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;
}
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);
}
static int eckey_pub_cmp(const EVP_PKEY *a, const EVP_PKEY *b)
{
int r;
const EC_GROUP *group = EC_KEY_get0_group(b->pkey.ec);
const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec),
*pb = EC_KEY_get0_public_key(b->pkey.ec);
r = EC_POINT_cmp(group, pa, pb, NULL);
if (r == 0)
return 1;
if (r == 1)
return 0;
return -2;
}
static int pub_cmp_gost01(const EVP_PKEY *a,const EVP_PKEY *b)
{
const EC_KEY *ea = EVP_PKEY_get0((EVP_PKEY *)a);
const EC_KEY *eb = EVP_PKEY_get0((EVP_PKEY *)b);
const EC_POINT *ka,*kb;
int ret=0;
if (!ea || !eb) return 0;
ka = EC_KEY_get0_public_key(ea);
kb = EC_KEY_get0_public_key(eb);
if (!ka || !kb) return 0;
ret = (0==EC_POINT_cmp(EC_KEY_get0_group(ea),ka,kb,NULL)) ;
return ret;
}
int EVP_PKEY_cmp(const EVP_PKEY *a, const EVP_PKEY *b)
{
if (a->type != b->type)
return -1;
if (EVP_PKEY_cmp_parameters(a, b) == 0)
return 0;
switch (a->type)
{
#ifndef OPENSSL_NO_RSA
case EVP_PKEY_RSA:
if (BN_cmp(b->pkey.rsa->n,a->pkey.rsa->n) != 0
|| BN_cmp(b->pkey.rsa->e,a->pkey.rsa->e) != 0)
return 0;
break;
#endif
#ifndef OPENSSL_NO_DSA
case EVP_PKEY_DSA:
if (BN_cmp(b->pkey.dsa->pub_key,a->pkey.dsa->pub_key) != 0)
return 0;
break;
#endif
#ifndef OPENSSL_NO_EC
case EVP_PKEY_EC:
{
int r;
const EC_GROUP *group = EC_KEY_get0_group(b->pkey.ec);
const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec),
*pb = EC_KEY_get0_public_key(b->pkey.ec);
r = EC_POINT_cmp(group, pa, pb, NULL);
if (r != 0)
{
if (r == 1)
return 0;
else
return -2;
}
}
break;
#endif
#ifndef OPENSSL_NO_DH
case EVP_PKEY_DH:
return -2;
#endif
default:
return -2;
}
return 1;
}
static int
pub_cmp_gost01(const EVP_PKEY *a, const EVP_PKEY *b)
{
const GOST_KEY *ea = a->pkey.gost;
const GOST_KEY *eb = b->pkey.gost;
const EC_POINT *ka, *kb;
int ret = 0;
if (ea == NULL || eb == NULL)
return 0;
ka = GOST_KEY_get0_public_key(ea);
kb = GOST_KEY_get0_public_key(eb);
if (ka == NULL || kb == NULL)
return 0;
ret = (0 == EC_POINT_cmp(GOST_KEY_get0_group(ea), ka, kb, NULL));
return ret;
}
int example_EC_POINT_mul() {
/* This example ensures that 10×∞ + G = G, in P-256. */
EC_GROUP *group = NULL;
EC_POINT *p = NULL, *result = NULL;
BIGNUM *n = NULL;
int ret = 0;
const EC_POINT *generator;
group = EC_GROUP_new_by_curve_name(NID_X9_62_prime256v1);
p = EC_POINT_new(group);
result = EC_POINT_new(group);
n = BN_new();
if (p == NULL ||
result == NULL ||
group == NULL ||
n == NULL ||
!EC_POINT_set_to_infinity(group, p) ||
!BN_set_word(n, 10)) {
goto err;
}
/* First check that 10×∞ = ∞. */
if (!EC_POINT_mul(group, result, NULL, p, n, NULL) ||
!EC_POINT_is_at_infinity(group, result)) {
goto err;
}
generator = EC_GROUP_get0_generator(group);
/* Now check that 10×∞ + G = G. */
if (!EC_POINT_mul(group, result, BN_value_one(), p, n, NULL) ||
EC_POINT_cmp(group, result, generator, NULL) != 0) {
goto err;
}
ret = 1;
err:
BN_free(n);
EC_POINT_free(result);
EC_POINT_free(p);
EC_GROUP_free(group);
return ret;
}
static int
server_pubkeybatch_equal(server_context_t *ctxp,
pubkeybatch_t *a, pubkeybatch_t *b)
