CSignerECDSA::CSignerECDSA(const uint8_t PrivData[32], unsigned char Signature[65])
{
order.setuint256(g_Order);
EC_KEY* pkey = EC_KEY_new_by_curve_name(NID_secp256k1);
const EC_GROUP *group = EC_KEY_get0_group(pkey);
CBigNum privkey;
BN_bin2bn(PrivData, 32, &privkey);
EC_KEY_regenerate_key(pkey, &privkey);
EC_POINT *tmp_point = EC_POINT_new(group);
EC_POINT *test_point = EC_POINT_new(group);
CBigNum r, X, Y;
bool which = false;
do
{
// get random k
do
BN_rand_range(&kinv, &order);
while (!kinv);
/* We do not want timing information to leak the length of k,
* so we compute G*k using an equivalent scalar of fixed
* bit-length. */
kinv += order;
if (BN_num_bits(&kinv) <= 256)
kinv += order;
// compute r the x-coordinate of generator * k
EC_POINT_mul(group, tmp_point, &kinv, NULL, NULL, ctx);
EC_POINT_get_affine_coordinates_GFp(group, tmp_point, &X, &Y, ctx);
EC_POINT_set_compressed_coordinates_GFp(group, test_point, &X, 0, ctx);
which = !!EC_POINT_cmp(group, tmp_point, test_point, ctx);
BN_nnmod(&r, &X, &order, ctx);
}
while (!r);
// compute the inverse of k
BN_mod_inverse(&kinv, &kinv, &order, ctx);
BN_mod_mul(&pmr, &privkey, &r, &order, ctx);
BN_mod_mul(&prk, &pmr, &kinv, &order, ctx);
memset(Signature, 0, 65);
int nBitsR = BN_num_bits(&r);
BN_bn2bin(&r, &Signature[33-(nBitsR+7)/8]);
Signature[0] = 27 + which;
EC_POINT_free(tmp_point);
EC_POINT_free(test_point);
EC_KEY_free(pkey);
}
EC_POINT *embed(const polypseud_ctx *ctx, const unsigned char *data, const size_t len) {
BIGNUM *t1 = BN_bin2bn(data, len, NULL);
BIGNUM *x = BN_new();
BN_mod(x, t1, ctx->p, ctx->bn_ctx);
EC_POINT *point = EC_POINT_new(ctx->ec_group);
unsigned char counter = 0;
int success = 0;
while(!success) {
success = EC_POINT_set_compressed_coordinates_GFp(ctx->ec_group, point, x, 1, ctx->bn_ctx);
if(!success) {
if(counter == 0) {
BN_lshift(x, x, 8);
}
BN_add(x, x, BN_value_one());
}
}
BN_free(x);
BN_free(t1);
return point;
}
static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
const uint8_t *buf, size_t len,
BN_CTX *ctx) {
point_conversion_form_t form;
int y_bit;
BN_CTX *new_ctx = NULL;
BIGNUM *x, *y;
size_t field_len, enc_len;
int ret = 0;
if (len == 0) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_BUFFER_TOO_SMALL);
return 0;
}
form = buf[0];
y_bit = form & 1;
form = form & ~1U;
if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) &&
(form != POINT_CONVERSION_UNCOMPRESSED) &&
(form != POINT_CONVERSION_HYBRID)) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
return 0;
}
if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
return 0;
}
if (form == 0) {
if (len != 1) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
return 0;
}
return EC_POINT_set_to_infinity(group, point);
}
field_len = BN_num_bytes(&group->field);
enc_len =
(form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
if (len != enc_len) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
return 0;
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL)
return 0;
}
BN_CTX_start(ctx);
x = BN_CTX_get(ctx);
y = BN_CTX_get(ctx);
if (y == NULL)
goto err;
if (!BN_bin2bn(buf + 1, field_len, x))
goto err;
if (BN_ucmp(x, &group->field) >= 0) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
goto err;
}
