int EC_KEY_check_key(const EC_KEY *eckey) {
int ok = 0;
BN_CTX *ctx = NULL;
EC_POINT *point = NULL;
if (!eckey || !eckey->group || !eckey->pub_key) {
OPENSSL_PUT_ERROR(EC, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY);
goto err;
}
ctx = BN_CTX_new();
if (ctx == NULL) {
goto err;
}
/* testing whether the pub_key is on the elliptic curve */
if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_IS_NOT_ON_CURVE);
goto err;
}
/* BoringSSL has a check here that pub_key * order is the point at infinity.
* That check isn't needed for the curves *ring* supports because all of the
* curves *ring* supports have cofactor 1 and prime order; see section A.3 of
* the NSA's "Suite B Implementer's Guide to FIPS 186-3 (ECDSA)". */
/* in case the priv_key is present :
* check if generator * priv_key == pub_key
*/
if (eckey->priv_key) {
/* XXX: |BN_cmp| is not constant time. */
if (BN_cmp(eckey->priv_key, &eckey->group->order) >= 0) {
OPENSSL_PUT_ERROR(EC, EC_R_WRONG_ORDER);
goto err;
}
point = EC_POINT_new(eckey->group);
if (point == NULL ||
!eckey->group->meth->mul_private(eckey->group, point, eckey->priv_key,
NULL, NULL, ctx)) {
OPENSSL_PUT_ERROR(EC, ERR_R_EC_LIB);
goto err;
}
if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, ctx) != 0) {
OPENSSL_PUT_ERROR(EC, EC_R_INVALID_PRIVATE_KEY);
goto err;
}
}
ok = 1;
err:
BN_CTX_free(ctx);
EC_POINT_free(point);
return ok;
}
int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx)
{
int ret = 0;
BIGNUM *order;
BN_CTX *new_ctx = NULL;
EC_POINT *point = NULL;
if (ctx == NULL) {
ctx = new_ctx = BN_CTX_new();
if (ctx == NULL) {
ECerr(EC_F_EC_GROUP_CHECK, ERR_R_MALLOC_FAILURE);
goto err;
}
}
BN_CTX_start(ctx);
if ((order = BN_CTX_get(ctx)) == NULL)
goto err;
/* check the discriminant */
if (!EC_GROUP_check_discriminant(group, ctx)) {
ECerr(EC_F_EC_GROUP_CHECK, EC_R_DISCRIMINANT_IS_ZERO);
goto err;
}
/* check the generator */
if (group->generator == NULL) {
ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_GENERATOR);
goto err;
}
if (!EC_POINT_is_on_curve(group, group->generator, ctx)) {
ECerr(EC_F_EC_GROUP_CHECK, EC_R_POINT_IS_NOT_ON_CURVE);
goto err;
}
/* check the order of the generator */
if ((point = EC_POINT_new(group)) == NULL)
goto err;
if (!EC_GROUP_get_order(group, order, ctx))
goto err;
if (BN_is_zero(order)) {
ECerr(EC_F_EC_GROUP_CHECK, EC_R_UNDEFINED_ORDER);
goto err;
}
if (!EC_POINT_mul(group, point, order, NULL, NULL, ctx))
goto err;
if (!EC_POINT_is_at_infinity(group, point)) {
ECerr(EC_F_EC_GROUP_CHECK, EC_R_INVALID_GROUP_ORDER);
goto err;
}
ret = 1;
err:
if (ctx != NULL)
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
EC_POINT_free(point);
return ret;
}
int verify_x962_octets_are_on_p256(const unsigned char* octets, size_t len) {
assert(octets);
assert(len);
EC_GROUP* p256group = EC_GROUP_new_by_curve_name(NID_X9_62_prime256v1);
if (!p256group) {
fprintf(stderr, "error: EC_GROUP_new_by_curve_name() failed.\n");
return 4;
}
EC_POINT* point = EC_POINT_new(p256group);
if (!point) {
fprintf(stderr, "error: EC_POINT_new() failed.\n");
EC_GROUP_free(p256group);
return 4;
}
if (0 == EC_POINT_oct2point(p256group, point, octets, len, NULL)) {
fprintf(stderr, "error: EC_POINT_oct2point() failed.\n");
EC_POINT_free(point);
EC_GROUP_free(p256group);
return 4;
}
if (0 == EC_POINT_is_on_curve(p256group, point, NULL)) {
