/* crypto/ec/ectest.c */
+/*
+ * Originally written by Bodo Moeller for the OpenSSL project.
+ */
/* ====================================================================
* Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
*
* Hudson (tjh@cryptsoft.com).
*
*/
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * Portions of the attached software ("Contribution") are developed by
+ * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
+ *
+ * The Contribution is licensed pursuant to the OpenSSL open source
+ * license provided above.
+ *
+ * The elliptic curve binary polynomial software is originally written by
+ * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
#include <stdio.h>
#include <stdlib.h>
+#ifdef FLAT_INC
+#include "e_os.h"
+#else
+#include "../e_os.h"
+#endif
+#include <string.h>
+#include <time.h>
#ifdef OPENSSL_NO_EC
#include <openssl/ec.h>
+#ifndef OPENSSL_NO_ENGINE
+#include <openssl/engine.h>
+#endif
#include <openssl/err.h>
+#include <openssl/obj_mac.h>
+#include <openssl/objects.h>
+#include <openssl/rand.h>
+#include <openssl/bn.h>
+
+#if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12)
+/* suppress "too big too optimize" warning */
+#pragma warning(disable:4959)
+#endif
#define ABORT do { \
+ fflush(stdout); \
fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
ERR_print_errors_fp(stderr); \
- exit(1); \
+ EXIT(1); \
} while (0)
-int main(int argc, char *argv[])
+#define TIMING_BASE_PT 0
+#define TIMING_RAND_PT 1
+#define TIMING_SIMUL 2
+
+#if 0
+static void timings(EC_GROUP *group, int type, BN_CTX *ctx)
+ {
+ clock_t clck;
+ int i, j;
+ BIGNUM *s;
+ BIGNUM *r[10], *r0[10];
+ EC_POINT *P;
+
+ s = BN_new();
+ if (s == NULL) ABORT;
+
+ fprintf(stdout, "Timings for %d-bit field, ", EC_GROUP_get_degree(group));
+ 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));
+
+ for (i = 0; i < 10; i++)
+ {
+ if ((r[i] = BN_new()) == NULL) ABORT;
+ if (!BN_pseudo_rand(r[i], BN_num_bits(s), 0, 0)) ABORT;
+ if (type != TIMING_BASE_PT)
+ {
+ if ((r0[i] = BN_new()) == NULL) ABORT;
+ if (!BN_pseudo_rand(r0[i], BN_num_bits(s), 0, 0)) ABORT;
+ }
+ }
+
+ clck = clock();
+ for (i = 0; i < 10; i++)
+ {
+ for (j = 0; j < 10; j++)
+ {
+ if (!EC_POINT_mul(group, P, (type != TIMING_RAND_PT) ? r[i] : NULL,
+ (type != TIMING_BASE_PT) ? P : NULL, (type != TIMING_BASE_PT) ? r0[i] : NULL, ctx)) ABORT;
+ }
+ }
+ clck = clock() - clck;
+
+ fprintf(stdout, "\n");
+
+#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
+
+ if (type == TIMING_BASE_PT) {
+ fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
+ "base point multiplications", (double)clck/CLOCKS_PER_SEC);
+ } else if (type == TIMING_RAND_PT) {
+ fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
+ "random point multiplications", (double)clck/CLOCKS_PER_SEC);
+ } else if (type == TIMING_SIMUL) {
+ fprintf(stdout, "%i %s in %.2f " UNIT "\n", i*j,
+ "s*P+t*Q operations", (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);
+ for (i = 0; i < 10; i++)
+ {
+ BN_free(r[i]);
+ if (type != TIMING_BASE_PT) BN_free(r0[i]);
+ }
+ }
+#endif
+
+/* test multiplication with group order, long and negative scalars */
+static void group_order_tests(EC_GROUP *group)
+ {
+ BIGNUM *n1, *n2, *order;
+ EC_POINT *P = EC_POINT_new(group);
+ EC_POINT *Q = EC_POINT_new(group);
+ BN_CTX *ctx = BN_CTX_new();
+
+ n1 = BN_new(); n2 = BN_new(); order = BN_new();
+ fprintf(stdout, "verify group order ...");
+ fflush(stdout);
+ if (!EC_GROUP_get_order(group, order, ctx)) ABORT;
+ if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, ".");
+ fflush(stdout);
+ if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
+ if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
+ fprintf(stdout, " ok\n");
+ fprintf(stdout, "long/negative scalar tests ... ");
