int ECDSA_verify(const char *msg, const struct affine_point *Q,
const gcry_mpi_t sig, const struct curve_params *cp)
{
gcry_mpi_t e, r, s;
struct affine_point X1, X2;
int res = 0;
r = gcry_mpi_new(0);
s = gcry_mpi_new(0);
gcry_mpi_div(s, r, sig, cp->dp.order, 0);
if (gcry_mpi_cmp_ui(s, 0) <= 0 || gcry_mpi_cmp(s, cp->dp.order) >= 0 ||
gcry_mpi_cmp_ui(r, 0) <= 0 || gcry_mpi_cmp(r, cp->dp.order) >= 0)
goto end;
gcry_mpi_scan(&e, GCRYMPI_FMT_USG, msg, 64, NULL);
gcry_mpi_mod(e, e, cp->dp.order);
gcry_mpi_invm(s, s, cp->dp.order);
gcry_mpi_mulm(e, e, s, cp->dp.order);
X1 = pointmul(&cp->dp.base, e, &cp->dp);
gcry_mpi_mulm(e, r, s, cp->dp.order);
X2 = pointmul(Q, e, &cp->dp);
point_add(&X1, &X2, &cp->dp);
gcry_mpi_release(e);
if (! point_is_zero(&X1)) {
gcry_mpi_mod(s, X1.x, cp->dp.order);
res = ! gcry_mpi_cmp(s, r);
}
point_release(&X1);
point_release(&X2);
end:
gcry_mpi_release(r);
gcry_mpi_release(s);
return res;
}
/* Algorithms 4.29 and 4.30 in the "Guide to Elliptic Curve Cryptography" */
gcry_mpi_t ECDSA_sign(const char *msg, const gcry_mpi_t d,
const struct curve_params *cp)
{
struct affine_point p1;
gcry_mpi_t e, k, r, s;
#if ECDSA_DETERMINISTIC
struct aes256cprng *cprng;
cprng = ecdsa_cprng_init(msg, d, cp);
#endif
r = gcry_mpi_snew(0);
s = gcry_mpi_snew(0);
Step1:
#if ECDSA_DETERMINISTIC
k = ecdsa_cprng_get_exponent(cprng, cp);
#else
k = get_random_exponent(cp);
#endif
p1 = pointmul(&cp->dp.base, k, &cp->dp);
gcry_mpi_mod(r, p1.x, cp->dp.order);
point_release(&p1);
if (! gcry_mpi_cmp_ui(r, 0)) {
gcry_mpi_release(k);
goto Step1;
}
gcry_mpi_scan(&e, GCRYMPI_FMT_USG, msg, 64, NULL);
gcry_mpi_set_flag(e, GCRYMPI_FLAG_SECURE);
gcry_mpi_mod(e, e, cp->dp.order);
gcry_mpi_mulm(s, d, r, cp->dp.order);
gcry_mpi_addm(s, s, e, cp->dp.order);
gcry_mpi_invm(e, k, cp->dp.order);
gcry_mpi_mulm(s, s, e, cp->dp.order);
gcry_mpi_release(e);
gcry_mpi_release(k);
if (! gcry_mpi_cmp_ui(s, 0))
goto Step1;
gcry_mpi_mul(s, s, cp->dp.order);
gcry_mpi_add(s, s, r);
gcry_mpi_release(r);
#if ECDSA_DETERMINISTIC
ecdsa_cprng_done(cprng);
#endif
return s;
}
static bigint_t
wrap_gcry_mpi_mod (const bigint_t a, const bigint_t b)
{
bigint_t r = _gnutls_mpi_alloc_like (b);
if (r == NULL)
return NULL;
gcry_mpi_mod (r, a, b);
return r;
}
gcry_mpi_t buf_to_exponent(const char *buf, int buflen,
const struct curve_params *cp)
{
gcry_mpi_t a, b;
gcry_mpi_scan(&a, GCRYMPI_FMT_USG, buf, buflen, NULL);
gcry_mpi_set_flag(a, GCRYMPI_FLAG_SECURE);
b = gcry_mpi_new(0);
gcry_mpi_sub_ui(b, cp->dp.order, 1);
gcry_mpi_mod(a, a, b);
gcry_mpi_add_ui(a, a, 1);