fprintf(stderr, "error: Public key point isn't on P-256 curve.\n");
EC_POINT_free(point);
EC_GROUP_free(p256group);
return 4;
}
EC_POINT_free(point);
EC_GROUP_free(p256group);
return 0;
}
int
conv_os2point(const EC_GROUP *grp, const ASN1_OCTET_STRING *os, EC_POINT *p,
BN_CTX *ctx)
{
if (EC_POINT_oct2point(grp, p, os->data, os->length, ctx) <= 0)
return ENOMEM;
if (EC_POINT_is_on_curve(grp, p, ctx) == 0)
return EINVAL;
if (EC_POINT_is_at_infinity(grp, p))
return EINVAL;
return 0;
}
int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point,
const BIGNUM *x, const BIGNUM *y,
BN_CTX *ctx) {
if (group->meth != point->meth) {
OPENSSL_PUT_ERROR(EC, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
if (!ec_GFp_simple_point_set_affine_coordinates(group, point, x, y, ctx)) {
return 0;
}
if (!EC_POINT_is_on_curve(group, point, ctx)) {
OPENSSL_PUT_ERROR(EC, EC_R_POINT_IS_NOT_ON_CURVE);
return 0;
}
return 1;
}
int EC_POINT_set_affine_coordinates(const EC_GROUP *group, EC_POINT *point,
const BIGNUM *x, const BIGNUM *y,
BN_CTX *ctx)
{
if (group->meth->point_set_affine_coordinates == NULL) {
ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES,
ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
if (!ec_point_is_compat(point, group)) {
ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES, EC_R_INCOMPATIBLE_OBJECTS);
return 0;
}
if (!group->meth->point_set_affine_coordinates(group, point, x, y, ctx))
return 0;
if (EC_POINT_is_on_curve(group, point, ctx) <= 0) {
ECerr(EC_F_EC_POINT_SET_AFFINE_COORDINATES, EC_R_POINT_IS_NOT_ON_CURVE);
return 0;
}
return 1;
}
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;
}
/*
* Converts an octet string representation to an EC_POINT. Note that the
* simple implementation only uses affine coordinates.
*/
int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point,
const unsigned char *buf, size_t len,
BN_CTX *ctx)
{
point_conversion_form_t form;
int y_bit;
BN_CTX *new_ctx = NULL;
BIGNUM *x, *y, *yxi;
size_t field_len, enc_len;
int ret = 0;
if (len == 0) {
ECerr(EC_F_EC_GF2M_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)) {
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
return 0;
}
if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) {
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
return 0;
}
if (form == 0) {
if (len != 1) {
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
return 0;
}
return EC_POINT_set_to_infinity(group, point);
}
field_len = (EC_GROUP_get_degree(group) + 7) / 8;
enc_len =
(form ==
POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2 * field_len;
if (len != enc_len) {
ECerr(EC_F_EC_GF2M_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);
yxi = BN_CTX_get(ctx);
if (yxi == NULL)
goto err;
if (!BN_bin2bn(buf + 1, field_len, x))
goto err;
if (BN_ucmp(x, &group->field) >= 0) {
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
goto err;
}
if (form == POINT_CONVERSION_COMPRESSED) {
if (!EC_POINT_set_compressed_coordinates_GF2m
(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) {
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
goto err;
}
if (form == POINT_CONVERSION_HYBRID) {
if (!group->meth->field_div(group, yxi, y, x, ctx))
goto err;
if (y_bit != BN_is_odd(yxi)) {
ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING);
goto err;
}
}
