[PATCH] crypto: ecc - Handle exceptional points in Shamir multiplication
From: Jérémy Jean
Date: Fri Sep 25 2026 - 09:26:11 EST
Shamir multiplication mishandles equal points, opposite points and the
point at infinity. This rejects valid ECDSA signatures and can accept
invalid digest/signature tuples when the public key is G or -G. The
kernel incorrectly rejects 16 valid signatures from Wycheproof.
Handle doubling, cancellation and the point at infinity in precomputation
and accumulation. Add regression tests for P-256 ECDSA and 256/512-bit
EC-RDSA. The vectors are Wycheproof P1363 secp256r1/SHA-256 cases 60 and
210 converted to X9.62, two constructed ECDSA signatures for Q = +/-G
with k = 2, and six constructed EC-RDSA signatures for Q = G, -G and -2G.
Fixes: 0d7a78643f69 ("crypto: ecrdsa - add EC-RDSA (GOST 34.10) algorithm")
Assisted-by: LLM
Signed-off-by: Jérémy Jean <Jeremy.Jean@xxxxxxxxxxxxxxxxx>
---
crypto/ecc.c | 33 +++++-
crypto/testmgr.h | 280 ++++++++++++++++++++++++++++++++++++++++++++++-
2 files changed, 310 insertions(+), 3 deletions(-)
diff --git a/crypto/ecc.c b/crypto/ecc.c
index 3250a464b852..c7366eb7ce1f 100644
--- a/crypto/ecc.c
+++ b/crypto/ecc.c
@@ -1423,9 +1423,22 @@ static void ecc_point_add(const struct ecc_point *result,
vli_set(result->x, q->x, ndigits);
vli_set(result->y, q->y, ndigits);
vli_mod_sub(z, result->x, p->x, curve->p, ndigits);
+ if (vli_is_zero(z, ndigits)) {
+ if (vli_cmp(p->y, q->y, ndigits)) {
+ /* P + (-P) is the point at infinity. */
+ vli_clear(result->x, ndigits);
+ vli_clear(result->y, ndigits);
+ return;
+ }
+ /* The co-Z addition formula does not handle P == Q. */
+ z[0] = 1;
+ ecc_point_double_jacobian(result->x, result->y, z, curve);
+ goto out;
+ }
vli_set(px, p->x, ndigits);
vli_set(py, p->y, ndigits);
xycz_add(px, py, result->x, result->y, curve);
+out:
vli_mod_inv(z, z, curve->p, ndigits);
apply_z(result->x, result->y, z, curve);
}
@@ -1465,22 +1478,38 @@ void ecc_point_mult_shamir(const struct ecc_point *result,
vli_set(rx, point->x, ndigits);
vli_set(ry, point->y, ndigits);
vli_clear(z + 1, ndigits - 1);
- z[0] = 1;
+ z[0] = !ecc_point_is_zero(point);
for (--i; i >= 0; i--) {
ecc_point_double_jacobian(rx, ry, z, curve);
idx = !!vli_test_bit(u1, i);
idx |= (!!vli_test_bit(u2, i)) << 1;
point = points[idx];
- if (point) {
+ if (point && !ecc_point_is_zero(point)) {