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) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
goto err;
}
if (form == POINT_CONVERSION_HYBRID) {
if (y_bit != BN_is_odd(y)) {
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_INVALID_ENCODING);
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 */
{
OPENSSL_PUT_ERROR(EC, ec_GFp_simple_oct2point, EC_R_POINT_IS_NOT_ON_CURVE);
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
if (new_ctx != NULL)
BN_CTX_free(new_ctx);
return ret;
}
// Perform ECDSA key recovery (see SEC1 4.1.6) for curves over (mod p)-fields
// recid selects which key is recovered
// if check is nonzero, additional checks are performed
int ECDSA_SIG_recover_key_GFp(EC_KEY *eckey, ECDSA_SIG *ecsig, const unsigned char *msg, int msglen, int recid, int check)
{
if (!eckey) return 0;
int ret = 0;
BN_CTX *ctx = NULL;
BIGNUM *x = NULL;
BIGNUM *e = NULL;
BIGNUM *order = NULL;
BIGNUM *sor = NULL;
BIGNUM *eor = NULL;
BIGNUM *field = NULL;
EC_POINT *R = NULL;
EC_POINT *O = NULL;
EC_POINT *Q = NULL;
BIGNUM *rr = NULL;
BIGNUM *zero = NULL;
int n = 0;
int i = recid / 2;
const EC_GROUP *group = EC_KEY_get0_group(eckey);
if ((ctx = BN_CTX_new()) == NULL) { ret = -1; goto err; }
BN_CTX_start(ctx);
order = BN_CTX_get(ctx);
if (!EC_GROUP_get_order(group, order, ctx)) { ret = -2; goto err; }
x = BN_CTX_get(ctx);
if (!BN_copy(x, order)) { ret=-1; goto err; }
if (!BN_mul_word(x, i)) { ret=-1; goto err; }
if (!BN_add(x, x, ecsig->r)) { ret=-1; goto err; }
field = BN_CTX_get(ctx);
if (!EC_GROUP_get_curve_GFp(group, field, NULL, NULL, ctx)) { ret=-2; goto err; }
if (BN_cmp(x, field) >= 0) { ret=0; goto err; }
if ((R = EC_POINT_new(group)) == NULL) { ret = -2; goto err; }
if (!EC_POINT_set_compressed_coordinates_GFp(group, R, x, recid % 2, ctx)) { ret=0; goto err; }
if (check)
{
if ((O = EC_POINT_new(group)) == NULL) { ret = -2; goto err; }
if (!EC_POINT_mul(group, O, NULL, R, order, ctx)) { ret=-2; goto err; }
if (!EC_POINT_is_at_infinity(group, O)) { ret = 0; goto err; }
}
if ((Q = EC_POINT_new(group)) == NULL) { ret = -2; goto err; }
n = EC_GROUP_get_degree(group);
e = BN_CTX_get(ctx);
if (!BN_bin2bn(msg, msglen, e)) { ret=-1; goto err; }
if (8*msglen > n) BN_rshift(e, e, 8-(n & 7));
zero = BN_CTX_get(ctx);
if (!BN_zero(zero)) { ret=-1; goto err; }
if (!BN_mod_sub(e, zero, e, order, ctx)) { ret=-1; goto err; }
rr = BN_CTX_get(ctx);
if (!BN_mod_inverse(rr, ecsig->r, order, ctx)) { ret=-1; goto err; }
sor = BN_CTX_get(ctx);
if (!BN_mod_mul(sor, ecsig->s, rr, order, ctx)) { ret=-1; goto err; }
eor = BN_CTX_get(ctx);
if (!BN_mod_mul(eor, e, rr, order, ctx)) { ret=-1; goto err; }
if (!EC_POINT_mul(group, Q, eor, R, sor, ctx)) { ret=-2; goto err; }
if (!EC_KEY_set_public_key(eckey, Q)) { ret=-2; goto err; }
ret = 1;
err:
if (ctx) {
BN_CTX_end(ctx);
BN_CTX_free(ctx);
}
if (R != NULL) EC_POINT_free(R);
if (O != NULL) EC_POINT_free(O);
if (Q != NULL) EC_POINT_free(Q);
return ret;
}
int
compute_password_element (pwd_session_t *sess, uint16_t grp_num,
char *password, int password_len,
char *id_server, int id_server_len,
char *id_peer, int id_peer_len,
uint32_t *token)
{
BIGNUM *x_candidate = NULL, *rnd = NULL, *cofactor = NULL;
HMAC_CTX ctx;
