Пример #1
0
int compute_scalar_element (pwd_session_t *sess, BN_CTX *bnctx) {
	BIGNUM *mask = NULL;
	int ret = -1;

	if (((sess->private_value = BN_new()) == NULL) ||
	    ((sess->my_element = EC_POINT_new(sess->group)) == NULL) ||
	    ((sess->my_scalar = BN_new()) == NULL) ||
	    ((mask = BN_new()) == NULL)) {
		DEBUG2("server scalar allocation failed");
		goto fail;
	}

	BN_rand_range(sess->private_value, sess->order);
	BN_rand_range(mask, sess->order);
	BN_add(sess->my_scalar, sess->private_value, mask);
	BN_mod(sess->my_scalar, sess->my_scalar, sess->order, bnctx);

	if (!EC_POINT_mul(sess->group, sess->my_element, NULL, sess->pwe, mask, bnctx)) {
		DEBUG2("server element allocation failed");
		goto fail;
	}

	if (!EC_POINT_invert(sess->group, sess->my_element, bnctx)) {
		DEBUG2("server element inversion failed");
		goto fail;
	}

	ret = 0;

fail:
	BN_free(mask);

	return ret;
}
size_t polypseud_decrypt(const polypseud_ctx *ctx, pseudonym *ep, const BIGNUM *privkey, const BIGNUM *closingkey, unsigned char **pp) {
   if(EC_POINT_mul(ctx->ec_group, ep->a, NULL, ep->a, privkey, ctx->bn_ctx) == 0) 
       return 0;
   
   if(EC_POINT_invert(ctx->ec_group, ep->a, ctx->bn_ctx) == 0) 
        return 0;

   if(EC_POINT_add(ctx->ec_group, ep->a, ep->b, ep->a, ctx->bn_ctx) == 0)
       return 0;

   if(EC_POINT_mul(ctx->ec_group, ep->a, NULL, ep->a, closingkey, ctx->bn_ctx) == 0) 
       return 0;
   
   unsigned char octstring[100];

   size_t len = EC_POINT_point2oct(ctx->ec_group, ep->a, POINT_CONVERSION_UNCOMPRESSED, octstring, 100, ctx->bn_ctx);
   
   return hash(octstring, len, pp); 
}
Пример #3
0
int compute_scalar_element(REQUEST *request, pwd_session_t *session, BN_CTX *bn_ctx)
{
	BIGNUM *mask = NULL;
	int ret = -1;

	MEM(session->private_value = BN_new());
	MEM(session->my_element = EC_POINT_new(session->group));
	MEM(session->my_scalar = BN_new());

	MEM(mask = BN_new());

	if (BN_rand_range(session->private_value, session->order) != 1) {
		REDEBUG("Unable to get randomness for private_value");
		goto error;
	}
	if (BN_rand_range(mask, session->order) != 1) {
		REDEBUG("Unable to get randomness for mask");
		goto error;
	}
	BN_add(session->my_scalar, session->private_value, mask);
	BN_mod(session->my_scalar, session->my_scalar, session->order, bn_ctx);

	if (!EC_POINT_mul(session->group, session->my_element, NULL, session->pwe, mask, bn_ctx)) {
		REDEBUG("Server element allocation failed");
		goto error;
	}

	if (!EC_POINT_invert(session->group, session->my_element, bn_ctx)) {
		REDEBUG("Server element inversion failed");
		goto error;
	}

	ret = 0;

error:
	BN_clear_free(mask);

	return ret;
}
Пример #4
0
static struct wpabuf *
eap_pwd_build_commit_req(struct eap_sm *sm, struct eap_pwd_data *data, u8 id)
{
	struct wpabuf *req = NULL;
	BIGNUM *mask = NULL, *x = NULL, *y = NULL;
	u8 *scalar = NULL, *element = NULL;
	u16 offset;

	wpa_printf(MSG_DEBUG, "EAP-pwd: Commit/Request");

	if (((data->private_value = BN_new()) == NULL) ||
	    ((data->my_element = EC_POINT_new(data->grp->group)) == NULL) ||
	    ((data->my_scalar = BN_new()) == NULL) ||
	    ((mask = BN_new()) == NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): scalar allocation "
			   "fail");
		goto fin;
	}

