, ix;
unsigned int seed;
char *senv;
clock_t start, stop;
double multime;
mp_int a, b, c;
if((senv = getenv("SEED")) != NULL)
seed = atoi(senv);
else
seed = (unsigned int)time(NULL);
if(argc < 3) {
fprintf(stderr, "Usage: %s <ntests> <nbits>\n", argv[0]);
return 1;
}
if((ntests = abs(atoi(argv[1]))) == 0) {
fprintf(stderr, "%s: must request at least 1 test.\n", argv[0]);
return 1;
}
if((prec = abs(atoi(argv[2]))) < CHAR_BIT) {
fprintf(stderr, "%s: must request at least %d bits.\n", argv[0],
CHAR_BIT);
return 1;
}
prec = (prec + (DIGIT_BIT - 1)) / DIGIT_BIT;
mp_init_size(&a, prec);
mp_init_size(&b, prec);
mp_init_size(&c, 2 * prec);
srand(seed);
start = clock();
for(ix = 0; ix < ntests; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_mul(&a, &a, &c);
}
stop = clock();
multime = (double)(stop - start) / CLOCKS_PER_SEC;
printf("Total: %.4f\n", multime);
printf("Individual: %.4f\n", multime / ntests);
mp_clear(&a); mp_clear(&b); mp_clear(&c);
return 0;
}
/* 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;
}
int main(int argc, char *argv[])
{
int ix, num, prec = PRECISION;
mp_int a, b, c, d;
instant_t start, finish;
time_t seed;
unsigned int d1, d2;
seed = time(NULL);
if(argc < 2) {
fprintf(stderr, "Usage: %s <num-tests>\n", argv[0]);
return 1;
}
if((num = atoi(argv[1])) < 0)
num = -num;
printf("Test 5a: Euclid vs. Binary, a GCD speed test\n\n"
"Number of tests: %d\n"
"Precision: %d digits\n\n", num, prec);
mp_init_size(&a, prec);
mp_init_size(&b, prec);
mp_init(&c);
mp_init(&d);
printf("Verifying accuracy ... \n");
srand((unsigned int)seed);
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_gcd(&a, &b, &c);
mp_bgcd(&a, &b, &d);
if(mp_cmp(&c, &d) != 0) {
printf("Error! Results not accurate:\n");
printf("a = "); mp_print(&a, stdout); fputc('\n', stdout);
printf("b = "); mp_print(&b, stdout); fputc('\n', stdout);
printf("c = "); mp_print(&c, stdout); fputc('\n', stdout);
printf("d = "); mp_print(&d, stdout); fputc('\n', stdout);
mp_clear(&a); mp_clear(&b); mp_clear(&c); mp_clear(&d);
return 1;
}
}
mp_clear(&d);
printf("Accuracy confirmed for the %d test samples\n", num);
printf("Testing Euclid ... \n");
srand((unsigned int)seed);
start = now();
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_gcd(&a, &b, &c);
}
finish = now();
d1 = (finish.sec - start.sec) * 1000000;
d1 -= start.usec; d1 += finish.usec;
printf("Testing binary ... \n");
srand((unsigned int)seed);
start = now();
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&b, prec);
mp_bgcd(&a, &b, &c);
}
finish = now();
d2 = (finish.sec - start.sec) * 1000000;
d2 -= start.usec; d2 += finish.usec;
printf("Euclidean algorithm time: %u usec\n", d1);
printf("Binary algorithm time: %u usec\n", d2);
printf("Improvement: %.2f%%\n",
(1.0 - ((double)d2 / (double)d1)) * 100.0);
mp_clear(&c);
mp_clear(&b);
mp_clear(&a);
return 0;
}
int main(int argc, char *argv[])
{
int ntests, prec, ix;
unsigned int seed;
clock_t start, stop;
double multime, sqrtime;
mp_int a, c;
seed = (unsigned int)time(NULL);
if(argc < 3) {
fprintf(stderr, "Usage: %s <ntests> <nbits>\n", argv[0]);
return 1;
}
if((ntests = abs(atoi(argv[1]))) == 0) {
fprintf(stderr, "%s: must request at least 1 test.\n", argv[0]);
return 1;
}
if((prec = abs(atoi(argv[2]))) < CHAR_BIT) {
fprintf(stderr, "%s: must request at least %d bits.\n", argv[0],
CHAR_BIT);
return 1;
}
prec = (prec + (DIGIT_BIT - 1)) / DIGIT_BIT;
mp_init_size(&a, prec);
mp_init_size(&c, 2 * prec);
/* Test multiplication by self */
srand(seed);
start = clock();
for(ix = 0; ix < ntests; ix++) {
mpp_random_size(&a, prec);
mp_mul(&a, &a, &c);
}
stop = clock();
multime = (double)(stop - start) / CLOCKS_PER_SEC;
/* Test squaring */
srand(seed);
start = clock();
for(ix = 0; ix < ntests; ix++) {
mpp_random_size(&a, prec);
mp_sqr(&a, &c);
}
stop = clock();
sqrtime = (double)(stop - start) / CLOCKS_PER_SEC;
printf("Multiply: %.4f\n", multime);
printf("Square: %.4f\n", sqrtime);
if(multime < sqrtime) {
printf("Speedup: %.1f%%\n", 100.0 * (1.0 - multime / sqrtime));
printf("Prefer: multiply\n");
} else {
printf("Speedup: %.1f%%\n", 100.0 * (1.0 - sqrtime / multime));
printf("Prefer: square\n");
}
mp_clear(&a); mp_clear(&c);
return 0;
}
/* 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;
}
int main(int argc, char *argv[])
{
int ix, num, prec = 8;
unsigned int seed;
clock_t start, stop;
double sec;
mp_int a, m, c;
if(getenv("SEED") != NULL)
seed = abs(atoi(getenv("SEED")));
else
seed = (unsigned int)time(NULL);
if(argc < 2) {
fprintf(stderr, "Usage: %s <num-tests> [<nbits>]\n", argv[0]);
return 1;
}
if((num = atoi(argv[1])) < 0)
num = -num;
if(!num) {
fprintf(stderr, "%s: must perform at least 1 test\n", argv[0]);
return 1;
}
if(argc > 2) {
if((prec = atoi(argv[2])) <= 0)
prec = 8;
else
prec = (prec + (DIGIT_BIT - 1)) / DIGIT_BIT;
}
printf("Modular exponentiation timing test\n"
"Precision: %d digits (%d bits)\n"
"# of tests: %d\n\n", prec, prec * DIGIT_BIT, num);
mp_init_size(&a, prec);
mp_init_size(&m, prec);
mp_init_size(&c, prec);
srand(seed);
start = clock();
for(ix = 0; ix < num; ix++) {
mpp_random_size(&a, prec);
mpp_random_size(&c, prec);
mpp_random_size(&m, prec);
/* set msb and lsb of m */
DIGIT(&m,0) |= 1;
DIGIT(&m, USED(&m)-1) |= (mp_digit)1 << (DIGIT_BIT - 1);
if (mp_cmp(&a, &m) > 0)
mp_sub(&a, &m, &a);
mp_exptmod(&a, &c, &m, &c);
}
stop = clock();
sec = clk_to_sec(start, stop);
printf("Total: %.3f seconds\n", sec);
printf("Individual: %.3f seconds\n", sec / num);
mp_clear(&c);
mp_clear(&a);
mp_clear(&m);
return 0;
}