u64 tx[ECC_MAX_DIGITS];
u64 ty[ECC_MAX_DIGITS];
u64 tz[ECC_MAX_DIGITS];
+ if (vli_is_zero(z, ndigits)) {
+ /* Adding to infinity starts a new accumulator. */
+ vli_set(rx, point->x, ndigits);
+ vli_set(ry, point->y, ndigits);
+ z[0] = 1;
+ continue;
+ }
vli_set(tx, point->x, ndigits);
vli_set(ty, point->y, ndigits);
apply_z(tx, ty, z, curve);
vli_mod_sub(tz, rx, tx, curve->p, ndigits);
+ if (vli_is_zero(tz, ndigits)) {
+ if (!vli_cmp(ry, ty, ndigits))
+ ecc_point_double_jacobian(rx, ry, z,
+ curve);
+ else
+ /* Adding opposite points yields infinity. */
+ vli_clear(z, ndigits);
+ continue;
+ }
xycz_add(tx, ty, rx, ry, curve);
vli_mod_mult_fast(z, z, tz, curve);
}
diff --git a/crypto/testmgr.h b/crypto/testmgr.h
index c4a15e714ecd..045a3e46fb09 100644
--- a/crypto/testmgr.h
+++ b/crypto/testmgr.h
@@ -1443,6 +1443,94 @@ static const struct sig_testvec x962_ecdsa_nist_p192_tv_template[] = {
};
static const struct sig_testvec x962_ecdsa_nist_p256_tv_template[] = {
+ /* Wycheproof secp256r1/SHA-256 tcId 60. */
+ {
+ .key =
+ "\x04\x29\x27\xb1\x05\x12\xba\xe3\xed\xdc\xfe\x46\x78\x28\x12\x8b"
+ "\xad\x29\x03\x26\x99\x19\xf7\x08\x60\x69\xc8\xc4\xdf\x6c\x73\x28"
+ "\x38\xc7\x78\x79\x64\xea\xac\x00\xe5\x92\x1f\xb1\x49\x8a\x60\xf4"
+ "\x60\x67\x66\xb3\xd9\x68\x50\x01\x55\x8d\x1a\x97\x4e\x73\x41\x51"
+ "\x3e",
+ .key_len = 65,
+ .m =
+ "\x70\x23\x9d\xd8\x77\xf7\xc9\x44\xc4\x22\xf4\x4d\xea\x4e\xd1\xa5"
+ "\x2f\x26\x27\x41\x6f\xaf\x2f\x07\x2f\xa5\x0c\x77\x2e\xd6\xf8\x07",
+ .m_size = 32,
+ .c =
+ "\x30\x44\x02\x20\x64\xa1\xaa\xb5\x00\x0d\x0e\x80\x4f\x3e\x2f\xc0"
+ "\x2b\xde\xe9\xbe\x8f\xf3\x12\x33\x4e\x2b\xa1\x6d\x11\x54\x7c\x97"
+ "\x71\x1c\x89\x8e\x02\x20\x6a\xf0\x15\x97\x1c\xc3\x0b\xe6\xd1\xa2"
+ "\x06\xd4\xe0\x13\xe0\x99\x77\x72\xa2\xf9\x1d\x73\x28\x6f\xfd\x68"
+ "\x3b\x9b\xb2\xcf\x4f\x1b",
+ .c_size = 70,
+ .public_key_vec = true,
+ },
+ /* Wycheproof secp256r1/SHA-256 tcId 210. */
+ {
+ .key =
+ "\x04\xc6\xa7\x71\x52\x70\x24\x22\x77\x92\x17\x0a\x6f\x8e\xee\x73"
+ "\x5b\xf3\x2b\x7f\x98\xaf\x66\x9e\xad\x29\x98\x02\xe3\x2d\x7c\x31"
+ "\x07\xbc\x3b\x4b\x5e\x65\xab\x88\x7b\xbd\x34\x35\x72\xb3\xe5\x61"
+ "\x92\x61\xfe\x3a\x07\x3e\x2f\xfd\x78\x41\x2f\x72\x68\x67\xdb\x58"
+ "\x9e",
+ .key_len = 65,
+ .m =
+ "\xbb\x5a\x52\xf4\x2f\x9c\x92\x61\xed\x43\x61\xf5\x94\x22\xa1\xe3"
+ "\x00\x36\xe7\xc3\x2b\x27\x0c\x88\x07\xa4\x19\xfe\xca\x60\x50\x23",