	BN_rand_range(data->private_value, data->grp->order);
	BN_rand_range(mask, data->grp->order);
	BN_add(data->my_scalar, data->private_value, mask);
	BN_mod(data->my_scalar, data->my_scalar, data->grp->order,
	       data->bnctx);

	if (!EC_POINT_mul(data->grp->group, data->my_element, NULL,
			  data->grp->pwe, mask, data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): element allocation "
			   "fail");
		eap_pwd_state(data, FAILURE);
		goto fin;
	}

	if (!EC_POINT_invert(data->grp->group, data->my_element, data->bnctx))
	{
		wpa_printf(MSG_INFO, "EAP-PWD (server): element inversion "
			   "fail");
		goto fin;
	}
	BN_free(mask);

	if (((x = BN_new()) == NULL) ||
	    ((y = BN_new()) == NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): point allocation "
			   "fail");
		goto fin;
	}
	if (!EC_POINT_get_affine_coordinates_GFp(data->grp->group,
						 data->my_element, x, y,
						 data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): point assignment "
			   "fail");
		goto fin;
	}

	if (((scalar = os_malloc(BN_num_bytes(data->grp->order))) == NULL) ||
	    ((element = os_malloc(BN_num_bytes(data->grp->prime) * 2)) ==
	     NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): data allocation fail");
		goto fin;
	}

	/*
	 * bignums occupy as little memory as possible so one that is
	 * sufficiently smaller than the prime or order might need pre-pending
	 * with zeros.
	 */
	os_memset(scalar, 0, BN_num_bytes(data->grp->order));
	os_memset(element, 0, BN_num_bytes(data->grp->prime) * 2);
	offset = BN_num_bytes(data->grp->order) -
		BN_num_bytes(data->my_scalar);
	BN_bn2bin(data->my_scalar, scalar + offset);

	offset = BN_num_bytes(data->grp->prime) - BN_num_bytes(x);
	BN_bn2bin(x, element + offset);
	offset = BN_num_bytes(data->grp->prime) - BN_num_bytes(y);
	BN_bn2bin(y, element + BN_num_bytes(data->grp->prime) + offset);

	req = eap_msg_alloc(EAP_VENDOR_IETF, EAP_TYPE_PWD,
			    sizeof(struct eap_pwd_hdr) +
			    (2 * BN_num_bytes(data->grp->prime)) +
			    BN_num_bytes(data->grp->order),
			    EAP_CODE_REQUEST, id);
	if (req == NULL)
		goto fin;
	wpabuf_put_u8(req, EAP_PWD_OPCODE_COMMIT_EXCH);

	/* We send the element as (x,y) followed by the scalar */
	wpabuf_put_data(req, element, (2 * BN_num_bytes(data->grp->prime)));
	wpabuf_put_data(req, scalar, BN_num_bytes(data->grp->order));

fin:
	os_free(scalar);
	os_free(element);
	BN_free(x);
	BN_free(y);
	if (req == NULL)
		eap_pwd_state(data, FAILURE);

	return req;
}
static void
eap_pwd_perform_commit_exchange(struct eap_sm *sm, struct eap_pwd_data *data,
				struct eap_method_ret *ret,
				const struct wpabuf *reqData,
				const u8 *payload, size_t payload_len)
{
	EC_POINT *K = NULL, *point = NULL;
	BIGNUM *mask = NULL, *x = NULL, *y = NULL, *cofactor = NULL;
	u16 offset;
	u8 *ptr, *scalar = NULL, *element = NULL;

	if (((data->private_value = BN_new()) == NULL) ||
	    ((data->my_element = EC_POINT_new(data->grp->group)) == NULL) ||
	    ((cofactor = BN_new()) == NULL) ||
	    ((data->my_scalar = BN_new()) == NULL) ||
	    ((mask = BN_new()) == NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): scalar allocation fail");
		goto fin;
	}

	if (!EC_GROUP_get_cofactor(data->grp->group, cofactor, NULL)) {
		wpa_printf(MSG_INFO, "EAP-pwd (peer): unable to get cofactor "
			   "for curve");
		goto fin;
	}