+ if (!BN_one(n1)) ABORT;
+ /* n1 = 1 - order */
+ if (!BN_sub(n1, n1, order)) ABORT;
+ if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
+ /* n2 = 1 + order */
+ if (!BN_add(n2, order, BN_value_one())) ABORT;
+ if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
+ /* n2 = (1 - order) * (1 + order) */
+ if (!BN_mul(n2, n1, n2, ctx)) ABORT;
+ if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT;
+ fprintf(stdout, "ok\n");
+ EC_POINT_free(P);
+ EC_POINT_free(Q);
+ BN_free(n1);
+ BN_free(n2);
+ BN_free(order);
+ BN_CTX_free(ctx);
+ }
+
+void prime_field_tests()
{
BN_CTX *ctx = NULL;
BIGNUM *p, *a, *b;
EC_GROUP *group;
+ EC_GROUP *P_160 = NULL, *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];
size_t i, len;
+ int k;
- 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
b = BN_new();
if (!p || !a || !b) ABORT;
- if (!BN_hex2bn(&p, "D")) ABORT;
- if (!BN_hex2bn(&a, "7")) ABORT;
- if (!BN_hex2bn(&b, "C")) ABORT;
+ if (!BN_hex2bn(&p, "17")) ABORT;
+ 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)) ABORT;
+ 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");
z = BN_new();
if (!x || !y || !z) ABORT;
- if (!BN_hex2bn(&x, "C")) ABORT;
+ if (!BN_hex2bn(&x, "D")) ABORT;
if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
if (!EC_POINT_is_on_curve(group, Q, ctx))
{
}
fprintf(stdout, "A cyclic subgroup:\n");
+ k = 100;
do
{
+ if (k-- == 0) ABORT;
+
if (EC_POINT_is_at_infinity(group, P))
fprintf(stdout, " point at infinity\n");
else
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 (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
- fprintf(stdout, "Generator as octect string, compressed form:\n ");
+ fprintf(stdout, "Generator as octet string, compressed form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
- fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n ");
+ fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
if (len == 0) ABORT;
if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
- fprintf(stdout, "\nGenerator as octect string, hybrid form:\n ");
+ fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT;
if (!EC_POINT_invert(group, P, ctx)) ABORT;
if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
- /* ... */
+
+ /* Curve secp160r1 (Certicom Research SEC 2 Version 1.0, section 2.4.2, 2000)
+ * -- not a NIST curve, but commonly used */
+
+ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF")) ABORT;
+ if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC")) ABORT;
+ if (!BN_hex2bn(&b, "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(group, p, a, b, ctx)) ABORT;
+
+ if (!BN_hex2bn(&x, "4A96B5688EF573284664698968C38BB913CBFC82")) ABORT;
+ if (!BN_hex2bn(&y, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
+ if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT;
+ if (!BN_hex2bn(&z, "0100000000000000000001F4C8F927AED3CA752257")) 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, "\nSEC2 curve secp160r1 -- 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, "23a628553168947d59dcc912042351377ac5fb32")) ABORT;
+ if (0 != BN_cmp(y, z)) ABORT;
+
+ fprintf(stdout, "verify degree ...");
+ if (EC_GROUP_get_degree(group) != 160) ABORT;
+ fprintf(stdout, " ok\n");
+
+ group_order_tests(group);
+
+ if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT;
+ if (!EC_GROUP_copy(P_160, group)) ABORT;
+
+
+ /* Curve P-192 (FIPS PUB 186-2, App. 6) */
+
+ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF")) ABORT;
+ if (1 != BN_is_prime_ex(p, BN_prime_checks, 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 degree ...");
+ if (EC_GROUP_get_degree(group) != 192) ABORT;
+ fprintf(stdout, " ok\n");
+
+ group_order_tests(group);
+
+ 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_ex(p, BN_prime_checks, 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 degree ...");