gcry_mpi_release(b);
return a;
}
/** @brief generates a random integer between 0 and max
* @returns 1 in case of success, 0 otherwise
*/
int ssh_gcry_rand_range(bignum dest, bignum max)
{
size_t bits;
bignum rnd;
int rc;
bits = bignum_num_bits(max) + 64;
rnd = bignum_new();
if (rnd == NULL) {
return 0;
}
rc = bignum_rand(rnd, bits);
if (rc != 1) {
return rc;
}
gcry_mpi_mod(dest, rnd, max);
bignum_safe_free(rnd);
return 1;
}
/* Compute and print missing RSA parameters. */
static void
compute_missing (gcry_mpi_t rsa_p, gcry_mpi_t rsa_q, gcry_mpi_t rsa_e)
{
gcry_mpi_t rsa_n, rsa_d, rsa_pm1, rsa_qm1, rsa_u;
gcry_mpi_t phi, tmp_g, tmp_f;
rsa_n = gcry_mpi_new (0);
rsa_d = gcry_mpi_new (0);
rsa_pm1 = gcry_mpi_new (0);
rsa_qm1 = gcry_mpi_new (0);
rsa_u = gcry_mpi_new (0);
phi = gcry_mpi_new (0);
tmp_f = gcry_mpi_new (0);
tmp_g = gcry_mpi_new (0);
/* Check that p < q; if not swap p and q. */
if (openpgp_mode && gcry_mpi_cmp (rsa_p, rsa_q) > 0)
{
fprintf (stderr, PGM ": swapping p and q\n");
gcry_mpi_swap (rsa_p, rsa_q);
}
gcry_mpi_mul (rsa_n, rsa_p, rsa_q);
/* Compute the Euler totient: phi = (p-1)(q-1) */
gcry_mpi_sub_ui (rsa_pm1, rsa_p, 1);
gcry_mpi_sub_ui (rsa_qm1, rsa_q, 1);
gcry_mpi_mul (phi, rsa_pm1, rsa_qm1);
if (!gcry_mpi_gcd (tmp_g, rsa_e, phi))
die ("parameter 'e' does match 'p' and 'q'\n");
/* Compute: f = lcm(p-1,q-1) = phi / gcd(p-1,q-1) */
gcry_mpi_gcd (tmp_g, rsa_pm1, rsa_qm1);
gcry_mpi_div (tmp_f, NULL, phi, tmp_g, -1);
/* Compute the secret key: d = e^{-1} mod lcm(p-1,q-1) */
gcry_mpi_invm (rsa_d, rsa_e, tmp_f);
/* Compute the CRT helpers: d mod (p-1), d mod (q-1) */
gcry_mpi_mod (rsa_pm1, rsa_d, rsa_pm1);
gcry_mpi_mod (rsa_qm1, rsa_d, rsa_qm1);
/* Compute the CRT value: OpenPGP: u = p^{-1} mod q
Standard: iqmp = q^{-1} mod p */
if (openpgp_mode)
gcry_mpi_invm (rsa_u, rsa_p, rsa_q);
else
gcry_mpi_invm (rsa_u, rsa_q, rsa_p);
gcry_mpi_release (phi);
gcry_mpi_release (tmp_f);
gcry_mpi_release (tmp_g);
/* Print everything. */
print_mpi_line ("n", rsa_n);
print_mpi_line ("e", rsa_e);
if (openpgp_mode)
print_mpi_line ("d", rsa_d);
print_mpi_line ("p", rsa_p);
print_mpi_line ("q", rsa_q);
if (openpgp_mode)
print_mpi_line ("u", rsa_u);
else
{
print_mpi_line ("dmp1", rsa_pm1);
print_mpi_line ("dmq1", rsa_qm1);
print_mpi_line ("iqmp", rsa_u);
}
gcry_mpi_release (rsa_n);
gcry_mpi_release (rsa_d);
gcry_mpi_release (rsa_pm1);
gcry_mpi_release (rsa_qm1);
gcry_mpi_release (rsa_u);
}
/* Check the math used with Twisted Edwards curves. */
static void
twistededwards_math (void)
{
gpg_error_t err;
