{
static const EC_METHOD ret = {
ec_GFp_simple_group_init,
- ec_GFp_simple_group_set_curve_GFp,
ec_GFp_simple_group_finish,
ec_GFp_simple_group_clear_finish,
ec_GFp_simple_group_copy,
+ ec_GFp_simple_group_set_curve_GFp,
+ ec_GFp_simple_group_get_curve_GFp,
ec_GFp_simple_group_set_generator,
- /* TODO: 'set' and 'get' functions for EC_GROUPs */
+ ec_GFp_simple_group_get0_generator,
+ ec_GFp_simple_group_get_order,
+ ec_GFp_simple_group_get_cofactor,
ec_GFp_simple_point_init,
ec_GFp_simple_point_finish,
ec_GFp_simple_point_clear_finish,
}
+void ec_GFp_simple_group_finish(EC_GROUP *group)
+ {
+ BN_free(&group->field);
+ BN_free(&group->a);
+ BN_free(&group->b);
+ if (group->generator != NULL)
+ EC_POINT_free(group->generator);
+ BN_free(&group->order);
+ BN_free(&group->cofactor);
+ }
+
+
+void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+ {
+ BN_clear_free(&group->field);
+ BN_clear_free(&group->a);
+ BN_clear_free(&group->b);
+ if (group->generator != NULL)
+ {
+ EC_POINT_clear_free(group->generator);
+ group->generator = NULL;
+ }
+ BN_clear_free(&group->order);
+ BN_clear_free(&group->cofactor);
+ }
+
+
+int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
+ {
+ if (!BN_copy(&dest->field, &src->field)) return 0;
+ if (!BN_copy(&dest->a, &src->a)) return 0;
+ if (!BN_copy(&dest->b, &src->b)) return 0;
+
+ dest->a_is_minus3 = src->a_is_minus3;
+
+ if (src->generator != NULL)
+ {
+ if (dest->generator == NULL)
+ {
+ dest->generator = EC_POINT_new(dest);
+ if (dest->generator == NULL) return 0;
+ }
+ if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
+ }
+ else
+ {
+ /* src->generator == NULL */
+ if (dest->generator != NULL)
+ {
+ EC_POINT_clear_free(dest->generator);
+ dest->generator = NULL;
+ }
+ }
+
+ if (!BN_copy(&dest->order, &src->order)) return 0;
+ if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
+
+ return 1;
+ }
+
+
int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *group,
const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
}
-void ec_GFp_simple_group_finish(EC_GROUP *group)
- {
- BN_free(&group->field);
- BN_free(&group->a);
- BN_free(&group->b);
- if (group->generator != NULL)
- EC_POINT_free(group->generator);
- BN_free(&group->order);
- BN_free(&group->cofactor);
- }
-
-
-void ec_GFp_simple_group_clear_finish(EC_GROUP *group)
+int ec_GFp_simple_group_get_curve_GFp(EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
{
- BN_clear_free(&group->field);
- BN_clear_free(&group->a);
- BN_clear_free(&group->b);
- if (group->generator != NULL)
+ int ret = 0;
+ BN_CTX *new_ctx = NULL;
+
+ if (p != NULL)
{
- EC_POINT_clear_free(group->generator);
- group->generator = NULL;
+ if (!BN_copy(p, &group->field)) return 0;
}
- BN_clear_free(&group->order);
- BN_clear_free(&group->cofactor);
- }
-
-int ec_GFp_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src)
- {
- if (!BN_copy(&dest->field, &src->field)) return 0;
- if (!BN_copy(&dest->a, &src->a)) return 0;
- if (!BN_copy(&dest->b, &src->b)) return 0;
-
- dest->a_is_minus3 = src->a_is_minus3;
-
- if (src->generator != NULL)
+ if (a != NULL || b != NULL)
{
- if (dest->generator == NULL)
+ if (group->meth->field_decode)
{
- dest->generator = EC_POINT_new(dest);
- if (dest->generator == NULL) return 0;
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+ if (a != NULL)
+ {
+ if (!group->meth->field_decode(group, a, &group->a, ctx)) goto err;
+ }