+ if (EC_GROUP_get_degree(group) != 224) ABORT;
+ fprintf(stdout, " ok\n");
+
+ group_order_tests(group);
+
+ 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_ex(p, BN_prime_checks, 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 degree ...");
+ if (EC_GROUP_get_degree(group) != 256) ABORT;
+ fprintf(stdout, " ok\n");
+
+ group_order_tests(group);
+
+ 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_ex(p, BN_prime_checks, 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 degree ...");
+ if (EC_GROUP_get_degree(group) != 384) ABORT;
+ fprintf(stdout, " ok\n");
+
+ group_order_tests(group);
+
+ 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_ex(p, BN_prime_checks, 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 degree ...");
+ if (EC_GROUP_get_degree(group) != 521) ABORT;
+ fprintf(stdout, " ok\n");
+
+ group_order_tests(group);
+
+ 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 */
+
+ {
+ const EC_POINT *points[4];
+ const BIGNUM *scalars[4];
+ BIGNUM scalar3;
+
+ if (EC_POINT_is_at_infinity(group, Q)) ABORT;
+ points[0] = Q;
+ points[1] = Q;
+ points[2] = Q;
+ points[3] = Q;
+
+ if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
+ if (!BN_add(y, z, BN_value_one())) ABORT;
+ if (BN_is_odd(y)) ABORT;
+ if (!BN_rshift1(y, y)) ABORT;
+ scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
+ scalars[1] = y;
+
+ fprintf(stdout, "combined multiplication ...");
+ fflush(stdout);
+
+ /* 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, ".");
+ fflush(stdout);
+
+ if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
+ if (!BN_add(z, z, y)) ABORT;
+ BN_set_negative(z, 1);
+ scalars[0] = y;
+ scalars[1] = z; /* z = -(order + y) */
+
+ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+ fprintf(stdout, ".");
+ fflush(stdout);
+
+ if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
+ if (!BN_add(z, x, y)) ABORT;
+ BN_set_negative(z, 1);
+ scalars[0] = x;
+ scalars[1] = y;
+ scalars[2] = z; /* z = -(x+y) */
+
+ BN_init(&scalar3);
+ BN_zero(&scalar3);
+ scalars[3] = &scalar3;
+
+ if (!EC_POINTs_mul(group, P, NULL, 4, points, scalars, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+ fprintf(stdout, " ok\n\n");
+
+ BN_free(&scalar3);
+ }
+
+
+#if 0
+ timings(P_160, TIMING_BASE_PT, ctx);
+ timings(P_160, TIMING_RAND_PT, ctx);
+ timings(P_160, TIMING_SIMUL, ctx);
+ timings(P_192, TIMING_BASE_PT, ctx);
+ timings(P_192, TIMING_RAND_PT, ctx);
+ timings(P_192, TIMING_SIMUL, ctx);
+ timings(P_224, TIMING_BASE_PT, ctx);
+ timings(P_224, TIMING_RAND_PT, ctx);
+ timings(P_224, TIMING_SIMUL, ctx);
+ timings(P_256, TIMING_BASE_PT, ctx);
+ timings(P_256, TIMING_RAND_PT, ctx);
+ timings(P_256, TIMING_SIMUL, ctx);
+ timings(P_384, TIMING_BASE_PT, ctx);
+ timings(P_384, TIMING_RAND_PT, ctx);
+ timings(P_384, TIMING_SIMUL, ctx);
+ timings(P_521, TIMING_BASE_PT, ctx);
+ timings(P_521, TIMING_RAND_PT, ctx);
+ timings(P_521, TIMING_SIMUL, ctx);
+#endif
+
if (ctx)
BN_CTX_free(ctx);
EC_POINT_free(R);
BN_free(x); BN_free(y); BN_free(z);
+ if (P_160) EC_GROUP_free(P_160);
+ 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);
+
+ }
+
+/* Change test based on whether binary point compression is enabled or not. */
+#ifdef OPENSSL_EC_BIN_PT_COMP
+#define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
+ if (!BN_hex2bn(&x, _x)) ABORT; \
+ if (!EC_POINT_set_compressed_coordinates_GF2m(group, P, x, _y_bit, ctx)) ABORT; \
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
+ if (!BN_hex2bn(&z, _order)) ABORT; \
+ if (!BN_hex2bn(&cof, _cof)) ABORT; \
+ if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
+ if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
+ fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
+ 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, _y)) ABORT; \