if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx))
goto err;
}
/* test required by X9.62 */
if (EC_POINT_is_on_curve(group, point, ctx) <= 0) {
ECerr(EC_F_EC_GF2M_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;
}
int ec_key_simple_check_key(const EC_KEY *eckey)
{
int ok = 0;
BN_CTX *ctx = NULL;
const BIGNUM *order = NULL;
EC_POINT *point = NULL;
if (eckey == NULL || eckey->group == NULL || eckey->pub_key == NULL) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
if (EC_POINT_is_at_infinity(eckey->group, eckey->pub_key)) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_POINT_AT_INFINITY);
goto err;
}
if ((ctx = BN_CTX_new()) == NULL)
goto err;
if ((point = EC_POINT_new(eckey->group)) == NULL)
goto err;
/* testing whether the pub_key is on the elliptic curve */
if (EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx) <= 0) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE);
goto err;
}
/* testing whether pub_key * order is the point at infinity */
order = eckey->group->order;
if (BN_is_zero(order)) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_INVALID_GROUP_ORDER);
goto err;
}
if (!EC_POINT_mul(eckey->group, point, NULL, eckey->pub_key, order, ctx)) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (!EC_POINT_is_at_infinity(eckey->group, point)) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_WRONG_ORDER);
goto err;
}
/*
* in case the priv_key is present : check if generator * priv_key ==
* pub_key
*/
if (eckey->priv_key != NULL) {
if (BN_cmp(eckey->priv_key, order) >= 0) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_WRONG_ORDER);
goto err;
}
if (!EC_POINT_mul(eckey->group, point, eckey->priv_key,
NULL, NULL, ctx)) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (EC_POINT_cmp(eckey->group, point, eckey->pub_key, ctx) != 0) {
ECerr(EC_F_EC_KEY_SIMPLE_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY);
goto err;
}
}
ok = 1;
err:
BN_CTX_free(ctx);
EC_POINT_free(point);
return ok;
}
int PKI_X509_KEYPAIR_get_curve ( PKI_X509_KEYPAIR *kp )
{
#ifdef ENABLE_ECDSA
PKI_X509_KEYPAIR_VALUE *pVal = NULL;
const EC_GROUP *gr;
EC_GROUP *gr2;
EC_KEY *ec = NULL;
EC_POINT *point = NULL;
BN_CTX *ctx = NULL;
int ret = PKI_ID_UNKNOWN;
EC_builtin_curve *curves = NULL;
size_t num_curves = 0;
int i;
BIGNUM *order;
unsigned long long keyBits = 0;
unsigned long long curveBits = 0;
pVal = kp->value;
if (!pVal ) return PKI_ID_UNKNOWN;
ctx = BN_CTX_new();
switch (EVP_PKEY_type(pVal->type))
{
case EVP_PKEY_EC:
ec = pVal->pkey.ec;
break;
default:
return PKI_ID_UNKNOWN;
break;
};
if (!ec) {
return PKI_ID_UNKNOWN;
};
if((gr = EC_KEY_get0_group(ec)) == NULL) {
return PKI_ID_UNKNOWN;
};
order = BN_new();
if (EC_GROUP_get_order(gr, order, NULL)) {
keyBits = (unsigned long long) BN_num_bits(order);
}
BN_free( order );
order = NULL;
if((point = EC_POINT_new( gr )) == NULL ) {
PKI_log_err("Can not generate a new point in Key's Group");
return PKI_ID_UNKNOWN;
};
/* Get the number of availabe ECDSA curves in OpenSSL */
if ((num_curves = EC_get_builtin_curves(NULL, 0)) < 1 ) {
/* No curves available! */
return PKI_ID_UNKNOWN;
}
/* Alloc the needed memory */
curves = OPENSSL_malloc(sizeof(EC_builtin_curve) * (int) num_curves);
if (curves == NULL) {
return PKI_ID_UNKNOWN;
};
/* Get the builtin curves */
if (!EC_get_builtin_curves(curves, num_curves)) {