	BN_rand_range(data->private_value, data->grp->order);
	BN_rand_range(mask, data->grp->order);
	BN_add(data->my_scalar, data->private_value, mask);
	BN_mod(data->my_scalar, data->my_scalar, data->grp->order,
	       data->bnctx);

	if (!EC_POINT_mul(data->grp->group, data->my_element, NULL,
			  data->grp->pwe, mask, data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): element allocation "
			   "fail");
		eap_pwd_state(data, FAILURE);
		goto fin;
	}

	if (!EC_POINT_invert(data->grp->group, data->my_element, data->bnctx))
	{
		wpa_printf(MSG_INFO, "EAP-PWD (peer): element inversion fail");
		goto fin;
	}
	BN_free(mask);

	if (((x = BN_new()) == NULL) ||
	    ((y = BN_new()) == NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): point allocation fail");
		goto fin;
	}

	/* process the request */
	if (((data->server_scalar = BN_new()) == NULL) ||
	    ((data->k = BN_new()) == NULL) ||
	    ((K = EC_POINT_new(data->grp->group)) == NULL) ||
	    ((point = EC_POINT_new(data->grp->group)) == NULL) ||
	    ((data->server_element = EC_POINT_new(data->grp->group)) == NULL))
	{
		wpa_printf(MSG_INFO, "EAP-PWD (peer): peer data allocation "
			   "fail");
		goto fin;
	}

	/* element, x then y, followed by scalar */
	ptr = (u8 *) payload;
	BN_bin2bn(ptr, BN_num_bytes(data->grp->prime), x);
	ptr += BN_num_bytes(data->grp->prime);
	BN_bin2bn(ptr, BN_num_bytes(data->grp->prime), y);
	ptr += BN_num_bytes(data->grp->prime);
	BN_bin2bn(ptr, BN_num_bytes(data->grp->order), data->server_scalar);
	if (!EC_POINT_set_affine_coordinates_GFp(data->grp->group,
						 data->server_element, x, y,
						 data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): setting peer element "
			   "fail");
		goto fin;
	}

	/* check to ensure server's element is not in a small sub-group */
	if (BN_cmp(cofactor, BN_value_one())) {
		if (!EC_POINT_mul(data->grp->group, point, NULL,
				  data->server_element, cofactor, NULL)) {
			wpa_printf(MSG_INFO, "EAP-PWD (peer): cannot multiply "
				   "server element by order!\n");
			goto fin;
		}
		if (EC_POINT_is_at_infinity(data->grp->group, point)) {
			wpa_printf(MSG_INFO, "EAP-PWD (peer): server element "
				   "is at infinity!\n");
			goto fin;
		}
	}

	/* compute the shared key, k */
	if ((!EC_POINT_mul(data->grp->group, K, NULL, data->grp->pwe,
			   data->server_scalar, data->bnctx)) ||
	    (!EC_POINT_add(data->grp->group, K, K, data->server_element,
			   data->bnctx)) ||
	    (!EC_POINT_mul(data->grp->group, K, NULL, K, data->private_value,
			   data->bnctx))) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): computing shared key "
			   "fail");
		goto fin;
	}

	/* ensure that the shared key isn't in a small sub-group */
	if (BN_cmp(cofactor, BN_value_one())) {
		if (!EC_POINT_mul(data->grp->group, K, NULL, K, cofactor,
				  NULL)) {
			wpa_printf(MSG_INFO, "EAP-PWD (peer): cannot multiply "
				   "shared key point by order");
			goto fin;
		}
	}

	/*
	 * This check is strictly speaking just for the case above where
	 * co-factor > 1 but it was suggested that even though this is probably
	 * never going to happen it is a simple and safe check "just to be
	 * sure" so let's be safe.
	 */
	if (EC_POINT_is_at_infinity(data->grp->group, K)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): shared key point is at "
			   "infinity!\n");
		goto fin;
	}

	if (!EC_POINT_get_affine_coordinates_GFp(data->grp->group, K, data->k,
						 NULL, data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): unable to extract "
			   "shared secret from point");
		goto fin;
	}