+ if (0 != BN_cmp(y, z)) ABORT;
+#else
+#define CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
+ if (!BN_hex2bn(&x, _x)) ABORT; \
+ if (!BN_hex2bn(&y, _y)) ABORT; \
+ if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT; \
+ if (!EC_POINT_is_on_curve(group, P, ctx)) ABORT; \
+ if (!BN_hex2bn(&z, _order)) ABORT; \
+ if (!BN_hex2bn(&cof, _cof)) ABORT; \
+ if (!EC_GROUP_set_generator(group, P, z, cof)) ABORT; \
+ fprintf(stdout, "\n%s -- Generator:\n x = 0x", _name); \
+ BN_print_fp(stdout, x); \
+ fprintf(stdout, "\n y = 0x"); \
+ BN_print_fp(stdout, y); \
+ fprintf(stdout, "\n");
+#endif
+
+#define CHAR2_CURVE_TEST(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
+ if (!BN_hex2bn(&p, _p)) ABORT; \
+ if (!BN_hex2bn(&a, _a)) ABORT; \
+ if (!BN_hex2bn(&b, _b)) ABORT; \
+ if (!EC_GROUP_set_curve_GF2m(group, p, a, b, ctx)) ABORT; \
+ CHAR2_CURVE_TEST_INTERNAL(_name, _p, _a, _b, _x, _y, _y_bit, _order, _cof, _degree, _variable) \
+ fprintf(stdout, "verify degree ..."); \
+ if (EC_GROUP_get_degree(group) != _degree) ABORT; \
+ fprintf(stdout, " ok\n"); \
+ group_order_tests(group); \
+ if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \
+ if (!EC_GROUP_copy(_variable, group)) ABORT; \
+
+
+void char2_field_tests()
+ {
+ BN_CTX *ctx = NULL;
+ BIGNUM *p, *a, *b;
+ EC_GROUP *group;
+ EC_GROUP *C2_K163 = NULL, *C2_K233 = NULL, *C2_K283 = NULL, *C2_K409 = NULL, *C2_K571 = NULL;
+ EC_GROUP *C2_B163 = NULL, *C2_B233 = NULL, *C2_B283 = NULL, *C2_B409 = NULL, *C2_B571 = NULL;
+ EC_POINT *P, *Q, *R;
+ BIGNUM *x, *y, *z, *cof;
+ unsigned char buf[100];
+ size_t i, len;
+ int k;
+
+#if 1 /* optional */
+ ctx = BN_CTX_new();
+ if (!ctx) ABORT;
+#endif
+
+ p = BN_new();
+ a = BN_new();
+ b = BN_new();
+ if (!p || !a || !b) ABORT;
+
+ if (!BN_hex2bn(&p, "13")) ABORT;
+ if (!BN_hex2bn(&a, "3")) ABORT;
+ if (!BN_hex2bn(&b, "1")) ABORT;
+
+ group = EC_GROUP_new(EC_GF2m_simple_method()); /* applications should use EC_GROUP_new_curve_GF2m
+ * so that the library gets to choose the EC_METHOD */
+ if (!group) ABORT;
+ if (!EC_GROUP_set_curve_GF2m(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)) ABORT;
+ EC_GROUP_free(group);
+ group = tmp;
+ }
+
+ if (!EC_GROUP_get_curve_GF2m(group, p, a, b, ctx)) ABORT;
+
+ fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 + x*y = x^3 + a*x^2 + b (mod 0x");
+ BN_print_fp(stdout, p);
+ fprintf(stdout, ")\n a = 0x");
+ BN_print_fp(stdout, a);
+ fprintf(stdout, "\n b = 0x");
+ BN_print_fp(stdout, b);
+ fprintf(stdout, "\n(0x... means binary polynomial)\n");
+
+ P = EC_POINT_new(group);
+ Q = EC_POINT_new(group);
+ R = EC_POINT_new(group);
+ if (!P || !Q || !R) ABORT;
+
+ if (!EC_POINT_set_to_infinity(group, P)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+ buf[0] = 0;
+ if (!EC_POINT_oct2point(group, Q, buf, 1, ctx)) ABORT;
+
+ if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+ x = BN_new();
+ y = BN_new();
+ z = BN_new();
+ cof = BN_new();
+ if (!x || !y || !z || !cof) ABORT;
+
+ if (!BN_hex2bn(&x, "6")) ABORT;
+/* Change test based on whether binary point compression is enabled or not. */
+#ifdef OPENSSL_EC_BIN_PT_COMP
+ if (!EC_POINT_set_compressed_coordinates_GF2m(group, Q, x, 1, ctx)) ABORT;
+#else
+ if (!BN_hex2bn(&y, "8")) ABORT;
+ if (!EC_POINT_set_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
+#endif
+ if (!EC_POINT_is_on_curve(group, Q, ctx))
+ {
+/* Change test based on whether binary point compression is enabled or not. */
+#ifdef OPENSSL_EC_BIN_PT_COMP
+ if (!EC_POINT_get_affine_coordinates_GF2m(group, Q, x, y, ctx)) ABORT;
+#endif
+ fprintf(stderr, "Point is not on curve: x = 0x");
+ BN_print_fp(stderr, x);
+ fprintf(stderr, ", y = 0x");
+ BN_print_fp(stderr, y);
+ fprintf(stderr, "\n");
+ ABORT;
+ }
+