+ if (b != NULL)
+ {
+ if (!group->meth->field_decode(group, b, &group->b, ctx)) goto err;
+ }
}
- if (!EC_POINT_copy(dest->generator, src->generator)) return 0;
- }
- else
- {
- /* src->generator == NULL */
- if (dest->generator != NULL)
+ else
{
- EC_POINT_clear_free(dest->generator);
- dest->generator = NULL;
+ if (a != NULL)
+ {
+ if (!BN_copy(a, &group->a)) goto err;
+ }
+ if (b != NULL)
+ {
+ if (!BN_copy(b, &group->b)) goto err;
+ }
}
}
-
- if (!BN_copy(&dest->order, &src->order)) return 0;
- if (!BN_copy(&dest->cofactor, &src->cofactor)) return 0;
-
- return 1;
+
+ ret = 1;
+
+ err:
+ if (new_ctx)
+ BN_CTX_free(new_ctx);
+ return ret;
}
+
int ec_GFp_simple_group_set_generator(EC_GROUP *group, const EC_POINT *generator,
const BIGNUM *order, const BIGNUM *cofactor)
{
}
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
+EC_POINT *ec_GFp_simple_group_get0_generator(EC_GROUP *group)
+ {
+ return group->generator;
+ }
+
+
+int ec_GFp_simple_group_get_order(EC_GROUP *group, BIGNUM *order, BN_CTX *ctx)
+ {
+ if (!BN_copy(order, &group->order))
+ return 0;
+
+ return !BN_is_zero(&group->order);
+ }
+
+
+int ec_GFp_simple_group_get_cofactor(EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx)
+ {
+ if (!BN_copy(cofactor, &group->cofactor))
+ return 0;
+
+ return !BN_is_zero(&group->cofactor);
+ }
int ec_GFp_simple_point_init(EC_POINT *point)
int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
-/* TODO */
+ const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ int ret = 0;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+ if (x != NULL)
+ {
+ if (!BN_nnmod(&point->X, x, &group->field, ctx)) goto err;
+ if (group->meth->field_encode)
+ {
+ if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
+ }
+ }
+
+ if (y != NULL)
+ {
+ if (!BN_nnmod(&point->Y, y, &group->field, ctx)) goto err;
+ if (group->meth->field_encode)
+ {
+ if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
+ }
+ }
+
+ if (z != NULL)
+ {
+ int Z_is_one;
-int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
- BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
-/* TODO */
+ if (!BN_nnmod(&point->Z, z, &group->field, ctx)) goto err;
+ Z_is_one = BN_is_one(&point->Z);
+ if (group->meth->field_encode)
+ {
+ if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
+ }
+ point->Z_is_one = Z_is_one;
+ }
+
+ ret = 1;
+
+ err:
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
-int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
+ BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx)
{
BN_CTX *new_ctx = NULL;
int ret = 0;
-
- if (!BN_copy(&point->X, x)) goto err;
- if (!BN_copy(&point->Y, y)) goto err;
- if (!BN_one(&point->Z)) goto err;
-
- if (group->meth->field_encode)
+
+ if (group->meth->field_decode != 0)
{
if (ctx == NULL)
{
if (ctx == NULL)
return 0;
}
-
- if (!group->meth->field_encode(group, &point->X, &point->X, ctx)) goto err;
- if (!group->meth->field_encode(group, &point->Y, &point->Y, ctx)) goto err;
- if (!group->meth->field_encode(group, &point->Z, &point->Z, ctx)) goto err;
- }
- point->Z_is_one = 1;
+ if (x != NULL)
+ {
+ if (!group->meth->field_decode(group, x, &point->X, ctx)) goto err;
+ }
+ if (y != NULL)
+ {
+ if (!group->meth->field_decode(group, y, &point->Y, ctx)) goto err;
+ }
+ if (z != NULL)
+ {
+ if (!group->meth->field_decode(group, z, &point->Z, ctx)) goto err;
+ }
+ }
+ else
+ {
+ if (x != NULL)
+ {