{
workitem_t *wipa, *wipb;
if (a->nitems != b->nitems)
return 0;
if (EC_POINT_cmp(EC_KEY_get0_group(ctxp->dummy_key),
a->pubkey, b->pubkey, NULL))
return 0;
for (wipa = workitem_avl_first(&a->items),
wipb = workitem_avl_first(&b->items);
wipa && wipb;
wipa = workitem_avl_next(wipa), wipb = workitem_avl_next(wipb)) {
if (!server_workitem_equal(wipa, wipb))
return 0;
}
return 1;
}
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);
}
int verifyRingSignature(data_chunk &keyImage, uint256 &txnHash, int nRingSize, const uint8_t *pPubkeys, const uint8_t *pSigc, const uint8_t *pSigr)
{
if (fDebugRingSig)
{
// LogPrintf("%s size %d\n", __func__, nRingSize); // happens often
};
int rv = 0;
BN_CTX_start(bnCtx);
BIGNUM *bnT = BN_CTX_get(bnCtx);
BIGNUM *bnH = BN_CTX_get(bnCtx);
BIGNUM *bnC = BN_CTX_get(bnCtx);
BIGNUM *bnR = BN_CTX_get(bnCtx);
BIGNUM *bnSum = BN_CTX_get(bnCtx);
EC_POINT *ptT1 = NULL;
EC_POINT *ptT2 = NULL;
EC_POINT *ptT3 = NULL;
EC_POINT *ptPk = NULL;
EC_POINT *ptKi = NULL;
EC_POINT *ptL = NULL;
EC_POINT *ptR = NULL;
EC_POINT *ptSi = NULL;
uint8_t tempData[66]; // hold raw point data to hash
uint256 commitHash;
CHashWriter ssCommitHash(SER_GETHASH, PROTOCOL_VERSION);
ssCommitHash << txnHash;
// zero sum
if (!bnSum || !(BN_zero(bnSum)))
{
LogPrintf("%s: BN_zero failed.\n", __func__);
rv = 1; goto End;
};
if ( !(ptT1 = EC_POINT_new(ecGrp))
|| !(ptT2 = EC_POINT_new(ecGrp))
|| !(ptT3 = EC_POINT_new(ecGrp))
|| !(ptPk = EC_POINT_new(ecGrp))
|| !(ptKi = EC_POINT_new(ecGrp))
|| !(ptL = EC_POINT_new(ecGrp))
|| !(ptSi = EC_POINT_new(ecGrp))
|| !(ptR = EC_POINT_new(ecGrp)))
{
LogPrintf("%s: EC_POINT_new failed.\n", __func__);
rv = 1; goto End;
};
// get keyimage as point
if (!(bnT = BN_bin2bn(&keyImage[0], EC_COMPRESSED_SIZE, bnT))
|| !(ptKi) || !(ptKi = EC_POINT_bn2point(ecGrp, bnT, ptKi, bnCtx)))
{
LogPrintf("%s: extract ptKi failed.\n", __func__);
rv = 1; goto End;
};
for (int i = 0; i < nRingSize; ++i)
{
// Li = ci * Pi + ri * G
// Ri = ci * I + ri * Hp(Pi)
if ( !bnC || !(bnC = BN_bin2bn(&pSigc[i * EC_SECRET_SIZE], EC_SECRET_SIZE, bnC))
|| !bnR || !(bnR = BN_bin2bn(&pSigr[i * EC_SECRET_SIZE], EC_SECRET_SIZE, bnR)))
{
LogPrintf("%s: extract bnC and bnR failed.\n", __func__);
rv = 1; goto End;
};
// get Pk i as point
if (!(bnT = BN_bin2bn(&pPubkeys[i * EC_COMPRESSED_SIZE], EC_COMPRESSED_SIZE, bnT))
|| !(ptPk) || !(ptPk = EC_POINT_bn2point(ecGrp, bnT, ptPk, bnCtx)))
{
LogPrintf("%s: extract ptPk failed.\n", __func__);
rv = 1; goto End;
};
// ptT1 = ci * Pi
if (!EC_POINT_mul(ecGrp, ptT1, NULL, ptPk, bnC, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
// ptT2 = ri * G
if (!EC_POINT_mul(ecGrp, ptT2, bnR, NULL, NULL, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
// ptL = ptT1 + ptT2
if (!EC_POINT_add(ecGrp, ptL, ptT1, ptT2, bnCtx))
{
LogPrintf("%s: EC_POINT_add failed.\n", __func__);
rv = 1; goto End;
};
// ptT3 = Hp(Pi)
if (hashToEC(&pPubkeys[i * EC_COMPRESSED_SIZE], EC_COMPRESSED_SIZE, bnT, ptT3) != 0)
{
LogPrintf("%s: hashToEC failed.\n", __func__);
rv = 1; goto End;
};
// DEBUGGING: ------- check if we can find the signer...
