#include <stdio.h>
#include <stdlib.h>
+#include <time.h>
#ifdef OPENSSL_NO_EC
#include <openssl/err.h>
#define ABORT do { \
+ fflush(stdout); \
fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
ERR_print_errors_fp(stderr); \
exit(1); \
} while (0)
+
+void timings(EC_GROUP *group, int simult, BN_CTX *ctx)
+ {
+ clock_t clck;
+ int i, j;
+ BIGNUM *s, *s0;
+ EC_POINT *P;
+ EC_POINT *points[1];
+ BIGNUM *scalars[1];
+
+ s = BN_new();
+ s0 = BN_new();
+ if (s == NULL || s0 == NULL) ABORT;
+
+ if (!EC_GROUP_get_curve_GFp(group, s, NULL, NULL, ctx)) ABORT;
+ fprintf(stdout, "Timings for %d bit prime, ", (int)BN_num_bits(s));
+ if (!EC_GROUP_get_order(group, s, ctx)) ABORT;
+ fprintf(stdout, "%d bit scalars ", (int)BN_num_bits(s));
+ fflush(stdout);
+
+ P = EC_POINT_new(group);
+ if (P == NULL) ABORT;
+ EC_POINT_copy(P, EC_GROUP_get0_generator(group));
+
+ points[0] = P;
+ scalars[0] = s0;
+
+ clck = clock();
+ for (i = 0; i < 10; i++)
+ {
+ if (!BN_pseudo_rand(s, BN_num_bits(s), 0, 0)) ABORT;
+ if (simult)
+ {
+ if (!BN_pseudo_rand(s0, BN_num_bits(s), 0, 0)) ABORT;
+ }
+ for (j = 0; j < 10; j++)
+ {
+ if (!EC_POINTs_mul(group, P, s, simult != 0, points, scalars, ctx)) ABORT;
+ }
+ fprintf(stdout, ".");
+ fflush(stdout);
+ }
+ fprintf(stdout, "\n");
+
+ clck = clock() - clck;
+
+#ifdef CLOCKS_PER_SEC
+ /* "To determine the time in seconds, the value returned
+ * by the clock function should be divided by the value
+ * of the macro CLOCKS_PER_SEC."
+ * -- ISO/IEC 9899 */
+# define UNIT "s"
+#else
+ /* "`CLOCKS_PER_SEC' undeclared (first use this function)"
+ * -- cc on NeXTstep/OpenStep */
+# define UNIT "units"
+# define CLOCKS_PER_SEC 1
+#endif
+
+ fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
+ simult ? "s*P+t*Q operations" : "point multiplications",
+ (double)clck/CLOCKS_PER_SEC);
+ fprintf(stdout, "average: %.4f " UNIT "\n", (double)clck/(CLOCKS_PER_SEC*i*j));
+
+ EC_POINT_free(P);
+ BN_free(s);
+ BN_free(s0);
+ }
+
+
int main(int argc, char *argv[])
{
BN_CTX *ctx = NULL;
BIGNUM *p, *a, *b;
EC_GROUP *group;
+ EC_GROUP *P_192 = NULL, *P_224 = NULL, *P_256 = NULL, *P_384 = NULL, *P_521 = NULL;
EC_POINT *P, *Q, *R;
BIGNUM *x, *y, *z;
unsigned char buf[100];
CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
ERR_load_crypto_strings();
-#if 0 /* optional */
+#if 1 /* optional */
ctx = BN_CTX_new();
if (!ctx) ABORT;
#endif
if (!BN_hex2bn(&a, "1")) ABORT;
if (!BN_hex2bn(&b, "1")) ABORT;
- group = EC_GROUP_new(EC_GFp_mont_method());
+ group = EC_GROUP_new(EC_GFp_mont_method()); /* applications should use EC_GROUP_new_curve_GFp
+ * so that the library gets to choose the EC_METHOD */
if (!group) ABORT;
+
if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ {
+ EC_GROUP *tmp;
+ tmp = EC_GROUP_new(EC_GROUP_method_of(group));
+ if (!tmp) ABORT;
+ if (!EC_GROUP_copy(tmp, group));
+ EC_GROUP_free(group);
+ group = tmp;
+ }
+
if (!EC_GROUP_get_curve_GFp(group, p, a, b, ctx)) ABORT;
fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + b (mod 0x");
if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
#if 0 /* optional */
- if (!EC_POINT_make_affine(group, P, ctx)) ABORT;
+ {
+ EC_POINT *points[3];
+
+ points[0] = R;
+ points[1] = Q;
+ points[2] = P;
+ if (!EC_POINTs_make_affine(group, 2, points, ctx)) ABORT;
+ }
#endif
+
}
while (!EC_POINT_is_at_infinity(group, P));
if (!EC_POINT_invert(group, P, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
- /* ... */
+
+ /* Curve P-192 (FIPS PUB 186-2, App. 6) */
+
+ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
+ if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC")) ABORT;
+ if (!BN_hex2bn(&b, "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ if (!BN_hex2bn(&x, "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012")) ABORT;
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831")) ABORT;
+ if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
+