+ if (!BN_copy(x, &point->X)) goto err;
+ }
+ if (y != NULL)
+ {
+ if (!BN_copy(y, &point->Y)) goto err;
+ }
+ if (z != NULL)
+ {
+ if (!BN_copy(z, &point->Z)) goto err;
+ }
+ }
+ ret = 1;
+
err:
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
}
+int ec_GFp_simple_point_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
+ const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx)
+ {
+ if (x == NULL || y == NULL)
+ {
+ /* unlike for projective coordinates, we do not tolerate this */
+ ECerr(EC_F_EC_GFP_SIMPLE_POINT_SET_AFFINE_COORDINATES_GFP, ERR_R_PASSED_NULL_PARAMETER);
+ return 0;
+ }
+
+ return EC_POINT_set_Jprojective_coordinates_GFp(group, point, x, y, BN_value_one(), ctx);
+ }
+
+
int ec_GFp_simple_point_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point,
BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
{
int ec_GFp_simple_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
- const BIGNUM *x, int y_bit, BN_CTX *);
-/* TODO */
+ const BIGNUM *x, int y_bit, BN_CTX *ctx)
+ {
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp1, *tmp2, *y;
+ int ret = 0;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return 0;
+ }
+
+ y_bit = (y_bit != 0);
+
+ BN_CTX_start(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ tmp2 = BN_CTX_get(ctx);
+ y = BN_CTX_get(ctx);
+ if (y == NULL) goto err;
+
+ /* Recover y. We have a Weierstrass equation
+ * y^2 = x^3 + a*x + b,
+ * so y is one of the square roots of x^3 + a*x + b.
+ */
+
+ /* tmp1 := x^3 */
+ if (!BN_mod_sqr(tmp2, x, &group->field, ctx)) goto err;
+ if (!BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) goto err;
+
+ /* tmp1 := tmp1 + a*x */
+ if (group->a_is_minus3)
+ {
+ if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
+ if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
+ if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+ else
+ {
+ if (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err;
+ if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
+ }
+
+ /* tmp1 := tmp1 + b */
+ if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
+
+ if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_BN_LIB);
+ goto err;
+ }
+ /* If tmp1 is not a square (i.e. there is no point on the curve with
+ * our x), then y now is a nonsense value too */
+
+ if (y_bit != BN_is_odd(y))
+ {
+ if (BN_is_zero(y))
+ {
+ int kron;
+
+ kron = BN_kronecker(x, &group->field, ctx);
+ if (kron == -2) goto err;
+
+ if (kron == 1)
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSION_BIT);
+ else
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, EC_R_INVALID_COMPRESSED_POINT);
+ goto err;
+ }
+ if (!BN_usub(y, &group->field, y)) goto err;
+ }
+ if (y_bit != BN_is_odd(y))
+ {
+ ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES_GFP, ERR_R_INTERNAL_ERROR);
+ goto err;
+ }
+
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
+
+ ret = 1;
+
+ err:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form,
goto err;
}
- if (form != POINT_CONVERSION_COMPRESSED)
+ if (form == POINT_CONVERSION_COMPRESSED)
+ {
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err;
+ }
+ else
{
if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err;
if (BN_ucmp(y, &group->field) >= 0)
goto err;
}
}
- }
- if (form == POINT_CONVERSION_COMPRESSED)
- {
- /* Recover y. We have a Weierstrass equation
- * y^2 = x^3 + a*x + b,
- * so y is one of the square roots of x^3 + a*x + b.