// ptSi = Pi * bnT
if ((!EC_POINT_mul(ecGrp, ptSi, NULL, ptPk, bnT, bnCtx)
|| false)
&& (rv = errorN(1, "%s: EC_POINT_mul failed.1", __func__)))
goto End;
if (0 == EC_POINT_cmp(ecGrp, ptSi, ptKi, bnCtx) )
LogPrintf("signer is index %d\n", i);
// DEBUGGING: - End - check if we can find the signer...
// ptT1 = k1 * I
if (!EC_POINT_mul(ecGrp, ptT1, NULL, ptKi, bnC, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
// ptT2 = k2 * ptT3
if (!EC_POINT_mul(ecGrp, ptT2, NULL, ptT3, bnR, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
// ptR = ptT1 + ptT2
if (!EC_POINT_add(ecGrp, ptR, ptT1, ptT2, bnCtx))
{
LogPrintf("%s: EC_POINT_add failed.\n", __func__);
rv = 1; goto End;
};
// sum = (sum + ci) % N
if (!BN_mod_add(bnSum, bnSum, bnC, bnOrder, bnCtx))
{
LogPrintf("%s: BN_mod_add failed.\n", __func__);
rv = 1; goto End;
};
// -- add ptL and ptR to hash
if ( !(EC_POINT_point2oct(ecGrp, ptL, POINT_CONVERSION_COMPRESSED, &tempData[0], 33, bnCtx) == (int) EC_COMPRESSED_SIZE)
|| !(EC_POINT_point2oct(ecGrp, ptR, POINT_CONVERSION_COMPRESSED, &tempData[33], 33, bnCtx) == (int) EC_COMPRESSED_SIZE))
{
LogPrintf("%s: extract ptL and ptR failed.\n", __func__);
rv = 1; goto End;
};
ssCommitHash.write((const char*)&tempData[0], 66);
};
commitHash = ssCommitHash.GetHash();
if (!(bnH) || !(bnH = BN_bin2bn(commitHash.begin(), EC_SECRET_SIZE, bnH)))
{
LogPrintf("%s: commitHash -> bnH failed.\n", __func__);
rv = 1; goto End;
};
if (!BN_mod(bnH, bnH, bnOrder, bnCtx))
{
LogPrintf("%s: BN_mod failed.\n", __func__);
rv = 1; goto End;
};
// bnT = (bnH - bnSum) % N
if (!BN_mod_sub(bnT, bnH, bnSum, bnOrder, bnCtx))
{
LogPrintf("%s: BN_mod_sub failed.\n", __func__);
rv = 1; goto End;
};
// test bnT == 0 (bnSum == bnH)
if (!BN_is_zero(bnT))
{
LogPrintf("%s: signature does not verify.\n", __func__);
rv = 2;
};
End:
EC_POINT_free(ptT1);
EC_POINT_free(ptT2);
EC_POINT_free(ptT3);
EC_POINT_free(ptPk);
EC_POINT_free(ptKi);
EC_POINT_free(ptL);
EC_POINT_free(ptR);
EC_POINT_free(ptSi);
BN_CTX_end(bnCtx);
return rv;
};
int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx)
{
int r = 0;
BIGNUM *a1, *a2, *a3, *b1, *b2, *b3;
BN_CTX *ctx_new = NULL;
/* compare the field types*/
if (EC_METHOD_get_field_type(EC_GROUP_method_of(a)) !=
EC_METHOD_get_field_type(EC_GROUP_method_of(b)))
return 1;
/* compare the curve name (if present) */
if (EC_GROUP_get_curve_name(a) && EC_GROUP_get_curve_name(b) &&
EC_GROUP_get_curve_name(a) == EC_GROUP_get_curve_name(b))
return 0;
if (!ctx)
ctx_new = ctx = BN_CTX_new();
if (!ctx)
return -1;
BN_CTX_start(ctx);
a1 = BN_CTX_get(ctx);
a2 = BN_CTX_get(ctx);
a3 = BN_CTX_get(ctx);
b1 = BN_CTX_get(ctx);
b2 = BN_CTX_get(ctx);
b3 = BN_CTX_get(ctx);
if (!b3)
{
BN_CTX_end(ctx);
if (ctx_new)
BN_CTX_free(ctx);
return -1;
}
/* XXX This approach assumes that the external representation
* of curves over the same field type is the same.
