/* t-mpi-point.c - Tests for mpi point functions
* Copyright (C) 2013 g10 Code GmbH
*
* This file is part of Libgcrypt.
*
* Libgcrypt is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as
* published by the Free Software Foundation; either version 2.1 of
* the License, or (at your option) any later version.
*
* Libgcrypt is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, see <http://www.gnu.org/licenses/>.
*/
#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <stdarg.h>
#include "../src/gcrypt-int.h"
#define PGM "t-mpi-point"
static const char *wherestr;
static int verbose;
static int debug;
static int error_count;
#define my_isascii(c) (!((c) & 0x80))
#define digitp(p) (*(p) >= '0' && *(p) <= '9')
#define hexdigitp(a) (digitp (a) \
|| (*(a) >= 'A' && *(a) <= 'F') \
|| (*(a) >= 'a' && *(a) <= 'f'))
#define xtoi_1(p) (*(p) <= '9'? (*(p)- '0'): \
*(p) <= 'F'? (*(p)-'A'+10):(*(p)-'a'+10))
#define xtoi_2(p) ((xtoi_1(p) * 16) + xtoi_1((p)+1))
#define xmalloc(a) gcry_xmalloc ((a))
#define xcalloc(a,b) gcry_xcalloc ((a),(b))
#define xfree(a) gcry_free ((a))
#define pass() do { ; } while (0)
static struct
{
const char *desc; /* Description of the curve. */
const char *p; /* Order of the prime field. */
const char *a, *b; /* The coefficients. */
const char *n; /* The order of the base point. */
const char *g_x, *g_y; /* Base point. */
} test_curve[] =
{
{
"NIST P-256",
"0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
"0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
"0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
"0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
"0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
"0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"
},
{
"NIST P-384",
"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
"ffffffff0000000000000000ffffffff",
"0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe"
"ffffffff0000000000000000fffffffc",
"0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875a"
"c656398d8a2ed19d2a85c8edd3ec2aef",
"0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf"
"581a0db248b0a77aecec196accc52973",
"0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a38"
"5502f25dbf55296c3a545e3872760ab7",
"0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c0"
"0a60b1ce1d7e819d7a431d7c90ea0e5f"
},
{
"NIST P-521",
"0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
"0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc",
"0x051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef10"
"9e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00",
"0x1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"
"ffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409",
"0xc6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3d"
"baa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66",
"0x11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e6"
"62c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650"
},
{
"Ed25519",
"0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED",
"-0x01",
"-0x2DFC9311D490018C7338BF8688861767FF8FF5B2BEBE27548A14B235ECA6874A",
"0x1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED",
"0x216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A",
"0x6666666666666666666666666666666666666666666666666666666666666658"
},
{ NULL, NULL, NULL, NULL, NULL }
};
/* A sample public key for NIST P-256. */
static const char sample_p256_q[] =
"04"
"42B927242237639A36CE9221B340DB1A9AB76DF2FE3E171277F6A4023DED146E"
"E86525E38CCECFF3FB8D152CC6334F70D23A525175C1BCBDDE6E023B2228770E";
static const char sample_p256_q_x[] =
"42B927242237639A36CE9221B340DB1A9AB76DF2FE3E171277F6A4023DED146E";
static const char sample_p256_q_y[] =
"00E86525E38CCECFF3FB8D152CC6334F70D23A525175C1BCBDDE6E023B2228770E";
/* A sample public key for Ed25519. */
static const char sample_ed25519_q[] =
"04"
"55d0e09a2b9d34292297e08d60d0f620c513d47253187c24b12786bd777645ce"
"1a5107f7681a02af2523a6daf372e10e3a0764c9d3fe4bd5b70ab18201985ad7";
static const char sample_ed25519_q_x[] =
"55d0e09a2b9d34292297e08d60d0f620c513d47253187c24b12786bd777645ce";
static const char sample_ed25519_q_y[] =
"1a5107f7681a02af2523a6daf372e10e3a0764c9d3fe4bd5b70ab18201985ad7";
static const char sample_ed25519_q_eddsa[] =
"d75a980182b10ab7d54bfed3c964073a0ee172f3daa62325af021a68f707511a";
static const char sample_ed25519_d[] =
"9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60";
static void
show (const char *format, ...)