gcry_ctx_t ctx;
gcry_mpi_point_t G, Q;
gcry_mpi_t k;
gcry_mpi_t w, a, x, y, z, p, n, b, I;
wherestr = "twistededwards_math";
show ("checking basic Twisted Edwards math\n");
err = gcry_mpi_ec_new (&ctx, NULL, "Ed25519");
if (err)
die ("gcry_mpi_ec_new failed: %s\n", gpg_strerror (err));
k = hex2mpi
("2D3501E723239632802454EE5DDC406EFB0BDF18486A5BDE9C0390A9C2984004"
"F47252B628C953625B8DEB5DBCB8DA97AA43A1892D11FA83596F42E0D89CB1B6");
G = gcry_mpi_ec_get_point ("g", ctx, 1);
if (!G)
die ("gcry_mpi_ec_get_point(G) failed\n");
Q = gcry_mpi_point_new (0);
w = gcry_mpi_new (0);
a = gcry_mpi_new (0);
x = gcry_mpi_new (0);
y = gcry_mpi_new (0);
z = gcry_mpi_new (0);
I = gcry_mpi_new (0);
p = gcry_mpi_ec_get_mpi ("p", ctx, 1);
n = gcry_mpi_ec_get_mpi ("n", ctx, 1);
b = gcry_mpi_ec_get_mpi ("b", ctx, 1);
/* Check: 2^{p-1} mod p == 1 */
gcry_mpi_sub_ui (a, p, 1);
gcry_mpi_powm (w, GCRYMPI_CONST_TWO, a, p);
if (gcry_mpi_cmp_ui (w, 1))
fail ("failed assertion: 2^{p-1} mod p == 1\n");
/* Check: p % 4 == 1 */
gcry_mpi_mod (w, p, GCRYMPI_CONST_FOUR);
if (gcry_mpi_cmp_ui (w, 1))
fail ("failed assertion: p % 4 == 1\n");
/* Check: 2^{n-1} mod n == 1 */
gcry_mpi_sub_ui (a, n, 1);
gcry_mpi_powm (w, GCRYMPI_CONST_TWO, a, n);
if (gcry_mpi_cmp_ui (w, 1))
fail ("failed assertion: 2^{n-1} mod n == 1\n");
/* Check: b^{(p-1)/2} mod p == p-1 */
gcry_mpi_sub_ui (a, p, 1);
gcry_mpi_div (x, NULL, a, GCRYMPI_CONST_TWO, -1);
gcry_mpi_powm (w, b, x, p);
gcry_mpi_abs (w);
if (gcry_mpi_cmp (w, a))
fail ("failed assertion: b^{(p-1)/2} mod p == p-1\n");
/* I := 2^{(p-1)/4} mod p */
gcry_mpi_sub_ui (a, p, 1);
gcry_mpi_div (x, NULL, a, GCRYMPI_CONST_FOUR, -1);
gcry_mpi_powm (I, GCRYMPI_CONST_TWO, x, p);
/* Check: I^2 mod p == p-1 */
gcry_mpi_powm (w, I, GCRYMPI_CONST_TWO, p);
if (gcry_mpi_cmp (w, a))
fail ("failed assertion: I^2 mod p == p-1\n");
/* Check: G is on the curve */
if (!gcry_mpi_ec_curve_point (G, ctx))
fail ("failed assertion: G is on the curve\n");
/* Check: nG == (0,1) */
gcry_mpi_ec_mul (Q, n, G, ctx);
if (gcry_mpi_ec_get_affine (x, y, Q, ctx))
fail ("failed to get affine coordinates\n");
if (gcry_mpi_cmp_ui (x, 0) || gcry_mpi_cmp_ui (y, 1))
fail ("failed assertion: nG == (0,1)\n");
/* Now two arbitrary point operations taken from the ed25519.py
sample data. */
gcry_mpi_release (a);
a = hex2mpi
("4f71d012df3c371af3ea4dc38385ca5bb7272f90cb1b008b3ed601c76de1d496"
"e30cbf625f0a756a678d8f256d5325595cccc83466f36db18f0178eb9925edd3");
gcry_mpi_ec_mul (Q, a, G, ctx);
if (gcry_mpi_ec_get_affine (x, y, Q, ctx))
fail ("failed to get affine coordinates\n");