*/
if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) ||
!b->meth->group_get_curve(b, b1, b2, b3, ctx))
r = 1;
if (r || BN_cmp(a1, b1) || BN_cmp(a2, b2) || BN_cmp(a3, b3))
r = 1;
/* XXX EC_POINT_cmp() assumes that the methods are equal */
if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a),
EC_GROUP_get0_generator(b), ctx))
r = 1;
if (!r)
{
/* compare the order and cofactor */
if (!EC_GROUP_get_order(a, a1, ctx) ||
!EC_GROUP_get_order(b, b1, ctx) ||
!EC_GROUP_get_cofactor(a, a2, ctx) ||
!EC_GROUP_get_cofactor(b, b2, ctx))
{
BN_CTX_end(ctx);
if (ctx_new)
BN_CTX_free(ctx);
return -1;
}
if (BN_cmp(a1, b1) || BN_cmp(a2, b2))
r = 1;
}
BN_CTX_end(ctx);
if (ctx_new)
BN_CTX_free(ctx);
return r;
}
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);
}
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;
}
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_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx)
{
int r = 0;
BIGNUM *a1, *a2, *a3, *b1, *b2, *b3;
BN_CTX *ctx_new = NULL;
/* compare the field types */
if (EC_METHOD_get_field_type(EC_GROUP_method_of(a)) !=
EC_METHOD_get_field_type(EC_GROUP_method_of(b)))
return 1;
/* compare the curve name (if present in both) */
if (EC_GROUP_get_curve_name(a) && EC_GROUP_get_curve_name(b) &&
EC_GROUP_get_curve_name(a) != EC_GROUP_get_curve_name(b))
return 1;
if (a->meth->flags & EC_FLAGS_CUSTOM_CURVE)
return 0;
if (ctx == NULL)
ctx_new = ctx = BN_CTX_new();
if (ctx == NULL)
return -1;
BN_CTX_start(ctx);
a1 = BN_CTX_get(ctx);
a2 = BN_CTX_get(ctx);
a3 = BN_CTX_get(ctx);
b1 = BN_CTX_get(ctx);
b2 = BN_CTX_get(ctx);
b3 = BN_CTX_get(ctx);
if (b3 == NULL) {
BN_CTX_end(ctx);
BN_CTX_free(ctx_new);
return -1;
}
/*
* XXX This approach assumes that the external representation of curves
* over the same field type is the same.