+ .m_size = 32,
+ .c =
+ "\x30\x45\x02\x20\x7c\xf2\x7b\x18\x8d\x03\x4f\x7e\x8a\x52\x38\x03"
+ "\x04\xb5\x1a\xc3\xc0\x89\x69\xe2\x77\xf2\x1b\x35\xa6\x0b\x48\xfc"
+ "\x47\x66\x99\x78\x02\x21\x00\xb6\xdb\x6d\xb6\x24\x92\x49\x25\x49"
+ "\x24\x92\x49\x24\x92\x49\x24\x62\x5b\xd7\xa0\x9b\xec\x4c\xa8\x1b"
+ "\xcd\xd9\xf8\xfd\x6b\x63\xcc",
+ .c_size = 71,
+ .public_key_vec = true,
+ },
+ /* Q = G, d = 1, k = 2. */
+ {
+ .key =
+ "\x04\x6b\x17\xd1\xf2\xe1\x2c\x42\x47\xf8\xbc\xe6\xe5\x63\xa4\x40"
+ "\xf2\x77\x03\x7d\x81\x2d\xeb\x33\xa0\xf4\xa1\x39\x45\xd8\x98\xc2"
+ "\x96\x4f\xe3\x42\xe2\xfe\x1a\x7f\x9b\x8e\xe7\xeb\x4a\x7c\x0f\x9e"
+ "\x16\x2b\xce\x33\x57\x6b\x31\x5e\xce\xcb\xb6\x40\x68\x37\xbf\x51"
+ "\xf5",
+ .key_len = 65,
+ .m =
+ "\x35\x9d\x17\x29\xb9\x1a\x52\xe9\x8b\xb5\x95\xc3\x86\x28\x3c\x10"
+ "\x30\x44\x95\x1a\xa1\x08\x20\xf0\xa0\x22\xc4\x18\xc2\x71\xa0\xcc",
+ .m_size = 32,
+ .c =
+ "\x30\x44\x02\x20\x7c\xf2\x7b\x18\x8d\x03\x4f\x7e\x8a\x52\x38\x03"
+ "\x04\xb5\x1a\xc3\xc0\x89\x69\xe2\x77\xf2\x1b\x35\xa6\x0b\x48\xfc"
+ "\x47\x66\x99\x78\x02\x20\x59\x47\xc9\x21\x23\x0e\xd1\x34\x0b\x03"
+ "\xe6\xe3\x45\x6e\xab\x69\xf8\x66\xff\x7e\x8c\x7d\x1e\x13\x23\x17"
+ "\x06\x8a\x84\xec\x1d\x22",
+ .c_size = 70,
+ .public_key_vec = true,
+ },
+ /* Q = -G, d = n - 1, k = 2. */
+ {
+ .key =
+ "\x04\x6b\x17\xd1\xf2\xe1\x2c\x42\x47\xf8\xbc\xe6\xe5\x63\xa4\x40"
+ "\xf2\x77\x03\x7d\x81\x2d\xeb\x33\xa0\xf4\xa1\x39\x45\xd8\x98\xc2"
+ "\x96\xb0\x1c\xbd\x1c\x01\xe5\x80\x65\x71\x18\x14\xb5\x83\xf0\x61"
+ "\xe9\xd4\x31\xcc\xa9\x94\xce\xa1\x31\x34\x49\xbf\x97\xc8\x40\xae"
+ "\x0a",
+ .key_len = 65,
+ .m =
+ "\x35\x9d\x17\x29\xb9\x1a\x52\xe9\x8b\xb5\x95\xc3\x86\x28\x3c\x10"
+ "\x30\x44\x95\x1a\xa1\x08\x20\xf0\xa0\x22\xc4\x18\xc2\x71\xa0\xcc",
+ .m_size = 32,
+ .c =
+ "\x30\x45\x02\x20\x7c\xf2\x7b\x18\x8d\x03\x4f\x7e\x8a\x52\x38\x03"
+ "\x04\xb5\x1a\xc3\xc0\x89\x69\xe2\x77\xf2\x1b\x35\xa6\x0b\x48\xfc"
+ "\x47\x66\x99\x78\x02\x21\x00\xdc\x55\x4e\x07\x96\x0b\x81\xb6\x80"
+ "\xb1\xae\xe0\x40\xb9\x90\xa5\xf4\xc4\x90\x49\xbb\xa2\xa1\x62\x70"
+ "\xc5\x88\x51\x39\xe8\xa8\xfb",
+ .c_size = 71,
+ .public_key_vec = true,
+ },
{
.key = /* secp256r1(sha1) */
"\x04\xb9\x7b\xbb\xd7\x17\x64\xd2\x7e\xfc\x81\x5d\x87\x06\x83\x41"
@@ -1827,7 +1915,8 @@ static const struct sig_testvec p1363_ecdsa_nist_p256_tv_template[] = {
};
/*
- * EC-RDSA test vectors are generated by gost-engine.