- */
-
- BIGNUM *tmp1, *tmp2;
-
- tmp1 = BN_CTX_get(ctx);
- tmp2 = BN_CTX_get(ctx);
- if (tmp2 == NULL) goto err;
-
- /* tmp1 := x^3 */
- if (!BN_mod_sqr(tmp2, x, &group->field, ctx)) goto err;
- if (!BN_mod_mul(tmp1, tmp2, x, &group->field, ctx)) goto err;
-
- /* tmp1 := tmp1 + a*x */
- if (group->a_is_minus3)
- {
- if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err;
- if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err;
- if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
- else
- {
- if (!BN_mod_mul(tmp2, &group->a, x, &group->field, ctx)) goto err;
- if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err;
- }
-
- /* tmp1 := tmp1 + b */
- if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err;
-
- if (!BN_mod_sqrt(y, tmp1, &group->field, ctx))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_BN_LIB);
- goto err;
- }
-
- if (y_bit != BN_is_odd(y))
- {
- if (BN_is_zero(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
- goto err;
- }
- if (!BN_usub(y, &group->field, y)) goto err;
- }
- if (y_bit != BN_is_odd(y))
- {
- ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, ERR_R_INTERNAL_ERROR);
- goto err;
- }
+ if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
}
- if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err;
-
if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */
{
ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE);
}
-int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
-/* TODO */
+int ec_GFp_simple_invert(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
+ {
+ if (EC_POINT_is_at_infinity(group, point) || BN_is_zero(&point->Y))
+ /* point is its own inverse */
+ return 1;
+
+ return BN_usub(&point->Y, &group->field, &point->Y);
+ }
int ec_GFp_simple_is_at_infinity(const EC_GROUP *group, const EC_POINT *point)
/* rh := rh + a*X*Z^4 */
if (!field_mul(group, tmp1, &point->X, Z4, ctx)) goto err;
- if (&group->a_is_minus3)
+ if (group->a_is_minus3)
{
if (!BN_mod_lshift1_quick(tmp2, tmp1, p)) goto err;
if (!BN_mod_add_quick(tmp2, tmp2, tmp1, p)) goto err;
/* point->Z_is_one */
/* rh := rh + a*X */
- if (&group->a_is_minus3)
+ if (group->a_is_minus3)
{
if (!BN_mod_lshift1_quick(tmp2, &point->X, p)) goto err;
if (!BN_mod_add_quick(tmp2, tmp2, &point->X, p)) goto err;
}
-int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
-/* TODO */
+int ec_GFp_simple_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx)
+ {
+ /* return values:
+ * -1 error
+ * 0 equal (in affine coordinates)
+ * 1 not equal
+ */
+
+ int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+ int (*field_sqr)(const EC_GROUP *, BIGNUM *, const BIGNUM *, BN_CTX *);
+ BN_CTX *new_ctx = NULL;
+ BIGNUM *tmp1, *tmp2, *Za23, *Zb23;
+ const BIGNUM *tmp1_, *tmp2_;
+ int ret = -1;
+
+ if (EC_POINT_is_at_infinity(group, a))
+ {
+ return EC_POINT_is_at_infinity(group, b) ? 0 : 1;
+ }
+
+ if (a->Z_is_one && b->Z_is_one)
+ {
+ return ((BN_cmp(&a->X, &b->X) == 0) && BN_cmp(&a->Y, &b->Y) == 0) ? 0 : 1;
+ }
+
+ field_mul = group->meth->field_mul;
+ field_sqr = group->meth->field_sqr;
+
+ if (ctx == NULL)
+ {
+ ctx = new_ctx = BN_CTX_new();
+ if (ctx == NULL)
+ return -1;
+ }
+
+ BN_CTX_start(ctx);
+ tmp1 = BN_CTX_get(ctx);
+ tmp2 = BN_CTX_get(ctx);
+ Za23 = BN_CTX_get(ctx);
+ Zb23 = BN_CTX_get(ctx);
+ if (Zb23 == NULL) goto end;
+
+ /* We have to decide whether
+ * (X_a/Z_a^2, Y_a/Z_a^3) = (X_b/Z_b^2, Y_b/Z_b^3),
+ * or equivalently, whether
+ * (X_a*Z_b^2, Y_a*Z_b^3) = (X_b*Z_a^2, Y_b*Z_a^3).