{
va_list arg_ptr;
if (!verbose)
return;
fprintf (stderr, "%s: ", PGM);
va_start (arg_ptr, format);
vfprintf (stderr, format, arg_ptr);
va_end (arg_ptr);
}
static void
fail (const char *format, ...)
{
va_list arg_ptr;
fflush (stdout);
fprintf (stderr, "%s: ", PGM);
if (wherestr)
fprintf (stderr, "%s: ", wherestr);
va_start (arg_ptr, format);
vfprintf (stderr, format, arg_ptr);
va_end (arg_ptr);
error_count++;
}
static void
die (const char *format, ...)
{
va_list arg_ptr;
fflush (stdout);
fprintf (stderr, "%s: ", PGM);
if (wherestr)
fprintf (stderr, "%s: ", wherestr);
va_start (arg_ptr, format);
vfprintf (stderr, format, arg_ptr);
va_end (arg_ptr);
exit (1);
}
static void
print_mpi_2 (const char *text, const char *text2, gcry_mpi_t a)
{
gcry_error_t err;
char *buf;
void *bufaddr = &buf;
err = gcry_mpi_aprint (GCRYMPI_FMT_HEX, bufaddr, NULL, a);
if (err)
fprintf (stderr, "%s%s: [error printing number: %s]\n",
text, text2? text2:"", gpg_strerror (err));
else
{
fprintf (stderr, "%s%s: %s\n", text, text2? text2:"", buf);
gcry_free (buf);
}
}
static void
print_mpi (const char *text, gcry_mpi_t a)
{
print_mpi_2 (text, NULL, a);
}
static void
print_point (const char *text, gcry_mpi_point_t a)
{
gcry_mpi_t x, y, z;
x = gcry_mpi_new (0);
y = gcry_mpi_new (0);
z = gcry_mpi_new (0);
gcry_mpi_point_get (x, y, z, a);
print_mpi_2 (text, ".x", x);
print_mpi_2 (text, ".y", y);
print_mpi_2 (text, ".z", z);
gcry_mpi_release (x);
gcry_mpi_release (y);
gcry_mpi_release (z);
}
static void
print_sexp (const char *prefix, gcry_sexp_t a)
{
char *buf;
size_t size;
if (prefix)
fputs (prefix, stderr);
size = gcry_sexp_sprint (a, GCRYSEXP_FMT_ADVANCED, NULL, 0);
buf = gcry_xmalloc (size);
gcry_sexp_sprint (a, GCRYSEXP_FMT_ADVANCED, buf, size);
fprintf (stderr, "%.*s", (int)size, buf);
gcry_free (buf);
}
static gcry_mpi_t
hex2mpi (const char *string)
{
gpg_error_t err;
gcry_mpi_t val;
err = gcry_mpi_scan (&val, GCRYMPI_FMT_HEX, string, 0, NULL);
if (err)
die ("hex2mpi '%s' failed: %s\n", string, gpg_strerror (err));
return val;
}
/* Convert STRING consisting of hex characters into its binary
representation and return it as an allocated buffer. The valid
length of the buffer is returned at R_LENGTH. The string is
delimited by end of string. The function returns NULL on
error. */
static void *
hex2buffer (const char *string, size_t *r_length)
{
const char *s;
unsigned char *buffer;
size_t length;
buffer = xmalloc (strlen(string)/2+1);
length = 0;
for (s=string; *s; s +=2 )
{
if (!hexdigitp (s) || !hexdigitp (s+1))
return NULL; /* Invalid hex digits. */
((unsigned char*)buffer)[length++] = xtoi_2 (s);
}
*r_length = length;
return buffer;
}
static gcry_mpi_t
hex2mpiopa (const char *string)
{
char *buffer;
size_t buflen;
gcry_mpi_t val;
buffer = hex2buffer (string, &buflen);
if (!buffer)
die ("hex2mpiopa '%s' failed: parser error\n", string);
val = gcry_mpi_set_opaque (NULL, buffer, buflen*8);
if (!buffer)
die ("hex2mpiopa '%s' failed: set_opaque error%s\n", string);