	/* now do the response */
	if (!EC_POINT_get_affine_coordinates_GFp(data->grp->group,
						 data->my_element, x, y,
						 data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): point assignment fail");
		goto fin;
	}

	if (((scalar = os_malloc(BN_num_bytes(data->grp->order))) == NULL) ||
	    ((element = os_malloc(BN_num_bytes(data->grp->prime) * 2)) ==
	     NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (peer): data allocation fail");
		goto fin;
	}

	/*
	 * bignums occupy as little memory as possible so one that is
	 * sufficiently smaller than the prime or order might need pre-pending
	 * with zeros.
	 */
	os_memset(scalar, 0, BN_num_bytes(data->grp->order));
	os_memset(element, 0, BN_num_bytes(data->grp->prime) * 2);
	offset = BN_num_bytes(data->grp->order) -
		BN_num_bytes(data->my_scalar);
	BN_bn2bin(data->my_scalar, scalar + offset);

	offset = BN_num_bytes(data->grp->prime) - BN_num_bytes(x);
	BN_bn2bin(x, element + offset);
	offset = BN_num_bytes(data->grp->prime) - BN_num_bytes(y);
	BN_bn2bin(y, element + BN_num_bytes(data->grp->prime) + offset);

	data->outbuf = wpabuf_alloc(BN_num_bytes(data->grp->order) +
				    2 * BN_num_bytes(data->grp->prime));
	if (data->outbuf == NULL)
		goto fin;

	/* we send the element as (x,y) follwed by the scalar */
	wpabuf_put_data(data->outbuf, element,
			2 * BN_num_bytes(data->grp->prime));
	wpabuf_put_data(data->outbuf, scalar, BN_num_bytes(data->grp->order));

fin:
	os_free(scalar);
	os_free(element);
	BN_free(x);
	BN_free(y);
	BN_free(cofactor);
	EC_POINT_free(K);
	EC_POINT_free(point);
	if (data->outbuf == NULL)
		eap_pwd_state(data, FAILURE);
	else
		eap_pwd_state(data, PWD_Confirm_Req);
}
Пример #6
0
static void eap_pwd_build_commit_req(struct eap_sm *sm,
				     struct eap_pwd_data *data, u8 id)
{
	BIGNUM *mask = NULL, *x = NULL, *y = NULL;
	u8 *scalar = NULL, *element = NULL;
	u16 offset;

	wpa_printf(MSG_DEBUG, "EAP-pwd: Commit/Request");
	/*
	 * if we're fragmenting then we already have an commit request, just
	 * return
	 */
	if (data->out_frag_pos)
		return;

	if (((data->private_value = BN_new()) == NULL) ||
	    ((data->my_element = EC_POINT_new(data->grp->group)) == NULL) ||
	    ((data->my_scalar = BN_new()) == NULL) ||
	    ((mask = BN_new()) == NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): scalar allocation "
			   "fail");
		goto fin;
	}

	if (BN_rand_range(data->private_value, data->grp->order) != 1 ||
	    BN_rand_range(mask, data->grp->order) != 1 ||
	    BN_add(data->my_scalar, data->private_value, mask) != 1 ||
	    BN_mod(data->my_scalar, data->my_scalar, data->grp->order,
		   data->bnctx) != 1) {
		wpa_printf(MSG_INFO,
			   "EAP-pwd (server): unable to get randomness");
		goto fin;
	}

	if (!EC_POINT_mul(data->grp->group, data->my_element, NULL,
			  data->grp->pwe, mask, data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): element allocation "
			   "fail");
		eap_pwd_state(data, FAILURE);
		goto fin;
	}

	if (!EC_POINT_invert(data->grp->group, data->my_element, data->bnctx))
	{
		wpa_printf(MSG_INFO, "EAP-PWD (server): element inversion "
			   "fail");
		goto fin;
	}
	BN_clear_free(mask);