+ */
+
+ if (!b->Z_is_one)
+ {
+ if (!field_sqr(group, Zb23, &b->Z, ctx)) goto end;
+ if (!field_mul(group, tmp1, &a->X, Zb23, ctx)) goto end;
+ tmp1_ = tmp1;
+ }
+ else
+ tmp1_ = &a->X;
+ if (!a->Z_is_one)
+ {
+ if (!field_sqr(group, Za23, &a->Z, ctx)) goto end;
+ if (!field_mul(group, tmp2, &b->X, Za23, ctx)) goto end;
+ tmp2_ = tmp2;
+ }
+ else
+ tmp2_ = &b->X;
+
+ /* compare X_a*Z_b^2 with X_b*Z_a^2 */
+ if (BN_cmp(tmp1_, tmp2_) != 0)
+ {
+ ret = 1; /* points differ */
+ goto end;
+ }
+
+
+ if (!b->Z_is_one)
+ {
+ if (!field_mul(group, Zb23, Zb23, &b->Z, ctx)) goto end;
+ if (!field_mul(group, tmp1, &a->Y, Zb23, ctx)) goto end;
+ }
+ if (!a->Z_is_one)
+ {
+ if (!field_mul(group, Za23, Za23, &a->Z, ctx)) goto end;
+ if (!field_mul(group, tmp2, &b->Y, Za23, ctx)) goto end;
+ }
+ /* tmp1_ and tmp2_ are still ok */
+
+ /* compare Y_a*Z_b^3 with Y_b*Z_a^3 */
+ if (BN_cmp(tmp1_, tmp2_) != 0)
+ {
+ ret = 1; /* points differ */
+ goto end;
+ }
+
+ /* points are equal */
+ ret = 0;
+
+ end:
+ BN_CTX_end(ctx);
+ if (new_ctx != NULL)
+ BN_CTX_free(new_ctx);
+ return ret;
+ }
int ec_GFp_simple_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx)
-/* TODO */
/* crypto/ec/ectest.c */
/* ====================================================================
* Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
#include <stdio.h>
#include <stdlib.h>
+
+#ifdef OPENSSL_NO_EC
+int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); return 0; }
+#else
+
+
#include <openssl/ec.h>
#include <openssl/err.h>
-
#define ABORT do { \
- fprintf(stderr, "%s:%d: Error\n", __FILE__, __LINE__); \
+ fprintf(stderr, "%s:%d: ABORT\n", __FILE__, __LINE__); \
ERR_print_errors_fp(stderr); \
exit(1); \
} while (0)
int main(int argc, char *argv[])
{
+ BN_CTX *ctx = NULL;
+ BIGNUM *p, *a, *b;
EC_GROUP *group;
-
+ EC_POINT *P, *Q, *R;
+ BIGNUM *x, *y, *z;
+ unsigned char buf[100];
+ size_t i, len;
+
+ CRYPTO_mem_ctrl(CRYPTO_MEM_CHECK_ON);
ERR_load_crypto_strings();
-#if 0
- group = EC_GROUP_new(NULL);
+#if 0 /* 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, "D")) ABORT;
+ if (!BN_hex2bn(&a, "7")) ABORT;
+ if (!BN_hex2bn(&b, "C")) ABORT;
+
+ group = EC_GROUP_new_curve_GFp(p, a, b, NULL);
if (!group) ABORT;
+
+ fprintf(stdout, "Curve defined by Weierstrass equation\n y^2 = x^3 + a*x + 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");
+
+ 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();
+ if (!x || !y || !z) ABORT;
+
+ if (!BN_hex2bn(&x, "C")) ABORT;
+ if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
+ if (!EC_POINT_is_on_curve(group, Q, ctx))
+ {
+ fprintf(stderr, "Point is not on curve, x = 0x");
+ BN_print_fp(stderr, x);
+ fprintf(stderr, "\n");
+ ABORT;
+ }
+
+ fprintf(stdout, "A cyclic subgroup:\n");
+ do
+ {
+ if (EC_POINT_is_at_infinity(group, P))
+ fprintf(stdout, " point at infinity\n");
+ else
+ {
+ if (!EC_POINT_get_affine_coordinates_GFp(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;
+
+#if 0 /* optional */
+ if (!EC_POINT_make_affine(group, P, ctx)) ABORT;
#endif
+ }
+ 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;
+ 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 octect 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 ");
+ 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 ");
+ 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;
+ fprintf(stdout, "\nA representation of the inverse of that generator in\nJacobian projective coordinates:\n X = 0x");
+ BN_print_fp(stdout, x);
+ fprintf(stdout, ", Y = 0x");
+ BN_print_fp(stdout, y);
+ fprintf(stdout, ", Z = 0x");
+ BN_print_fp(stdout, z);
+ fprintf(stdout, "\n");
+
+ if (!EC_POINT_invert(group, P, ctx)) ABORT;
+ if (0 != EC_POINT_cmp(group, P, R, ctx)) ABORT;
+
+ /* ... */
+
+ 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);
+
+ ERR_free_strings();
+ ERR_remove_state(0);
+ CRYPTO_mem_leaks_fp(stderr);
+
return 0;
}
+#endif
projects / oweals / openssl.git / commitdiff