+ fprintf(stdout, "A cyclic subgroup:\n");
+ k = 100;
+ do
+ {
+ if (k-- == 0) ABORT;
+
+ if (EC_POINT_is_at_infinity(group, P))
+ fprintf(stdout, " point at infinity\n");
+ else
+ {
+ if (!EC_POINT_get_affine_coordinates_GF2m(group, P, x, y, ctx)) ABORT;
+
+ fprintf(stdout, " x = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, ", y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, "\n");
+ }
+
+ if (!EC_POINT_copy(R, P)) ABORT;
+ if (!EC_POINT_add(group, P, P, Q, ctx)) ABORT;
+ }
+ while (!EC_POINT_is_at_infinity(group, P));
+
+ if (!EC_POINT_add(group, P, Q, R, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+/* Change test based on whether binary point compression is enabled or not. */
+#ifdef OPENSSL_EC_BIN_PT_COMP
+ len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_COMPRESSED, buf, sizeof buf, ctx);
+ if (len == 0) ABORT;
+ if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
+ fprintf(stdout, "Generator as octet string, compressed form:\n ");
+ for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
+#endif
+
+ len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx);
+ if (len == 0) ABORT;
+ if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
+ fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n ");
+ for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
+
+/* Change test based on whether binary point compression is enabled or not. */
+#ifdef OPENSSL_EC_BIN_PT_COMP
+ len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx);
+ if (len == 0) ABORT;
+ if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT;
+ fprintf(stdout, "\nGenerator as octet string, hybrid form:\n ");
+ for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]);
+#endif
+
+ fprintf(stdout, "\n");
+
+ if (!EC_POINT_invert(group, P, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
+
+
+ /* Curve K-163 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve K-163",
+ "0800000000000000000000000000000000000000C9",
+ "1",
+ "1",
+ "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8",
+ "0289070FB05D38FF58321F2E800536D538CCDAA3D9",
+ 1,
+ "04000000000000000000020108A2E0CC0D99F8A5EF",
+ "2",
+ 163,
+ C2_K163
+ );
+
+ /* Curve B-163 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve B-163",
+ "0800000000000000000000000000000000000000C9",
+ "1",
+ "020A601907B8C953CA1481EB10512F78744A3205FD",
+ "03F0EBA16286A2D57EA0991168D4994637E8343E36",
+ "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1",
+ 1,
+ "040000000000000000000292FE77E70C12A4234C33",
+ "2",
+ 163,
+ C2_B163
+ );
+
+ /* Curve K-233 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve K-233",
+ "020000000000000000000000000000000000000004000000000000000001",
+ "0",
+ "1",
+ "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126",
+ "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3",
+ 0,
+ "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF",
+ "4",
+ 233,
+ C2_K233
+ );
+
+ /* Curve B-233 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve B-233",
+ "020000000000000000000000000000000000000004000000000000000001",
+ "000000000000000000000000000000000000000000000000000000000001",
+ "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD",
+ "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B",
+ "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052",
+ 1,
+ "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7",
+ "2",
+ 233,
+ C2_B233
+ );
+
+ /* Curve K-283 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve K-283",
+ "0800000000000000000000000000000000000000000000000000000000000000000010A1",
+ "0",
+ "1",
+ "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836",
+ "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259",
+ 0,
+ "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61",
+ "4",