uint8_t pwe_digest[SHA256_DIGEST_LENGTH], *prfbuf = NULL, ctr;
int nid, is_odd, primebitlen, primebytelen, ret = 0;
switch (grp_num) { /* from IANA registry for IKE D-H groups */
case 19:
nid = NID_X9_62_prime256v1;
break;
case 20:
nid = NID_secp384r1;
break;
case 21:
nid = NID_secp521r1;
break;
case 25:
nid = NID_X9_62_prime192v1;
break;
case 26:
nid = NID_secp224r1;
break;
default:
DEBUG("unknown group %d", grp_num);
goto fail;
}
sess->pwe = NULL;
sess->order = NULL;
sess->prime = NULL;
if ((sess->group = EC_GROUP_new_by_curve_name(nid)) == NULL) {
DEBUG("unable to create EC_GROUP");
goto fail;
}
if (((rnd = BN_new()) == NULL) ||
((cofactor = BN_new()) == NULL) ||
((sess->pwe = EC_POINT_new(sess->group)) == NULL) ||
((sess->order = BN_new()) == NULL) ||
((sess->prime = BN_new()) == NULL) ||
((x_candidate = BN_new()) == NULL)) {
DEBUG("unable to create bignums");
goto fail;
}
if (!EC_GROUP_get_curve_GFp(sess->group, sess->prime, NULL, NULL, NULL))
{
DEBUG("unable to get prime for GFp curve");
goto fail;
}
if (!EC_GROUP_get_order(sess->group, sess->order, NULL)) {
DEBUG("unable to get order for curve");
goto fail;
}
if (!EC_GROUP_get_cofactor(sess->group, cofactor, NULL)) {
DEBUG("unable to get cofactor for curve");
goto fail;
}
primebitlen = BN_num_bits(sess->prime);
primebytelen = BN_num_bytes(sess->prime);
if ((prfbuf = talloc_zero_array(sess, uint8_t, primebytelen)) == NULL) {
DEBUG("unable to alloc space for prf buffer");
goto fail;
}
ctr = 0;
while (1) {
if (ctr > 10) {
DEBUG("unable to find random point on curve for group %d, something's fishy", grp_num);
goto fail;
}
ctr++;
/*
* compute counter-mode password value and stretch to prime
* pwd-seed = H(token | peer-id | server-id | password |
* counter)
*/
H_Init(&ctx);
H_Update(&ctx, (uint8_t *)token, sizeof(*token));
H_Update(&ctx, (uint8_t *)id_peer, id_peer_len);
H_Update(&ctx, (uint8_t *)id_server, id_server_len);
H_Update(&ctx, (uint8_t *)password, password_len);
H_Update(&ctx, (uint8_t *)&ctr, sizeof(ctr));
H_Final(&ctx, pwe_digest);
BN_bin2bn(pwe_digest, SHA256_DIGEST_LENGTH, rnd);
eap_pwd_kdf(pwe_digest, SHA256_DIGEST_LENGTH,
"EAP-pwd Hunting And Pecking",
strlen("EAP-pwd Hunting And Pecking"),
prfbuf, primebitlen);
BN_bin2bn(prfbuf, primebytelen, x_candidate);
/*
* eap_pwd_kdf() returns a string of bits 0..primebitlen but
* BN_bin2bn will treat that string of bits as a big endian
* number. If the primebitlen is not an even multiple of 8
* then excessive bits-- those _after_ primebitlen-- so now
* we have to shift right the amount we masked off.
*/
if (primebitlen % 8) {
BN_rshift(x_candidate, x_candidate, (8 - (primebitlen % 8)));
}
if (BN_ucmp(x_candidate, sess->prime) >= 0) {
continue;
}
/*
* need to unambiguously identify the solution, if there is
* one...
*/
if (BN_is_odd(rnd)) {
is_odd = 1;
} else {
is_odd = 0;
}
/*
* solve the quadratic equation, if it's not solvable then we
* don't have a point
*/
if (!EC_POINT_set_compressed_coordinates_GFp(sess->group,
sess->pwe,
x_candidate,
is_odd, NULL)) {
continue;
}
/*
* If there's a solution to the equation then the point must be
* on the curve so why check again explicitly? OpenSSL code
* says this is required by X9.62. We're not X9.62 but it can't
* hurt just to be sure.