if (cmp_mpihex (x, ("157f7361c577aad36f67ed33e38dc7be"
"00014fecc2165ca5cee9eee19fe4d2c1"))
|| cmp_mpihex (y, ("5a69dbeb232276b38f3f5016547bb2a2"
"4025645f0b820e72b8cad4f0a909a092")))
{
fail ("sample point multiply failed:\n");
print_mpi ("r", a);
print_mpi ("Rx", x);
print_mpi ("Ry", y);
}
gcry_mpi_release (a);
a = hex2mpi
("2d3501e723239632802454ee5ddc406efb0bdf18486a5bde9c0390a9c2984004"
"f47252b628c953625b8deb5dbcb8da97aa43a1892d11fa83596f42e0d89cb1b6");
gcry_mpi_ec_mul (Q, a, G, ctx);
if (gcry_mpi_ec_get_affine (x, y, Q, ctx))
fail ("failed to get affine coordinates\n");
if (cmp_mpihex (x, ("6218e309d40065fcc338b3127f468371"
"82324bd01ce6f3cf81ab44e62959c82a"))
|| cmp_mpihex (y, ("5501492265e073d874d9e5b81e7f8784"
"8a826e80cce2869072ac60c3004356e5")))
{
fail ("sample point multiply failed:\n");
print_mpi ("r", a);
print_mpi ("Rx", x);
print_mpi ("Ry", y);
}
gcry_mpi_release (I);
gcry_mpi_release (b);
gcry_mpi_release (n);
gcry_mpi_release (p);
gcry_mpi_release (w);
gcry_mpi_release (a);
gcry_mpi_release (x);
gcry_mpi_release (y);
gcry_mpi_release (z);
gcry_mpi_point_release (Q);
gcry_mpi_point_release (G);
gcry_mpi_release (k);
gcry_ctx_release (ctx);
}
/* Decompose $x \in Z_n$ into $(xp,xq) \in Z_p \times Z_q$ using Chinese Remainder Theorem */
static void CRT_decompose(gcry_mpi_t *xp, gcry_mpi_t *xq, const gcry_mpi_t x, const gcry_mpi_t p, const gcry_mpi_t q) {
*xp = gcry_mpi_new(0);
*xq = gcry_mpi_new(0);
gcry_mpi_mod(*xp, x, p);
gcry_mpi_mod(*xq, x, q);
}
guchar*
gkm_data_der_write_private_key_rsa (gcry_sexp_t s_key, gsize *n_key)
{
GNode *asn = NULL;
gcry_mpi_t n, e, d, p, q, u, e1, e2, tmp;
guchar *result = NULL;
n = e = d = p = q = u = e1 = e2 = tmp = NULL;
asn = egg_asn1x_create (pk_asn1_tab, "RSAPrivateKey");
g_return_val_if_fail (asn, NULL);
if (!gkm_sexp_extract_mpi (s_key, &n, "rsa", "n", NULL) ||
!gkm_sexp_extract_mpi (s_key, &e, "rsa", "e", NULL) ||
!gkm_sexp_extract_mpi (s_key, &d, "rsa", "d", NULL) ||
!gkm_sexp_extract_mpi (s_key, &p, "rsa", "p", NULL) ||
!gkm_sexp_extract_mpi (s_key, &q, "rsa", "q", NULL) ||
!gkm_sexp_extract_mpi (s_key, &u, "rsa", "u", NULL))
goto done;
if (!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "modulus", NULL), n) ||
!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "publicExponent", NULL), e) ||
!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "privateExponent", NULL), d) ||
!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "prime1", NULL), p) ||
!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "prime2", NULL), q) ||