*/
if (!a->meth->group_get_curve(a, a1, a2, a3, ctx) ||
!b->meth->group_get_curve(b, b1, b2, b3, ctx))
r = 1;
if (r || BN_cmp(a1, b1) || BN_cmp(a2, b2) || BN_cmp(a3, b3))
r = 1;
/* XXX EC_POINT_cmp() assumes that the methods are equal */
if (r || EC_POINT_cmp(a, EC_GROUP_get0_generator(a),
EC_GROUP_get0_generator(b), ctx))
r = 1;
if (!r) {
const BIGNUM *ao, *bo, *ac, *bc;
/* compare the order and cofactor */
ao = EC_GROUP_get0_order(a);
bo = EC_GROUP_get0_order(b);
ac = EC_GROUP_get0_cofactor(a);
bc = EC_GROUP_get0_cofactor(b);
if (ao == NULL || bo == NULL) {
BN_CTX_end(ctx);
BN_CTX_free(ctx_new);
return -1;
}
if (BN_cmp(ao, bo) || BN_cmp(ac, bc))
r = 1;
}
BN_CTX_end(ctx);
BN_CTX_free(ctx_new);
return r;
}
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);
}
int verifyRingSignatureAB(data_chunk &keyImage, uint256 &txnHash, int nRingSize, const uint8_t *pPubkeys, const data_chunk &sigC, const uint8_t *pSigS)
{
// https://bitcointalk.org/index.php?topic=972541.msg10619684
// forall_{i=1..n} compute e_i=s_i*G+c_i*P_i and E_i=s_i*H(P_i)+c_i*I_j and c_{i+1}=h(P_1,...,P_n,e_i,E_i)
// check c_{n+1}=c_1
if (fDebugRingSig)
{
//LogPrintf("%s size %d\n", __func__, nRingSize); // happens often
};
if (sigC.size() != EC_SECRET_SIZE)
return errorN(1, "%s: sigC size != EC_SECRET_SIZE.", __func__);
if (keyImage.size() != EC_COMPRESSED_SIZE)
return errorN(1, "%s: keyImage size != EC_COMPRESSED_SIZE.", __func__);
int rv = 0;
uint256 tmpPkHash;
uint256 tmpHash;
uint8_t tempData[66]; // hold raw point data to hash
CHashWriter ssPkHash(SER_GETHASH, PROTOCOL_VERSION);
CHashWriter ssCjHash(SER_GETHASH, PROTOCOL_VERSION);
for (int i = 0; i < nRingSize; ++i)
{
ssPkHash.write((const char*)&pPubkeys[i * EC_COMPRESSED_SIZE], EC_COMPRESSED_SIZE);
};
tmpPkHash = ssPkHash.GetHash();
BN_CTX_start(bnCtx);
BIGNUM *bnC = BN_CTX_get(bnCtx);
BIGNUM *bnC1 = BN_CTX_get(bnCtx);
BIGNUM *bnT = BN_CTX_get(bnCtx);
BIGNUM *bnS = BN_CTX_get(bnCtx);
EC_POINT *ptKi = NULL;
EC_POINT *ptT1 = NULL;
EC_POINT *ptT2 = NULL;
EC_POINT *ptT3 = NULL;
EC_POINT *ptPk = NULL;
EC_POINT *ptSi = NULL;
if ( !(ptKi = EC_POINT_new(ecGrp))
|| !(ptT1 = EC_POINT_new(ecGrp))
|| !(ptT2 = EC_POINT_new(ecGrp))
|| !(ptT3 = EC_POINT_new(ecGrp))
|| !(ptPk = EC_POINT_new(ecGrp))
|| !(ptSi = EC_POINT_new(ecGrp)))
{
LogPrintf("%s: EC_POINT_new failed.\n", __func__);
rv = 1; goto End;
};
// get keyimage as point
if (!EC_POINT_oct2point(ecGrp, ptKi, &keyImage[0], EC_COMPRESSED_SIZE, bnCtx))
{
LogPrintf("%s: extract ptKi failed.\n", __func__);
rv = 1; goto End;
};
if (!bnC1 || !BN_bin2bn(&sigC[0], EC_SECRET_SIZE, bnC1))
{
LogPrintf("%s: BN_bin2bn failed.\n", __func__);
rv = 1; goto End;
};
if (!BN_copy(bnC, bnC1))
{
LogPrintf("%s: BN_copy failed.\n", __func__);
rv = 1; goto End;
};
for (int i = 0; i < nRingSize; ++i)
{
if (!bnS || !(BN_bin2bn(&pSigS[i * EC_SECRET_SIZE], EC_SECRET_SIZE, bnS)))
{
LogPrintf("%s: BN_bin2bn failed.\n", __func__);
rv = 1; goto End;
};
// ptT2 <- pk
if (!EC_POINT_oct2point(ecGrp, ptPk, &pPubkeys[i * EC_COMPRESSED_SIZE], EC_COMPRESSED_SIZE, bnCtx))
{
LogPrintf("%s: EC_POINT_oct2point failed.\n", __func__);
rv = 1; goto End;
};
// ptT1 = e_i=s_i*G+c_i*P_i
if (!EC_POINT_mul(ecGrp, ptT1, bnS, ptPk, bnC, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
if (!(EC_POINT_point2oct(ecGrp, ptT1, POINT_CONVERSION_COMPRESSED, &tempData[0], 33, bnCtx) == (int) EC_COMPRESSED_SIZE))
{
LogPrintf("%s: extract ptT1 failed.\n", __func__);
rv = 1; goto End;
};
// ptT2 =E_i=s_i*H(P_i)+c_i*I_j
// ptT2 =H(P_i)
if (hashToEC(&pPubkeys[i * EC_COMPRESSED_SIZE], EC_COMPRESSED_SIZE, bnT, ptT2) != 0)
{
LogPrintf("%s: hashToEC failed.\n", __func__);
rv = 1; goto End;
};
// DEBUGGING: ------- check if we can find the signer...