*/
if (!EC_POINT_is_on_curve(sess->group, sess->pwe, NULL)) {
DEBUG("EAP-pwd: point is not on curve");
continue;
}
if (BN_cmp(cofactor, BN_value_one())) {
/* make sure the point is not in a small sub-group */
if (!EC_POINT_mul(sess->group, sess->pwe, NULL, sess->pwe,
cofactor, NULL)) {
DEBUG("EAP-pwd: cannot multiply generator by order");
continue;
}
if (EC_POINT_is_at_infinity(sess->group, sess->pwe)) {
DEBUG("EAP-pwd: point is at infinity");
continue;
}
}
/* if we got here then we have a new generator. */
break;
}
sess->group_num = grp_num;
if (0) {
fail: /* DON'T free sess, it's in handler->opaque */
ret = -1;
}
/* cleanliness and order.... */
BN_free(cofactor);
BN_free(x_candidate);
BN_free(rnd);
talloc_free(prfbuf);
return ret;
}
/*
* compute a "random" secret point on an elliptic curve based
* on the password and identities.
*/
int compute_password_element(EAP_PWD_group *grp, u16 num,
u8 *password, int password_len,
u8 *id_server, int id_server_len,
u8 *id_peer, int id_peer_len, u8 *token)
{
BIGNUM *x_candidate = NULL, *rnd = NULL, *cofactor = NULL;
struct crypto_hash *hash;
unsigned char pwe_digest[SHA256_MAC_LEN], *prfbuf = NULL, ctr;
int nid, is_odd, ret = 0;
size_t primebytelen, primebitlen;
switch (num) { /* from IANA registry for IKE D-H groups */
case 19:
nid = NID_X9_62_prime256v1;
break;
case 20:
nid = NID_secp384r1;
break;
case 21:
nid = NID_secp521r1;
break;
case 25:
nid = NID_X9_62_prime192v1;
break;
case 26:
nid = NID_secp224r1;
break;
default:
wpa_printf(MSG_INFO, "EAP-pwd: unsupported group %d", num);
return -1;
}
grp->pwe = NULL;
grp->order = NULL;
grp->prime = NULL;
if ((grp->group = EC_GROUP_new_by_curve_name(nid)) == NULL) {
wpa_printf(MSG_INFO, "EAP-pwd: unable to create EC_GROUP");
goto fail;
}
if (((rnd = BN_new()) == NULL) ||
((cofactor = BN_new()) == NULL) ||
((grp->pwe = EC_POINT_new(grp->group)) == NULL) ||
((grp->order = BN_new()) == NULL) ||
((grp->prime = BN_new()) == NULL) ||
((x_candidate = BN_new()) == NULL)) {
wpa_printf(MSG_INFO, "EAP-pwd: unable to create bignums");
goto fail;
}
if (!EC_GROUP_get_curve_GFp(grp->group, grp->prime, NULL, NULL, NULL))
{
wpa_printf(MSG_INFO, "EAP-pwd: unable to get prime for GFp "
"curve");
goto fail;
}
if (!EC_GROUP_get_order(grp->group, grp->order, NULL)) {
wpa_printf(MSG_INFO, "EAP-pwd: unable to get order for curve");
goto fail;
}
if (!EC_GROUP_get_cofactor(grp->group, cofactor, NULL)) {
wpa_printf(MSG_INFO, "EAP-pwd: unable to get cofactor for "
"curve");
goto fail;
}
primebitlen = BN_num_bits(grp->prime);
primebytelen = BN_num_bytes(grp->prime);
if ((prfbuf = os_malloc(primebytelen)) == NULL) {
wpa_printf(MSG_INFO, "EAP-pwd: unable to malloc space for prf "
"buffer");
goto fail;
}
os_memset(prfbuf, 0, primebytelen);
ctr = 0;
while (1) {
if (ctr > 30) {
wpa_printf(MSG_INFO, "EAP-pwd: unable to find random "
"point on curve for group %d, something's "
"fishy", num);
goto fail;
}
ctr++;
/*
* compute counter-mode password value and stretch to prime
* pwd-seed = H(token | peer-id | server-id | password |
* counter)
*/
hash = eap_pwd_h_init();
if (hash == NULL)
goto fail;
eap_pwd_h_update(hash, token, sizeof(u32));
eap_pwd_h_update(hash, id_peer, id_peer_len);
eap_pwd_h_update(hash, id_server, id_server_len);
eap_pwd_h_update(hash, password, password_len);
eap_pwd_h_update(hash, &ctr, sizeof(ctr));
eap_pwd_h_final(hash, pwe_digest);
BN_bin2bn(pwe_digest, SHA256_MAC_LEN, rnd);
if (eap_pwd_kdf(pwe_digest, SHA256_MAC_LEN,
(u8 *) "EAP-pwd Hunting And Pecking",
os_strlen("EAP-pwd Hunting And Pecking"),
prfbuf, primebitlen) < 0)
goto fail;
BN_bin2bn(prfbuf, primebytelen, x_candidate);
/*
* eap_pwd_kdf() returns a string of bits 0..primebitlen but
* BN_bin2bn will treat that string of bits as a big endian
* number. If the primebitlen is not an even multiple of 8
* then excessive bits-- those _after_ primebitlen-- so now
* we have to shift right the amount we masked off.