+ * EC-RDSA test vectors generated by gost-engine, followed by constructed
+ * exceptional-point regression vectors.
*/
static const struct sig_testvec ecrdsa_tv_template[] = {
{
@@ -1973,6 +2062,195 @@ static const struct sig_testvec ecrdsa_tv_template[] = {
.m_size = 64,
.public_key_vec = true,
},
+ /*
+ * Constructed EC-RDSA exceptional-point vectors.
+ * With Q = dG, choose k = z1 + d*z2 (mod n), r = x(kG) mod n,
+ * e = -r/z2 (mod n), and s = r*d + k*e (mod n).
+ * The input digest is e, encoded little-endian.
+ */
+ /* cp256a: Q=G, z1 = 3, z2 = 1. */
+ {
+ .key =
+ "\x04\x40\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x14\x1e\x9f\x9e\x9c\xc9\xac\x22\xb1\xe3\x23\xdf\x2d\x4f"
+ "\x29\x35\x76\x2b\x3f\x45\x5a\x50\xdf\x27\xda\x9c\x98\xe0\x71\xe4"
+ "\x91\x8d",
+ .key_len = 66,
+ .params = /* OID_gostCPSignA */
+ "\x30\x13\x06\x07\x2a\x85\x03\x02\x02\x23\x01\x06\x08\x2a\x85\x03"
+ "\x07\x01\x01\x02\x02",
+ .param_len = 21,
+ .c =
+ "\x1a\xed\x44\xae\xd4\x4a\xed\x44\xae\xd4\x4a\xed\x44\xae\xd4\x49"
+ "\x32\x67\xe0\x26\x16\xfd\xb7\xaf\xa4\xd7\x3e\x61\xd4\xf9\x7b\x94"
+ "\xf7\x06\x3e\x70\x63\xe7\x06\x3e\x70\x63\xe7\x06\x3e\x70\x63\xe7"
+ "\x06\x3e\x70\x63\xe7\x06\x3e\x70\x63\xe7\x06\x3e\x70\x63\xe4\xb7",
+ .c_size = 64,
+ .m =
+ "\xdc\xd3\xfd\x46\xcb\x14\x9d\xe1\x8f\x92\x54\xb2\x0c\xa0\x22\x66"
+ "\x18\x9c\x8f\xc1\xf9\x18\x9c\x8f\xc1\xf9\x18\x9c\x8f\xc1\xf9\x08",
+ .m_size = 32,
+ .algo = OID_gost2012PKey256,
+ .public_key_vec = true,
+ },
+ /* cp256a: Q=-G, z1 = 7, z2 = 6. */
+ {
+ .key =
+ "\x04\x40\x01\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x83\xdf\x60\x61\x63\x36\x53\xdd\x4e\x1c\xdc\x20\xd2\xb0"
+ "\xd6\xca\x89\xd4\xc0\xba\xa5\xaf\x20\xd8\x25\x63\x67\x1f\x8e\x1b"
+ "\x6e\x72",
+ .key_len = 66,
+ .params = /* OID_gostCPSignA */
+ "\x30\x13\x06\x07\x2a\x85\x03\x02\x02\x23\x01\x06\x08\x2a\x85\x03"
+ "\x07\x01\x01\x02\x02",
+ .param_len = 21,
+ .c =
+ "\x2a\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa"
+ "\x92\x10\x2d\x68\x19\x8f\x22\xd5\x60\xeb\x59\xd6\xf3\xe5\x9e\xc2"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01",
+ .c_size = 64,
+ .m =
+ "\xc3\x9e\xe5\xf3\xd6\x59\xeb\x60\xd5\x22\x8f\x19\x68\x2d\x10\x92"
+ "\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\xaa\x2a",
+ .m_size = 32,
+ .algo = OID_gost2012PKey256,
+ .public_key_vec = true,
+ },
+ /* cp256a: Q=-2G, z1 = 5, z2 = 2. */
+ {
+ .key =