// ptSi = Pi * bnT
if ((!EC_POINT_mul(ecGrp, ptSi, NULL, ptPk, bnT, bnCtx)
|| false)
&& (rv = errorN(1, "%s: EC_POINT_mul failed.", __func__)))
goto End;
if (0 == EC_POINT_cmp(ecGrp, ptSi, ptKi, bnCtx) )
LogPrintf("signer is index %d\n", i);
// DEBUGGING: - End - check if we can find the signer...
// ptT3 = s_i*ptT2
if (!EC_POINT_mul(ecGrp, ptT3, NULL, ptT2, bnS, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
// ptT1 = c_i*I_j
if (!EC_POINT_mul(ecGrp, ptT1, NULL, ptKi, bnC, bnCtx))
{
LogPrintf("%s: EC_POINT_mul failed.\n", __func__);
rv = 1; goto End;
};
// ptT2 = ptT3 + ptT1
if (!EC_POINT_add(ecGrp, ptT2, ptT3, ptT1, bnCtx))
{
LogPrintf("%s: EC_POINT_add failed.\n", __func__);
rv = 1; goto End;
};
if (!(EC_POINT_point2oct(ecGrp, ptT2, POINT_CONVERSION_COMPRESSED, &tempData[33], 33, bnCtx) == (int) EC_COMPRESSED_SIZE))
{
LogPrintf("%s: extract ptT2 failed.\n", __func__);
rv = 1; goto End;
};
CHashWriter ssCHash(SER_GETHASH, PROTOCOL_VERSION);
ssCHash.write((const char*)tmpPkHash.begin(), 32);
ssCHash.write((const char*)&tempData[0], 66);
tmpHash = ssCHash.GetHash();
if (!bnC || !(BN_bin2bn(tmpHash.begin(), EC_SECRET_SIZE, bnC))
|| !BN_mod(bnC, bnC, bnOrder, bnCtx))
{
LogPrintf("%s: tmpHash -> bnC failed.\n", __func__);
rv = 1; goto End;
};
};
// bnT = (bnC - bnC1) % N
if (!BN_mod_sub(bnT, bnC, bnC1, bnOrder, bnCtx))
{
LogPrintf("%s: BN_mod_sub failed.\n", __func__);
rv = 1; goto End;
};
// test bnT == 0 (bnC == bnC1)
if (!BN_is_zero(bnT))
{
LogPrintf("%s: signature does not verify.\n", __func__);
rv = 2;
};
End:
BN_CTX_end(bnCtx);
EC_POINT_free(ptKi);
EC_POINT_free(ptT1);
EC_POINT_free(ptT2);
EC_POINT_free(ptT3);
EC_POINT_free(ptPk);
EC_POINT_free(ptSi);
return rv;
};
/*
* NIST SP800-56A co-factor ECDH tests.
* KATs taken from NIST documents with parameters:
*
* - (QCAVSx,QCAVSy) is the public key for CAVS.
* - dIUT is the private key for IUT.
* - (QIUTx,QIUTy) is the public key for IUT.
* - ZIUT is the shared secret KAT.