if( curves ) free (curves);
return PKI_ID_UNKNOWN;
}
order = BN_new();
/* Cycle through the curves and display the names */
for( i = 0; i < num_curves; i++ ) {
int nid;
nid = curves[i].nid;
if(( gr2 = EC_GROUP_new_by_curve_name( nid )) == NULL) {
PKI_log_err("Can not get default curve [%d]", i);
break;
};
if (EC_GROUP_get_order(gr2, order, NULL)) {
curveBits = (unsigned long long) BN_num_bits(order);
};
if ( curveBits == keyBits ) {
if( EC_POINT_is_on_curve( gr2, point, ctx ) ) {
ret = nid;
break;
};
};
if( gr2 ) EC_GROUP_free ( gr2 );
};
if ( order ) BN_free ( order );
if( curves ) free ( curves );
BN_CTX_free ( ctx );
return ret;
#else
return PKI_ID_UNKNOWN;
#endif
};
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);
}
/*
* 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;
}
int process_peer_commit(REQUEST *request, pwd_session_t *session, uint8_t *in, size_t in_len, BN_CTX *bn_ctx)
{
uint8_t *ptr;
size_t data_len;
BIGNUM *x = NULL, *y = NULL, *cofactor = NULL;
EC_POINT *K = NULL, *point = NULL;
int ret = 1;
MEM(session->peer_scalar = BN_new());
MEM(session->k = BN_new());
MEM(session->peer_element = EC_POINT_new(session->group));
MEM(point = EC_POINT_new(session->group));
MEM(K = EC_POINT_new(session->group));
MEM(cofactor = BN_new());
MEM(x = BN_new());
MEM(y = BN_new());
if (!EC_GROUP_get_cofactor(session->group, cofactor, NULL)) {
REDEBUG("Unable to get group co-factor");
goto finish;
}
/* element, x then y, followed by scalar */
ptr = (uint8_t *)in;
data_len = BN_num_bytes(session->prime);
/*
* Did the peer send enough data?
*/
if (in_len < (2 * data_len + BN_num_bytes(session->order))) {
REDEBUG("Invalid commit packet");
goto finish;
}
BN_bin2bn(ptr, data_len, x);
ptr += data_len;
BN_bin2bn(ptr, data_len, y);
ptr += data_len;
data_len = BN_num_bytes(session->order);
BN_bin2bn(ptr, data_len, session->peer_scalar);
/* validate received scalar */
if (BN_is_zero(session->peer_scalar) ||
BN_is_one(session->peer_scalar) ||
BN_cmp(session->peer_scalar, session->order) >= 0) {
REDEBUG("Peer's scalar is not within the allowed range");
goto finish;
}
if (!EC_POINT_set_affine_coordinates_GFp(session->group, session->peer_element, x, y, bn_ctx)) {
REDEBUG("Unable to get coordinates of peer's element");
goto finish;
}
/* validate received element */
if (!EC_POINT_is_on_curve(session->group, session->peer_element, bn_ctx) ||
EC_POINT_is_at_infinity(session->group, session->peer_element)) {
REDEBUG("Peer's element is not a point on the elliptic curve");
goto finish;
}
/* check to ensure peer's element is not in a small sub-group */
if (BN_cmp(cofactor, BN_value_one())) {
if (!EC_POINT_mul(session->group, point, NULL, session->peer_element, cofactor, NULL)) {
REDEBUG("Unable to multiply element by co-factor");
goto finish;
}
if (EC_POINT_is_at_infinity(session->group, point)) {
REDEBUG("Peer's element is in small sub-group");
goto finish;
}
}
/* detect reflection attacks */
if (BN_cmp(session->peer_scalar, session->my_scalar) == 0 ||
EC_POINT_cmp(session->group, session->peer_element, session->my_element, bn_ctx) == 0) {
REDEBUG("Reflection attack detected");
goto finish;
}
/* compute the shared key, k */
if ((!EC_POINT_mul(session->group, K, NULL, session->pwe, session->peer_scalar, bn_ctx)) ||
(!EC_POINT_add(session->group, K, K, session->peer_element, bn_ctx)) ||