+ if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+ fprintf(stdout, "\nNIST curve P-192 -- Generator:\n x = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, "\n y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, "\n");
+ /* G_y value taken from the standard: */
+ if (!BN_hex2bn(&z, "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811")) ABORT;
+ if (0 != BN_cmp(y, z)) ABORT;
+
+ fprintf(stdout, "verify group order ... ");
+ if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
+ if (!EC_POINTs_mul(group, Q, z, 0, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, "ok\n");
+
+ if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
+ if (!EC_GROUP_copy(P_192, group)) ABORT;
+
+
+ /* Curve P-224 (FIPS PUB 186-2, App. 6) */
+
+ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
+ if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
+ if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
+ if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
+
+ if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+ fprintf(stdout, "\nNIST curve P-224 -- Generator:\n x = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, "\n y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, "\n");
+ /* G_y value taken from the standard: */
+ if (!BN_hex2bn(&z, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
+ if (0 != BN_cmp(y, z)) ABORT;
+
+ fprintf(stdout, "verify group order ... ");
+ if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
+ if (!EC_POINTs_mul(group, Q, z, 0, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, "ok\n");
+
+ if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
+ if (!EC_GROUP_copy(P_224, group)) ABORT;
+
+
+ /* Curve P-256 (FIPS PUB 186-2, App. 6) */
+
+ if (!BN_hex2bn(&p, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
+ if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
+ if (!BN_hex2bn(&b, "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ if (!BN_hex2bn(&x, "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296")) ABORT;
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!BN_hex2bn(&z, "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E"
+ "84F3B9CAC2FC632551")) ABORT;
+ if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
+
+ if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+ fprintf(stdout, "\nNIST curve P-256 -- Generator:\n x = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, "\n y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, "\n");
+ /* G_y value taken from the standard: */
+ if (!BN_hex2bn(&z, "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5")) ABORT;
+ if (0 != BN_cmp(y, z)) ABORT;
+
+ fprintf(stdout, "verify group order ... ");
+ if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
+ if (!EC_POINTs_mul(group, Q, z, 0, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, "ok\n");
+
+ if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
+ if (!EC_GROUP_copy(P_256, group)) ABORT;
+
+
+ /* Curve P-384 (FIPS PUB 186-2, App. 6) */
+
+ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF")) ABORT;
+ if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC")) ABORT;
+ if (!BN_hex2bn(&b, "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141"
+ "120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ if (!BN_hex2bn(&x, "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B"
+ "9859F741E082542A385502F25DBF55296C3A545E3872760AB7")) ABORT;
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 1, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!BN_hex2bn(&z, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973")) ABORT;
+ if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
+
+ if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+ fprintf(stdout, "\nNIST curve P-384 -- Generator:\n x = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, "\n y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, "\n");
+ /* G_y value taken from the standard: */
+ if (!BN_hex2bn(&z, "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A14"