	if (((x = BN_new()) == NULL) ||
	    ((y = BN_new()) == NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): point allocation "
			   "fail");
		goto fin;
	}
	if (!EC_POINT_get_affine_coordinates_GFp(data->grp->group,
						 data->my_element, x, y,
						 data->bnctx)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): point assignment "
			   "fail");
		goto fin;
	}

	if (((scalar = os_malloc(BN_num_bytes(data->grp->order))) == NULL) ||
	    ((element = os_malloc(BN_num_bytes(data->grp->prime) * 2)) ==
	     NULL)) {
		wpa_printf(MSG_INFO, "EAP-PWD (server): data allocation fail");
		goto fin;
	}

	/*
	 * bignums occupy as little memory as possible so one that is
	 * sufficiently smaller than the prime or order might need pre-pending
	 * with zeros.
	 */
	os_memset(scalar, 0, BN_num_bytes(data->grp->order));
	os_memset(element, 0, BN_num_bytes(data->grp->prime) * 2);
	offset = BN_num_bytes(data->grp->order) -
		BN_num_bytes(data->my_scalar);
	BN_bn2bin(data->my_scalar, scalar + offset);

	offset = BN_num_bytes(data->grp->prime) - BN_num_bytes(x);
	BN_bn2bin(x, element + offset);
	offset = BN_num_bytes(data->grp->prime) - BN_num_bytes(y);
	BN_bn2bin(y, element + BN_num_bytes(data->grp->prime) + offset);

	data->outbuf = wpabuf_alloc(2 * BN_num_bytes(data->grp->prime) +
				    BN_num_bytes(data->grp->order));
	if (data->outbuf == NULL)
		goto fin;

	/* We send the element as (x,y) followed by the scalar */
	wpabuf_put_data(data->outbuf, element,
			2 * BN_num_bytes(data->grp->prime));
	wpabuf_put_data(data->outbuf, scalar, BN_num_bytes(data->grp->order));

fin:
	os_free(scalar);
	os_free(element);
	BN_clear_free(x);
	BN_clear_free(y);
	if (data->outbuf == NULL)
		eap_pwd_state(data, FAILURE);
}
Пример #7
0
/*-
 * Recovers the y-coordinate of r using Eq. (8) from Brier-Joye, "Weierstrass
 * Elliptic Curves and Side-Channel Attacks", modified to work in projective
 * coordinates and return r in Jacobian projective coordinates.
 *
 * X4 = two*Y1*X2*Z3*Z2*Z1;
 * Y4 = two*b*Z3*SQR(Z2*Z1) + Z3*(a*Z2*Z1+X1*X2)*(X1*Z2+X2*Z1) - X3*SQR(X1*Z2-X2*Z1);
 * Z4 = two*Y1*Z3*SQR(Z2)*Z1;
 *
 * Z4 != 0 because:
 *  - Z1==0 implies p is at infinity, which would have caused an early exit in
 *    the caller;
 *  - Z2==0 implies r is at infinity (handled by the BN_is_zero(r->Z) branch);
 *  - Z3==0 implies s is at infinity (handled by the BN_is_zero(s->Z) branch);
 *  - Y1==0 implies p has order 2, so either r or s are infinity and handled by
 *    one of the BN_is_zero(...) branches.
 */
int ec_GFp_simple_ladder_post(const EC_GROUP *group,
                              EC_POINT *r, EC_POINT *s,
                              EC_POINT *p, BN_CTX *ctx)
{
    int ret = 0;
    BIGNUM *t0, *t1, *t2, *t3, *t4, *t5, *t6 = NULL;

    if (BN_is_zero(r->Z))
        return EC_POINT_set_to_infinity(group, r);

    if (BN_is_zero(s->Z)) {
        /* (X,Y,Z) -> (XZ,YZ**2,Z) */
        if (!group->meth->field_mul(group, r->X, p->X, p->Z, ctx)
            || !group->meth->field_sqr(group, r->Z, p->Z, ctx)
            || !group->meth->field_mul(group, r->Y, p->Y, r->Z, ctx)
            || !BN_copy(r->Z, p->Z)
            || !EC_POINT_invert(group, r, ctx))
            return 0;
        return 1;
    }