(!EC_POINT_mul(session->group, K, NULL, K, session->private_value, bn_ctx))) {
REDEBUG("Unable to compute shared key, k");
goto finish;
}
/* ensure that the shared key isn't in a small sub-group */
if (BN_cmp(cofactor, BN_value_one())) {
if (!EC_POINT_mul(session->group, K, NULL, K, cofactor, NULL)) {
REDEBUG("Unable to multiply k by co-factor");
goto finish;
}
}
/*
* 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(session->group, K)) {
REDEBUG("K is point-at-infinity");
goto finish;
}
if (!EC_POINT_get_affine_coordinates_GFp(session->group, K, session->k, NULL, bn_ctx)) {
REDEBUG("Unable to get shared secret from K");
goto finish;
}
ret = 0;
finish:
EC_POINT_clear_free(K);
EC_POINT_clear_free(point);
BN_clear_free(cofactor);
BN_clear_free(x);
BN_clear_free(y);
return ret;
}
int GOST_KEY_check_key(const GOST_KEY *key)
{
int ok = 0;
BN_CTX *ctx = NULL;
BIGNUM *order = NULL;
EC_POINT *point = NULL;
if (!key || !key->group || !key->pub_key) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
if (EC_POINT_is_at_infinity(key->group, key->pub_key)) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, EC_R_POINT_AT_INFINITY);
goto err;
}
if ((ctx = BN_CTX_new()) == NULL)
goto err;
if ((point = EC_POINT_new(key->group)) == NULL)
goto err;
/* testing whether the pub_key is on the elliptic curve */
if (EC_POINT_is_on_curve(key->group, key->pub_key, ctx) <= 0) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE);
goto err;
}
/* testing whether pub_key * order is the point at infinity */
if ((order = BN_new()) == NULL)
goto err;
if (!EC_GROUP_get_order(key->group, order, ctx)) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, EC_R_INVALID_GROUP_ORDER);
goto err;
}
if (!EC_POINT_mul(key->group, point, NULL, key->pub_key, order, ctx)) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (!EC_POINT_is_at_infinity(key->group, point)) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, EC_R_WRONG_ORDER);
goto err;
}
/*
* in case the priv_key is present : check if generator * priv_key ==
* pub_key
*/
if (key->priv_key) {
if (BN_cmp(key->priv_key, order) >= 0) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, EC_R_WRONG_ORDER);
goto err;
}
if (!EC_POINT_mul(key->group, point, key->priv_key, NULL, NULL, ctx)) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (EC_POINT_cmp(key->group, point, key->pub_key, ctx) != 0) {
GOSTerr(GOST_F_GOST_KEY_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY);
goto err;
}
}
ok = 1;
err:
BN_free(order);
BN_CTX_free(ctx);
EC_POINT_free(point);
return (ok);
}
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);
}
int EC_KEY_check_key(const EC_KEY *eckey)
{
int ok = 0;
BN_CTX *ctx = NULL;
BIGNUM *order = NULL;
EC_POINT *point = NULL;
if (!eckey || !eckey->group || !eckey->pub_key)
{
ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_PASSED_NULL_PARAMETER);
return 0;
}
if ((ctx = BN_CTX_new()) == NULL)
goto err;
if ((order = BN_new()) == NULL)
goto err;
if ((point = EC_POINT_new(eckey->group)) == NULL)
goto err;
/* testing whether the pub_key is on the elliptic curve */
if (!EC_POINT_is_on_curve(eckey->group, eckey->pub_key, ctx))
{
ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_POINT_IS_NOT_ON_CURVE);
goto err;
}
/* testing whether pub_key * order is the point at infinity */