+ "\x04\x40\x95\xfd\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xff\xff\x14\x1e\x9f\x9e\x9c\xc9\xac\x22\xb1\xe3\x23\xdf\x2d\x4f"
+ "\x29\x35\x76\x2b\x3f\x45\x5a\x50\xdf\x27\xda\x9c\x98\xe0\x71\xe4"
+ "\x91\x8d",
+ .key_len = 66,
+ .params = /* OID_gostCPSignA */
+ "\x30\x13\x06\x07\x2a\x85\x03\x02\x02\x23\x01\x06\x08\x2a\x85\x03"
+ "\x07\x01\x01\x02\x02",
+ .param_len = 21,
+ .c =
+ "\x7f\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xb6\x30\x88\x38\x4c\xad\x68\x80\x22\xc2\x0d\x84\xdb\xb0\xdc\x47"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x01",
+ .c_size = 64,
+ .m =
+ "\x49\xdc\xb0\xdb\x84\x0d\xc2\x22\x80\x68\xad\x4c\x38\x88\x30\xb6"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\x7f",
+ .m_size = 32,
+ .algo = OID_gost2012PKey256,
+ .public_key_vec = true,
+ },
+ /* tc512a: Q=G, z1 = 3, z2 = 1. */
+ {
+ .key =
+ "\x04\x81\x80\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\xa4\xf2\x15\x52\xcb\x89\xa5\x89\xb8\xf5\x35\xc2\x5f"
+ "\xfe\x28\x80\xe9\x41\x3a\x0e\xa5\xe6\x75\x3d\xe9\x36\xd0\x4f\xbe"
+ "\x26\x16\xdf\x21\xa9\xef\xcb\xfd\x64\x80\x77\xc1\xab\xf1\xac\x93"
+ "\x1c\x5e\xce\xe6\x50\x54\xe2\x16\x88\x1b\xa6\xe3\x6a\x83\x7a\xe8"
+ "\xcf\x03\x75",
+ .key_len = 131,
+ .params = /* OID_gostTC26Sign512A */
+ "\x30\x0b\x06\x09\x2a\x85\x03\x07\x01\x02\x01\x02\x01",
+ .param_len = 13,
+ .c =
+ "\xd8\xc0\xd7\xe3\xfb\xa6\xca\xff\x6a\xd1\xb4\xb4\x82\x1d\x15\x6f"
+ "\xa7\xc7\xbd\x63\x95\xb8\x29\x0d\xd4\xfa\xb1\x1c\x36\xbd\x32\x8d"
+ "\x1a\xba\xf1\x2e\xbc\x7b\xf2\x02\x96\xf8\xef\x2a\x5e\x72\x64\x86"
+ "\x67\x62\xfb\x62\x8e\x83\x53\x63\xb7\xe6\x78\x3c\x42\xd7\x0d\x1d"
+ "\xb7\xbf\xb8\x09\x56\xc8\x67\x00\x31\xba\x19\x19\x29\xf6\x4e\x30"
+ "\x1d\x68\x16\x34\x23\x6d\x47\xa6\x0e\x57\x1a\x4b\xed\xc0\xef\x25"
+ "\x74\x52\xef\x78\xb5\xb9\x8d\xbb\x3d\x9f\x31\x29\xd9\x34\x94\x33"
+ "\xce\x2a\x3a\x35\xcb\x51\x9c\x91\xe2\xd6\x33\xd7\xb3\x73\xae\x16",
+ .c_size = 128,
+ .m =
+ "\x5f\x04\x9d\x6b\x69\x7d\xf7\xe7\xcb\x1b\x81\x2f\x76\xfe\x20\xcd"
+ "\x2c\xcc\xd0\x74\x63\xfa\x52\x32\x56\xfb\xd3\x3e\xba\xa5\x93\xb3"
+ "\xd9\x10\x3f\x12\xb4\xe5\xa8\xf1\x59\xb8\x92\xdc\xcb\xe9\x97\xe2"
+ "\xcf\xb1\x09\xd6\xe6\xe6\x45\xce\xff\x98\x37\xa9\xf6\x47\x40\x48",
+ .m_size = 64,
+ .algo = OID_gost2012PKey512,
+ .public_key_vec = true,
+ },
+ /* tc512a: Q=-G, z1 = 7, z2 = 6. */
+ {
+ .key =
+ "\x04\x81\x80\x03\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x23\x0b\xea\xad\x34\x76\x5a\x76\x47\x0a\xca\x3d\xa0"