!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "coefficient", NULL), u))
goto done;
/* Calculate e1 and e2 */
tmp = gcry_mpi_snew (1024);
gcry_mpi_sub_ui (tmp, p, 1);
e1 = gcry_mpi_snew (1024);
gcry_mpi_mod (e1, d, tmp);
gcry_mpi_sub_ui (tmp, q, 1);
e2 = gcry_mpi_snew (1024);
gcry_mpi_mod (e2, d, tmp);
/* Write out calculated */
if (!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "exponent1", NULL), e1) ||
!gkm_data_asn1_write_mpi (egg_asn1x_node (asn, "exponent2", NULL), e2))
goto done;
/* Write out the version */
if (!egg_asn1x_set_integer_as_ulong (egg_asn1x_node (asn, "version", NULL), 0))
goto done;
result = egg_asn1x_encode (asn, egg_secure_realloc, n_key);
if (result == NULL)
g_warning ("couldn't encode private rsa key: %s", egg_asn1x_message (asn));
done:
egg_asn1x_destroy (asn);
gcry_mpi_release (n);
gcry_mpi_release (e);
gcry_mpi_release (d);
gcry_mpi_release (p);
gcry_mpi_release (q);
gcry_mpi_release (u);
gcry_mpi_release (tmp);
gcry_mpi_release (e1);
gcry_mpi_release (e2);
return result;
}
/* Parse a private key S-expression and retutn a malloced array with
the RSA paramaters in pkcs#12 order. The caller needs to
deep-release this array. */
static gcry_mpi_t *
sexp_to_kparms (gcry_sexp_t sexp)
{
gcry_sexp_t list, l2;
const char *name;
const char *s;
size_t n;
int idx;
const char *elems;
gcry_mpi_t *array;
list = gcry_sexp_find_token (sexp, "private-key", 0 );
if(!list)
return NULL;
l2 = gcry_sexp_cadr (list);
gcry_sexp_release (list);
list = l2;
name = gcry_sexp_nth_data (list, 0, &n);
if(!name || n != 3 || memcmp (name, "rsa", 3))
{
gcry_sexp_release (list);
return NULL;
}
/* Parameter names used with RSA in the pkcs#12 order. */
elems = "nedqp--u";
array = xtrycalloc (strlen(elems) + 1, sizeof *array);
if (!array)
{
gcry_sexp_release (list);
return NULL;
}
for (idx=0, s=elems; *s; s++, idx++ )
{
if (*s == '-')
continue; /* Computed below */
l2 = gcry_sexp_find_token (list, s, 1);
if (l2)
{
array[idx] = gcry_sexp_nth_mpi (l2, 1, GCRYMPI_FMT_USG);
gcry_sexp_release (l2);
}
if (!array[idx]) /* Required parameter not found or invalid. */
{
for (idx=0; array[idx]; idx++)
gcry_mpi_release (array[idx]);
xfree (array);
gcry_sexp_release (list);
return NULL;
}
}
gcry_sexp_release (list);
array[5] = gcry_mpi_snew (0); /* compute d mod (q-1) */
gcry_mpi_sub_ui (array[5], array[3], 1);
gcry_mpi_mod (array[5], array[2], array[5]);
array[6] = gcry_mpi_snew (0); /* compute d mod (p-1) */
gcry_mpi_sub_ui (array[6], array[4], 1);
gcry_mpi_mod (array[6], array[3], array[6]);
return array;
}