+ 283,
+ C2_K283
+ );
+
+ /* Curve B-283 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve B-283",
+ "0800000000000000000000000000000000000000000000000000000000000000000010A1",
+ "000000000000000000000000000000000000000000000000000000000000000000000001",
+ "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5",
+ "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053",
+ "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4",
+ 1,
+ "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307",
+ "2",
+ 283,
+ C2_B283
+ );
+
+ /* Curve K-409 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve K-409",
+ "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
+ "0",
+ "1",
+ "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746",
+ "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B",
+ 1,
+ "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF",
+ "4",
+ 409,
+ C2_K409
+ );
+
+ /* Curve B-409 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve B-409",
+ "02000000000000000000000000000000000000000000000000000000000000000000000000000000008000000000000000000001",
+ "00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
+ "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F",
+ "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7",
+ "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706",
+ 1,
+ "010000000000000000000000000000000000000000000000000001E2AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173",
+ "2",
+ 409,
+ C2_B409
+ );
+
+ /* Curve K-571 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve K-571",
+ "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
+ "0",
+ "1",
+ "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA44370958493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972",
+ "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3",
+ 0,
+ "020000000000000000000000000000000000000000000000000000000000000000000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001",
+ "4",
+ 571,
+ C2_K571
+ );
+
+ /* Curve B-571 (FIPS PUB 186-2, App. 6) */
+ CHAR2_CURVE_TEST
+ (
+ "NIST curve B-571",
+ "80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000425",
+ "000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
+ "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A",
+ "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19",
+ "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B",
+ 1,
+ "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47",
+ "2",
+ 571,
+ C2_B571
+ );
+
+ /* 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 */
+
+ {
+ const EC_POINT *points[3];
+ const BIGNUM *scalars[3];
+
+ if (EC_POINT_is_at_infinity(group, Q)) ABORT;
+ points[0] = Q;
+ points[1] = Q;
+ points[2] = Q;
+
+ if (!BN_add(y, z, BN_value_one())) ABORT;
+ if (BN_is_odd(y)) ABORT;
+ if (!BN_rshift1(y, y)) ABORT;
+ scalars[0] = y; /* (group order + 1)/2, so y*Q + y*Q = Q */
+ scalars[1] = y;
+
+ fprintf(stdout, "combined multiplication ...");
+ fflush(stdout);
+
+ /* 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, ".");
+ fflush(stdout);
+
+ if (!BN_pseudo_rand(y, BN_num_bits(y), 0, 0)) ABORT;
+ if (!BN_add(z, z, y)) ABORT;
+ BN_set_negative(z, 1);
+ scalars[0] = y;
+ scalars[1] = z; /* z = -(order + y) */
+
+ if (!EC_POINTs_mul(group, P, NULL, 2, points, scalars, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+ fprintf(stdout, ".");
+ fflush(stdout);
+
+ if (!BN_pseudo_rand(x, BN_num_bits(y) - 1, 0, 0)) ABORT;
+ if (!BN_add(z, x, y)) ABORT;
+ BN_set_negative(z, 1);
+ scalars[0] = x;
+ scalars[1] = y;
+ scalars[2] = z; /* z = -(x+y) */
+
+ if (!EC_POINTs_mul(group, P, NULL, 3, points, scalars, ctx)) ABORT;
+ if (!EC_POINT_is_at_infinity(group, P)) ABORT;
+
+ fprintf(stdout, " ok\n\n");
+ }
+
+
+#if 0
+ timings(C2_K163, TIMING_BASE_PT, ctx);