+ "\x01\xd7\x7f\x16\xbe\xc5\xf1\x5a\x19\x8a\xc2\x16\xc9\x2f\xb0\x41"
+ "\xd9\xe9\x20\xde\x56\x10\x34\x02\x9b\x7f\x88\x3e\x54\x0e\x53\x6c"
+ "\xe3\xa1\x31\x19\xaf\xab\x1d\xe9\x77\xe4\x59\x1c\x95\x7c\x85\x17"
+ "\x30\xfc\x8a",
+ .key_len = 131,
+ .params = /* OID_gostTC26Sign512A */
+ "\x30\x0b\x06\x09\x2a\x85\x03\x07\x01\x02\x01\x02\x01",
+ .param_len = 13,
+ .c =
+ "\x7f\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\x93\xf3\x4a\x99\x7a\x46\xc4\x88\xb7\xf9\x15\xc6\xa7\x02\xb0\x30"
+ "\x4d\xa5\x9c\x55\xfd\x69\x5c\x2e\xe5\x66\xd8\xa0\x8f\x88\x59\x37"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x03",
+ .c_size = 128,
+ .m =
+ "\x3a\x59\x88\x8f\xa0\xd8\x66\xe5\x2e\x5c\x69\xfd\x55\x9c\xa5\x4d"
+ "\x30\xb0\x02\xa7\xc6\x15\xf9\xb7\x88\xc4\x46\x7a\x99\x4a\xf3\x93"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\x7f",
+ .m_size = 64,
+ .algo = OID_gost2012PKey512,
+ .public_key_vec = true,
+ },
+ /* tc512a: Q=-2G, z1 = 5, z2 = 2. */
+ {
+ .key =
+ "\x04\x81\x80\x7c\x13\xea\xd2\xd9\xaf\x82\xb9\x1f\xb2\xfd\xe1\x8d"
+ "\xf4\x5b\x37\xe4\xf2\x04\x6a\x2a\x1d\x15\x16\x95\x2a\x5d\x40\xcd"
+ "\xbb\x34\x44\x2f\x2b\x13\x0a\x47\xb0\xf6\xe5\xa5\x58\x3a\xf4\x54"
+ "\x09\xb0\x1d\xf5\x5c\xf1\xbf\x9d\x86\xa5\x97\xab\x96\x29\x62\xfc"
+ "\xdc\x89\x3b\x76\x3d\x50\x6e\x8a\xcf\x02\x4c\x74\x0e\x6e\xe0\x1f"
+ "\x28\xab\x27\x9b\x20\x02\xc8\xc4\x12\xcb\x8a\xe3\xa4\x27\xce\x39"
+ "\x62\xdf\x35\x6d\xc1\x65\x7f\x7b\x48\x90\x11\x8f\x19\x7c\x1e\x67"
+ "\x91\x97\xeb\x90\x85\x25\xfc\x86\xb3\x88\x6e\x5c\x57\x1f\x1d\x1d"
+ "\x3b\xec\x37",
+ .key_len = 131,
+ .params = /* OID_gostTC26Sign512A */
+ "\x30\x0b\x06\x09\x2a\x85\x03\x07\x01\x02\x01\x02\x01",
+ .param_len = 13,
+ .c =
+ "\x7f\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\x93\xf3\x4a\x99\x7a\x46\xc4\x88\xb7\xf9\x15\xc6\xa7\x02\xb0\x30"
+ "\x4d\xa5\x9c\x55\xfd\x69\x5c\x2e\xe5\x66\xd8\xa0\x8f\x88\x59\x33"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00"
+ "\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x03",
+ .c_size = 128,
+ .m =
+ "\x39\x59\x88\x8f\xa0\xd8\x66\xe5\x2e\x5c\x69\xfd\x55\x9c\xa5\x4d"
+ "\x30\xb0\x02\xa7\xc6\x15\xf9\xb7\x88\xc4\x46\x7a\x99\x4a\xf3\x93"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff"
+ "\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\xff\x7f",
+ .m_size = 64,
+ .algo = OID_gost2012PKey512,
+ .public_key_vec = true,
+ },
};
/*
base-commit: 165768bb70265b5c38cf0b73fafd75be235f8b14
--
2.47.3