*
* CAVS: Cryptographic Algorithm Validation System
* IUT: Implementation Under Test
*
* This function tests two things:
*
* 1. dIUT * G = (QIUTx,QIUTy)
* i.e. public key for IUT computes correctly.
* 2. x-coord of cofactor * dIUT * (QCAVSx,QCAVSy) = ZIUT
* i.e. co-factor ECDH key computes correctly.
*
* returns zero on failure or unsupported curve. One otherwise.
*/
static int ecdh_cavs_kat(BIO *out, const ecdh_cavs_kat_t *kat)
{
int rv = 0, is_char_two = 0;
EC_KEY *key1 = NULL;
EC_POINT *pub = NULL;
const EC_GROUP *group = NULL;
BIGNUM *bnz = NULL, *x = NULL, *y = NULL;
unsigned char *Ztmp = NULL, *Z = NULL;
size_t Ztmplen, Zlen;
BIO_puts(out, "Testing ECC CDH Primitive SP800-56A with ");
BIO_puts(out, OBJ_nid2sn(kat->nid));
/* dIUT is IUT's private key */
if ((key1 = mk_eckey(kat->nid, kat->dIUT)) == NULL)
goto err;
/* these are cofactor ECDH KATs */
EC_KEY_set_flags(key1, EC_FLAG_COFACTOR_ECDH);
if ((group = EC_KEY_get0_group(key1)) == NULL)
goto err;
if ((pub = EC_POINT_new(group)) == NULL)
goto err;
if (EC_METHOD_get_field_type(EC_GROUP_method_of(group)) == NID_X9_62_characteristic_two_field)
is_char_two = 1;
/* (QIUTx, QIUTy) is IUT's public key */
if(!BN_hex2bn(&x, kat->QIUTx))
goto err;
if(!BN_hex2bn(&y, kat->QIUTy))
goto err;
if (is_char_two) {
#ifdef OPENSSL_NO_EC2M
goto err;
#else
if (!EC_POINT_set_affine_coordinates_GF2m(group, pub, x, y, NULL))
goto err;
#endif
}
else {
if (!EC_POINT_set_affine_coordinates_GFp(group, pub, x, y, NULL))
goto err;
}
/* dIUT * G = (QIUTx, QIUTy) should hold */
if (EC_POINT_cmp(group, EC_KEY_get0_public_key(key1), pub, NULL))
goto err;
/* (QCAVSx, QCAVSy) is CAVS's public key */
if(!BN_hex2bn(&x, kat->QCAVSx))
goto err;
if(!BN_hex2bn(&y, kat->QCAVSy))
goto err;
if (is_char_two) {
#ifdef OPENSSL_NO_EC2M
goto err;
#else
if (!EC_POINT_set_affine_coordinates_GF2m(group, pub, x, y, NULL))
goto err;
#endif
}
else {
if (!EC_POINT_set_affine_coordinates_GFp(group, pub, x, y, NULL))
goto err;
}
/* ZIUT is the shared secret */
if(!BN_hex2bn(&bnz, kat->ZIUT))
goto err;
Ztmplen = (EC_GROUP_get_degree(EC_KEY_get0_group(key1)) + 7) / 8;
Zlen = BN_num_bytes(bnz);
if (Zlen > Ztmplen)
goto err;
if((Ztmp = OPENSSL_zalloc(Ztmplen)) == NULL)
goto err;
if((Z = OPENSSL_zalloc(Ztmplen)) == NULL)
goto err;
if(!BN_bn2binpad(bnz, Z, Ztmplen))
goto err;
if (!ECDH_compute_key(Ztmp, Ztmplen, pub, key1, 0))
goto err;
/* shared secrets should be identical */
if (memcmp(Ztmp, Z, Ztmplen))
goto err;
rv = 1;
err:
EC_KEY_free(key1);
EC_POINT_free(pub);
BN_free(bnz);
BN_free(x);
BN_free(y);
OPENSSL_free(Ztmp);
OPENSSL_free(Z);
if (rv) {
BIO_puts(out, " ok\n");
}
else {
fprintf(stderr, "Error in ECC CDH routines\n");
ERR_print_errors_fp(stderr);
}
return rv;
}
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;
}