+ timings(C2_K163, TIMING_RAND_PT, ctx);
+ timings(C2_K163, TIMING_SIMUL, ctx);
+ timings(C2_B163, TIMING_BASE_PT, ctx);
+ timings(C2_B163, TIMING_RAND_PT, ctx);
+ timings(C2_B163, TIMING_SIMUL, ctx);
+ timings(C2_K233, TIMING_BASE_PT, ctx);
+ timings(C2_K233, TIMING_RAND_PT, ctx);
+ timings(C2_K233, TIMING_SIMUL, ctx);
+ timings(C2_B233, TIMING_BASE_PT, ctx);
+ timings(C2_B233, TIMING_RAND_PT, ctx);
+ timings(C2_B233, TIMING_SIMUL, ctx);
+ timings(C2_K283, TIMING_BASE_PT, ctx);
+ timings(C2_K283, TIMING_RAND_PT, ctx);
+ timings(C2_K283, TIMING_SIMUL, ctx);
+ timings(C2_B283, TIMING_BASE_PT, ctx);
+ timings(C2_B283, TIMING_RAND_PT, ctx);
+ timings(C2_B283, TIMING_SIMUL, ctx);
+ timings(C2_K409, TIMING_BASE_PT, ctx);
+ timings(C2_K409, TIMING_RAND_PT, ctx);
+ timings(C2_K409, TIMING_SIMUL, ctx);
+ timings(C2_B409, TIMING_BASE_PT, ctx);
+ timings(C2_B409, TIMING_RAND_PT, ctx);
+ timings(C2_B409, TIMING_SIMUL, ctx);
+ timings(C2_K571, TIMING_BASE_PT, ctx);
+ timings(C2_K571, TIMING_RAND_PT, ctx);
+ timings(C2_K571, TIMING_SIMUL, ctx);
+ timings(C2_B571, TIMING_BASE_PT, ctx);
+ timings(C2_B571, TIMING_RAND_PT, ctx);
+ timings(C2_B571, TIMING_SIMUL, ctx);
+#endif
+
+
+ if (ctx)
+ BN_CTX_free(ctx);
+ BN_free(p); BN_free(a); BN_free(b);
+ EC_GROUP_free(group);
+ EC_POINT_free(P);
+ EC_POINT_free(Q);
+ EC_POINT_free(R);
+ BN_free(x); BN_free(y); BN_free(z); BN_free(cof);
+
+ if (C2_K163) EC_GROUP_free(C2_K163);
+ if (C2_B163) EC_GROUP_free(C2_B163);
+ if (C2_K233) EC_GROUP_free(C2_K233);
+ if (C2_B233) EC_GROUP_free(C2_B233);
+ if (C2_K283) EC_GROUP_free(C2_K283);
+ if (C2_B283) EC_GROUP_free(C2_B283);
+ if (C2_K409) EC_GROUP_free(C2_K409);
+ if (C2_B409) EC_GROUP_free(C2_B409);
+ if (C2_K571) EC_GROUP_free(C2_K571);
+ if (C2_B571) EC_GROUP_free(C2_B571);
+
+ }
+
+void internal_curve_test(void)
+ {
+ EC_builtin_curve *curves = NULL;
+ size_t crv_len = 0, n = 0;
+ int ok = 1;
+
+ crv_len = EC_get_builtin_curves(NULL, 0);
+
+ curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * crv_len);
+
+ if (curves == NULL)
+ return;
+
+ if (!EC_get_builtin_curves(curves, crv_len))
+ {
+ OPENSSL_free(curves);
+ return;
+ }
+
+ fprintf(stdout, "testing internal curves: ");
+
+ for (n = 0; n < crv_len; n++)
+ {
+ EC_GROUP *group = NULL;
+ int nid = curves[n].nid;
+ if ((group = EC_GROUP_new_by_curve_name(nid)) == NULL)
+ {
+ ok = 0;
+ fprintf(stdout, "\nEC_GROUP_new_curve_name() failed with"
+ " curve %s\n", OBJ_nid2sn(nid));
+ /* try next curve */
+ continue;
+ }
+ if (!EC_GROUP_check(group, NULL))
+ {
+ ok = 0;
+ fprintf(stdout, "\nEC_GROUP_check() failed with"
+ " curve %s\n", OBJ_nid2sn(nid));
+ EC_GROUP_free(group);
+ /* try the next curve */
+ continue;
+ }
+ fprintf(stdout, ".");
+ fflush(stdout);
+ EC_GROUP_free(group);
+ }
+ if (ok)
+ fprintf(stdout, " ok\n\n");
+ else
+ fprintf(stdout, " failed\n\n");
+ OPENSSL_free(curves);
+ return;
+ }
+
+#ifdef EC_NISTP224_64_GCC_128
+void nistp224_test()
+ {
+ fprintf(stdout, "\nNIST curve P-224 (optimised implementation):\n");
+ BIGNUM *p, *a, *b, *x, *y, *n, *m, *order;
+ p = BN_new();
+ a = BN_new();
+ b = BN_new();
+ x = BN_new(); y = BN_new();
+ m = BN_new(); n = BN_new(); order = BN_new();
+ BN_CTX *ctx = BN_CTX_new();
+ EC_GROUP *NISTP224;
+ EC_POINT *G, *P, *Q, *Q_CHECK;
+
+ NISTP224 = EC_GROUP_new(EC_GFp_nistp224_method());
+ if(!NISTP224) ABORT;
+ if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
+ if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
+ if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
+ if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
+ if (!EC_GROUP_set_curve_GFp(NISTP224, p, a, b, ctx)) ABORT;
+ G = EC_POINT_new(NISTP224);
+ P = EC_POINT_new(NISTP224);
+ Q = EC_POINT_new(NISTP224);
+ Q_CHECK = EC_POINT_new(NISTP224);