*/
if (primebitlen % 8)
BN_rshift(x_candidate, x_candidate,
(8 - (primebitlen % 8)));
if (BN_ucmp(x_candidate, grp->prime) >= 0)
continue;
wpa_hexdump(MSG_DEBUG, "EAP-pwd: x_candidate",
prfbuf, primebytelen);
/*
* need to unambiguously identify the solution, if there is
* one...
*/
if (BN_is_odd(rnd))
is_odd = 1;
else
is_odd = 0;
/*
* solve the quadratic equation, if it's not solvable then we
* don't have a point
*/
if (!EC_POINT_set_compressed_coordinates_GFp(grp->group,
grp->pwe,
x_candidate,
is_odd, NULL))
continue;
/*
* If there's a solution to the equation then the point must be
* on the curve so why check again explicitly? OpenSSL code
* says this is required by X9.62. We're not X9.62 but it can't
* hurt just to be sure.
*/
if (!EC_POINT_is_on_curve(grp->group, grp->pwe, NULL)) {
wpa_printf(MSG_INFO, "EAP-pwd: point is not on curve");
continue;
}
if (BN_cmp(cofactor, BN_value_one())) {
/* make sure the point is not in a small sub-group */
if (!EC_POINT_mul(grp->group, grp->pwe, NULL, grp->pwe,
cofactor, NULL)) {
wpa_printf(MSG_INFO, "EAP-pwd: cannot "
"multiply generator by order");
continue;
}
if (EC_POINT_is_at_infinity(grp->group, grp->pwe)) {
wpa_printf(MSG_INFO, "EAP-pwd: point is at "
"infinity");
continue;
}
}
/* if we got here then we have a new generator. */
break;
}
wpa_printf(MSG_DEBUG, "EAP-pwd: found a PWE in %d tries", ctr);
grp->group_num = num;
if (0) {
fail:
EC_GROUP_free(grp->group);
grp->group = NULL;
EC_POINT_free(grp->pwe);
grp->pwe = NULL;
BN_free(grp->order);
grp->order = NULL;
BN_free(grp->prime);
grp->prime = NULL;
ret = 1;
}
/* cleanliness and order.... */
BN_free(cofactor);
BN_free(x_candidate);
BN_free(rnd);
os_free(prfbuf);
return ret;
}
static int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
const uint8_t *buf, size_t len,
BN_CTX *ctx) {
point_conversion_form_t form;
int y_bit;
BN_CTX *new_ctx = NULL;
BIGNUM *x, *y;
size_t field_len, enc_len;
int ret = 0;
if (len == 0) {
OPENSSL_PUT_ERROR(EC, EC_R_BUFFER_TOO_SMALL);
return 0;
}
form = buf[0];
y_bit = form & 1;
form = form & ~1U;
if ((form != POINT_CONVERSION_COMPRESSED &&
form != POINT_CONVERSION_UNCOMPRESSED) ||
(form == POINT_CONVERSION_UNCOMPRESSED && y_bit)) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
return 0;
}
field_len = BN_num_bytes(&group->field);
enc_len =
(form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
if (len != enc_len) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
return 0;
}
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
return 0;
}
}
BN_CTX_start(ctx);
x = BN_CTX_get(ctx);
y = BN_CTX_get(ctx);
if (x == NULL || y == NULL) {
goto err;
}
if (!BN_bin2bn(buf + 1, field_len, x)) {
goto err;
}
if (BN_ucmp(x, &group->field) >= 0) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
goto err;
}
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) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_ENCODING);
goto err;
}
if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) {
goto err;
}
}
ret = 1;
err:
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
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);
}