if (!EC_GROUP_get_order(eckey->group, order, ctx))
{
ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_GROUP_ORDER);
goto err;
}
if (!EC_POINT_copy(point, eckey->pub_key))
{
ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (!EC_POINT_mul(eckey->group, point, order, NULL, NULL, ctx))
{
ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (!EC_POINT_is_at_infinity(eckey->group, point))
{
ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER);
goto err;
}
/* in case the priv_key is present :
* check if generator * priv_key == pub_key
*/
if (eckey->priv_key)
{
if (BN_cmp(eckey->priv_key, order) >= 0)
{
ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_WRONG_ORDER);
goto err;
}
if (!EC_POINT_mul(eckey->group, point, eckey->priv_key,
NULL, NULL, ctx))
{
ECerr(EC_F_EC_KEY_CHECK_KEY, ERR_R_EC_LIB);
goto err;
}
if (EC_POINT_cmp(eckey->group, point, eckey->pub_key,
ctx) != 0)
{
ECerr(EC_F_EC_KEY_CHECK_KEY, EC_R_INVALID_PRIVATE_KEY);
goto err;
}
}
ok = 1;
err:
if (ctx != NULL)
BN_CTX_free(ctx);
if (order != NULL)
BN_free(order);
if (point != NULL)
EC_POINT_free(point);
return(ok);
}
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;
}
static void CheckPublicKey(X509 *x509, struct tm tm_after)
{
EVP_PKEY *pkey = X509_get_pubkey(x509);
if (pkey == NULL)
{
SetError(ERR_UNKNOWN_PUBLIC_KEY_TYPE);
}
else if (EVP_PKEY_base_id(pkey) == EVP_PKEY_RSA)
{
RSA *rsa = EVP_PKEY_get1_RSA(pkey);
if (rsa == NULL)
{
SetError(ERR_INVALID);
RSA_free(rsa);
return;
}
const BIGNUM *n, *e;
RSA_get0_key(rsa, &n, &e, NULL);
if (n == NULL || e == NULL)
{
SetError(ERR_INVALID);
RSA_free(rsa);
return;
}
if (!GetBit(errors, ERR_INVALID_TIME_FORMAT))
{
if (tm_after.tm_year >= 114 && BN_num_bits(n) < 2048)
{
SetError(ERR_RSA_SIZE_2048);
}
}
if (BN_is_odd(e) == 0)
{
SetError(ERR_RSA_EXP_NOT_ODD);
}
BIGNUM *i = BN_new();
BN_set_word(i, 3);
if (BN_cmp(e, i) < 0)
{
SetError(ERR_RSA_EXP_3);
}
else
{
BN_set_word(i, 0x10001);
if (BN_cmp(e, i) < 0)
{
SetWarning(WARN_RSA_EXP_RANGE);
}
BN_hex2bn(&i, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF");
if (BN_cmp(e, i) > 0)
{
SetWarning(WARN_RSA_EXP_RANGE);
}
}
BN_CTX *ctx = BN_CTX_new();
if (BN_gcd(i, n, bn_factors, ctx) == 0 || !BN_is_one(i))
{
SetError(ERR_RSA_SMALL_FACTOR);
}
BN_free(i);
BN_CTX_free(ctx);
RSA_free(rsa);
}
else if (EVP_PKEY_base_id(pkey) == EVP_PKEY_EC)
{
EC_KEY *ec_key = EVP_PKEY_get1_EC_KEY(pkey);
const EC_GROUP *group = EC_KEY_get0_group(ec_key);
const EC_POINT *point = EC_KEY_get0_public_key(ec_key);
BN_CTX *ctx = BN_CTX_new();
BIGNUM *order = BN_new();
EC_GROUP_get_order(group, order, ctx);
if (EC_POINT_is_at_infinity(group, point))
{
SetError(ERR_EC_AT_INFINITY);
}
if (EC_POINT_is_on_curve(group, point, ctx) != 1)
{
SetError(ERR_EC_POINT_NOT_ON_CURVE);
}
EC_POINT *result = EC_POINT_new(group);
if (BN_is_zero(order))
{
SetError(ERR_EC_INVALID_GROUP_ORDER);
}
EC_POINT_mul(group, result, NULL, point, order, ctx);
if (!EC_POINT_is_at_infinity(group, result))
{
SetError(ERR_EC_INCORRECT_ORDER);
}
int nid = EC_GROUP_get_curve_name(group);
if (nid != NID_X9_62_prime256v1 && nid != NID_secp384r1 && nid != NID_secp521r1)
{
SetError(ERR_EC_NON_ALLOWED_CURVE);
}
EC_POINT_free(result);
BN_free(order);
BN_CTX_free(ctx);
EC_KEY_free(ec_key);
}
else
{
SetError(ERR_UNKNOWN_PUBLIC_KEY_TYPE);
}
if (pkey != NULL)
{
EVP_PKEY_free(pkey);
}
}