    BN_CTX_start(ctx);
    t0 = BN_CTX_get(ctx);
    t1 = BN_CTX_get(ctx);
    t2 = BN_CTX_get(ctx);
    t3 = BN_CTX_get(ctx);
    t4 = BN_CTX_get(ctx);
    t5 = BN_CTX_get(ctx);
    t6 = BN_CTX_get(ctx);

    if (t6 == NULL
        || !BN_mod_lshift1_quick(t0, p->Y, group->field)
        || !group->meth->field_mul(group, t1, r->X, p->Z, ctx)
        || !group->meth->field_mul(group, t2, r->Z, s->Z, ctx)
        || !group->meth->field_mul(group, t2, t1, t2, ctx)
        || !group->meth->field_mul(group, t3, t2, t0, ctx)
        || !group->meth->field_mul(group, t2, r->Z, p->Z, ctx)
        || !group->meth->field_sqr(group, t4, t2, ctx)
        || !BN_mod_lshift1_quick(t5, group->b, group->field)
        || !group->meth->field_mul(group, t4, t4, t5, ctx)
        || !group->meth->field_mul(group, t6, t2, group->a, ctx)
        || !group->meth->field_mul(group, t5, r->X, p->X, ctx)
        || !BN_mod_add_quick(t5, t6, t5, group->field)
        || !group->meth->field_mul(group, t6, r->Z, p->X, ctx)
        || !BN_mod_add_quick(t2, t6, t1, group->field)
        || !group->meth->field_mul(group, t5, t5, t2, ctx)
        || !BN_mod_sub_quick(t6, t6, t1, group->field)
        || !group->meth->field_sqr(group, t6, t6, ctx)
        || !group->meth->field_mul(group, t6, t6, s->X, ctx)
        || !BN_mod_add_quick(t4, t5, t4, group->field)
        || !group->meth->field_mul(group, t4, t4, s->Z, ctx)
        || !BN_mod_sub_quick(t4, t4, t6, group->field)
        || !group->meth->field_sqr(group, t5, r->Z, ctx)
        || !group->meth->field_mul(group, r->Z, p->Z, s->Z, ctx)
        || !group->meth->field_mul(group, r->Z, t5, r->Z, ctx)
        || !group->meth->field_mul(group, r->Z, r->Z, t0, ctx)
        /* t3 := X, t4 := Y */
        /* (X,Y,Z) -> (XZ,YZ**2,Z) */
        || !group->meth->field_mul(group, r->X, t3, r->Z, ctx)
        || !group->meth->field_sqr(group, t3, r->Z, ctx)
        || !group->meth->field_mul(group, r->Y, t4, t3, ctx))
        goto err;

    ret = 1;

 err:
    BN_CTX_end(ctx);
    return ret;
}
Пример #8
0
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);

	}
Пример #9
0
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;
	
#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, "17")) ABORT;
	if (!BN_hex2bn(&a, "1")) ABORT;
	if (!BN_hex2bn(&b, "1")) ABORT;
	
	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");
	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, "D")) ABORT;
	if (!EC_POINT_set_compressed_coordinates_GFp(group, Q, x, 1, ctx)) ABORT;
	if (!EC_POINT_is_on_curve(group, Q, ctx))
		{
		if (!EC_POINT_get_affine_coordinates_GFp(group, Q, x, y, ctx)) ABORT;
		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_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 */
		{
			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_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;


	/* 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");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, 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, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, " ok\n");

	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");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, 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_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");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, 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_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");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, 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_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");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, 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_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");
	
	fprintf(stdout, "verify group order ...");
	fflush(stdout);
	if (!EC_GROUP_get_order(group, z, ctx)) ABORT;
	if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT;
	if (!EC_POINT_is_at_infinity(group, Q)) ABORT;
	fprintf(stdout, ".");
	fflush(stdout);
#if 0
	if (!EC_GROUP_precompute_mult(group, ctx)) ABORT;
#endif
	if (!EC_POINT_mul(group, Q, z, 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 */

	{
		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(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);
	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);

	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);

	}