+ if(!BN_hex2bn(&x, "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E")) ABORT;
+ if(!BN_hex2bn(&y, "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555")) ABORT;
+ if(!EC_POINT_set_affine_coordinates_GFp(NISTP224, Q_CHECK, x, y, ctx)) ABORT;
+ if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
+ if (!BN_hex2bn(&y, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
+ if (!EC_POINT_set_affine_coordinates_GFp(NISTP224, G, x, y, ctx)) ABORT;
+ if (!BN_hex2bn(&order, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
+ if (!EC_GROUP_set_generator(NISTP224, G, order, BN_value_one())) ABORT;
+
+ fprintf(stdout, "verify degree ... ");
+ if (EC_GROUP_get_degree(NISTP224) != 224) ABORT;
+ fprintf(stdout, "ok\n");
+
+ fprintf(stdout, "NIST test vectors ... ");
+ if (!BN_hex2bn(&n, "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8")) ABORT;
+ /* fixed point multiplication */
+ EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+ /* random point multiplication */
+ EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+
+ /* set generator to P = 2*G, where G is the standard generator */
+ if (!EC_POINT_dbl(NISTP224, P, G, ctx)) ABORT;
+ if (!EC_GROUP_set_generator(NISTP224, P, order, BN_value_one())) ABORT;
+ /* set the scalar to m=n/2, where n is the NIST test scalar */
+ if (!BN_rshift(m, n, 1)) ABORT;
+
+ /* test the non-standard generator */
+ /* fixed point multiplication */
+ EC_POINT_mul(NISTP224, Q, m, NULL, NULL, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+ /* random point multiplication */
+ EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+
+ /* now repeat all tests with precomputation */
+ if (!EC_GROUP_precompute_mult(NISTP224, ctx)) ABORT;
+
+ /* fixed point multiplication */
+ EC_POINT_mul(NISTP224, Q, m, NULL, NULL, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+ /* random point multiplication */
+ EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+
+ /* reset generator */
+ if (!EC_GROUP_set_generator(NISTP224, G, order, BN_value_one())) ABORT;
+ /* fixed point multiplication */
+ EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+ /* random point multiplication */
+ EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx);
+ if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
+
+ fprintf(stdout, "ok\n");
+ group_order_tests(NISTP224);
+#if 0
+ timings(NISTP224, TIMING_BASE_PT, ctx);
+ timings(NISTP224, TIMING_RAND_PT, ctx);
+#endif
+ EC_GROUP_free(NISTP224);
+ EC_POINT_free(G);
+ EC_POINT_free(P);
+ EC_POINT_free(Q);
+ EC_POINT_free(Q_CHECK);
+ BN_free(n);
+ BN_free(m);
+ BN_free(p);
+ BN_free(a);
+ BN_free(b);
+ BN_free(x);
+ BN_free(y);
+ BN_free(order);
+ BN_CTX_free(ctx);
+ }
+#endif
+
+static const char rnd_seed[] = "string to make the random number generator think it has entropy";
+
+int main(int argc, char *argv[])
+ {
+
+ /* enable memory leak checking unless explicitly disabled */
+ if (!((getenv("OPENSSL_DEBUG_MEMORY") != NULL) && (0 == strcmp(getenv("OPENSSL_DEBUG_MEMORY"), "off"))))
+ {
+ CRYPTO_malloc_debug_init();
+ CRYPTO_set_mem_debug_options(V_CRYPTO_MDEBUG_ALL);
+ }
+ else
+ {
+ /* OPENSSL_DEBUG_MEMORY=off */
+ CRYPTO_set_mem_debug_functions(0, 0, 0, 0, 0);
+ }
+ CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
+ ERR_load_crypto_strings();
+
+ RAND_seed(rnd_seed, sizeof rnd_seed); /* or BN_generate_prime may fail */
+
+ prime_field_tests();
+ puts("");
+ char2_field_tests();
+#ifdef EC_NISTP224_64_GCC_128
+ nistp224_test();
+#endif
+ /* test the internal curves */
+ internal_curve_test();
+
+#ifndef OPENSSL_NO_ENGINE
+ ENGINE_cleanup();
+#endif
+ CRYPTO_cleanup_all_ex_data();
ERR_free_strings();
- ERR_remove_state(0);
+ ERR_remove_thread_state(NULL);
CRYPTO_mem_leaks_fp(stderr);
return 0;
projects / openssl.git / blobdiff