+ "7CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F")) ABORT;
+ if (0 != BN_cmp(y, z)) ABORT;
+
+ fprintf(stdout, "verify group order ... ");
+ if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
+ if (!EC_POINTs_mul(group, Q, z, 0, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, "ok\n");
+
+ if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
+ if (!EC_GROUP_copy(P_384, group)) ABORT;
+
+
+ /* Curve P-521 (FIPS PUB 186-2, App. 6) */
+
+ if (!BN_hex2bn(&p, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFF")) ABORT;
+ if (1 != BN_is_prime(p, BN_prime_checks, 0, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFC")) ABORT;
+ if (!BN_hex2bn(&b, "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B"
+ "315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573"
+ "DF883D2C34F1EF451FD46B503F00")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ if (!BN_hex2bn(&x, "C6858E06B70404E9CD9E3ECB662395B4429C648139053F"
+ "B521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B"
+ "3C1856A429BF97E7E31C2E5BD66")) ABORT;
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, P, x, 0, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!BN_hex2bn(&z, "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
+ "FFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5"
+ "C9B8899C47AEBB6FB71E91386409")) ABORT;
+ if (!EC_GROUP_set_generator(group, P, z, BN_value_one())) ABORT;
+
+ if (!EC_POINT_get_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+ fprintf(stdout, "\nNIST curve P-521 -- Generator:\n x = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, "\n y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, "\n");
+ /* G_y value taken from the standard: */
+ if (!BN_hex2bn(&z, "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579"
+ "B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C"
+ "7086A272C24088BE94769FD16650")) ABORT;
+ if (0 != BN_cmp(y, z)) ABORT;
+
+ fprintf(stdout, "verify group order ... ");
+ if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
+ if (!EC_POINTs_mul(group, Q, z, 0, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, "ok\n");
+
+ if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
+ if (!EC_GROUP_copy(P_521, group)) ABORT;
+
+
+ /* more tests using the last curve */
+
+ if (!EC_POINT_copy(Q, P)) ABORT;
+ if (EC_POINT_is_at_infinity(group, Q)) ABORT;
+ if (!EC_POINT_dbl(group, P, P, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!EC_POINT_invert(group, Q, ctx)) ABORT; /* P = -2Q */
+
+ if (!EC_POINT_add(group, R, P, Q, ctx)) ABORT;
+ if (!EC_POINT_add(group, R, R, Q, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, R)) ABORT; /* R = P + 2Q */
+
+ {
+ EC_POINT *points[2];
+ BIGNUM *scalars[2];
+
+ if (EC_POINT_is_at_infinity(group, Q)) ABORT;
+
+ if (!BN_add(y, z, BN_value_one())) ABORT;
+ if (BN_is_odd(y)) ABORT;
+ if (!BN_rshift1(y, y)) ABORT;
+
+ points[0] = Q;
+ points[1] = Q;
+ scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
+ scalars[1] = y;
+
+ fprintf(stdout, "simultaneous multiplication ... ");
+
+ /* z is still the group order */
+ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
+ if (!EC_POINTs_mul(group, R, z, 2, points, scalars, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, R, Q, ctx)) ABORT;
+
+ fprintf(stdout, "ok\n\n");
+ }
+
+
+#if 0
+ timings(P_192, 0, ctx);
+ timings(P_192, 1, ctx);
+ timings(P_224, 0, ctx);
+ timings(P_224, 1, ctx);
+ timings(P_256, 0, ctx);
+ timings(P_256, 1, ctx);
+ timings(P_384, 0, ctx);
+ timings(P_384, 1, ctx);
+ timings(P_521, 0, ctx);
+ timings(P_521, 1, ctx);
+#endif
+
if (ctx)
BN_CTX_free(ctx);
EC_POINT_free(R);
BN_free(x); BN_free(y); BN_free(z);
+ if (P_192) EC_GROUP_free(P_192);
+ if (P_224) EC_GROUP_free(P_224);
+ if (P_256) EC_GROUP_free(P_256);
+ if (P_384) EC_GROUP_free(P_384);
+ if (P_521) EC_GROUP_free(P_521);
+
ERR_free_strings();
ERR_remove_state(0);
CRYPTO_mem_leaks_fp(stderr);
projects / openssl.git / blobdiff