return val;
}
/* Compare A to B, where B is given as a hex string. */
static int
cmp_mpihex (gcry_mpi_t a, const char *b)
{
gcry_mpi_t bval;
int res;
if (gcry_mpi_get_flag (a, GCRYMPI_FLAG_OPAQUE))
bval = hex2mpiopa (b);
else
bval = hex2mpi (b);
res = gcry_mpi_cmp (a, bval);
gcry_mpi_release (bval);
return res;
}
/* Wrapper to emulate the libgcrypt internal EC context allocation
function. */
static gpg_error_t
ec_p_new (gcry_ctx_t *r_ctx, gcry_mpi_t p, gcry_mpi_t a)
{
gpg_error_t err;
gcry_sexp_t sexp;
if (p && a)
err = gcry_sexp_build (&sexp, NULL, "(ecdsa (p %m)(a %m))", p, a);
else if (p)
err = gcry_sexp_build (&sexp, NULL, "(ecdsa (p %m))", p);
else if (a)
err = gcry_sexp_build (&sexp, NULL, "(ecdsa (a %m))", a);
else
err = gcry_sexp_build (&sexp, NULL, "(ecdsa)");
if (err)
return err;
err = gcry_mpi_ec_new (r_ctx, sexp, NULL);
gcry_sexp_release (sexp);
return err;
}
static void
set_get_point (void)
{
gcry_mpi_point_t point;
gcry_mpi_t x, y, z;
wherestr = "set_get_point";
show ("checking point setting functions\n");
point = gcry_mpi_point_new (0);
x = gcry_mpi_set_ui (NULL, 17);
y = gcry_mpi_set_ui (NULL, 42);
z = gcry_mpi_set_ui (NULL, 11371);
gcry_mpi_point_get (x, y, z, point);
if (gcry_mpi_cmp_ui (x, 0)
|| gcry_mpi_cmp_ui (y, 0) || gcry_mpi_cmp_ui (z, 0))
fail ("new point not initialized to (0,0,0)\n");
gcry_mpi_point_snatch_get (x, y, z, point);
point = NULL;
if (gcry_mpi_cmp_ui (x, 0)
|| gcry_mpi_cmp_ui (y, 0) || gcry_mpi_cmp_ui (z, 0))
fail ("snatch_get failed\n");
gcry_mpi_release (x);
gcry_mpi_release (y);
gcry_mpi_release (z);
point = gcry_mpi_point_new (0);
x = gcry_mpi_set_ui (NULL, 17);
y = gcry_mpi_set_ui (NULL, 42);
z = gcry_mpi_set_ui (NULL, 11371);
gcry_mpi_point_set (point, x, y, z);
gcry_mpi_set_ui (x, 23);
gcry_mpi_set_ui (y, 24);
gcry_mpi_set_ui (z, 25);
gcry_mpi_point_get (x, y, z, point);
if (gcry_mpi_cmp_ui (x, 17)
|| gcry_mpi_cmp_ui (y, 42) || gcry_mpi_cmp_ui (z, 11371))
fail ("point_set/point_get failed\n");
gcry_mpi_point_snatch_set (point, x, y, z);
x = gcry_mpi_new (0);
y = gcry_mpi_new (0);
z = gcry_mpi_new (0);
gcry_mpi_point_get (x, y, z, point);
if (gcry_mpi_cmp_ui (x, 17)
|| gcry_mpi_cmp_ui (y, 42) || gcry_mpi_cmp_ui (z, 11371))
fail ("point_snatch_set/point_get failed\n");
gcry_mpi_point_release (point);
gcry_mpi_release (x);
gcry_mpi_release (y);
gcry_mpi_release (z);
}
static void
context_alloc (void)
{
gpg_error_t err;
gcry_ctx_t ctx;
gcry_mpi_t p, a;
wherestr = "context_alloc";
show ("checking context functions\n");
p = gcry_mpi_set_ui (NULL, 1);
a = gcry_mpi_set_ui (NULL, 1);
err = ec_p_new (&ctx, p, a);
if (err)
die ("ec_p_new returned an error: %s\n", gpg_strerror (err));
gcry_mpi_release (p);
gcry_mpi_release (a);
gcry_ctx_release (ctx);
p = gcry_mpi_set_ui (NULL, 0);
a = gcry_mpi_set_ui (NULL, 0);
err = ec_p_new (&ctx, p, a);
if (!err || gpg_err_code (err) != GPG_ERR_EINVAL)
fail ("ec_p_new: bad parameter detection failed (1)\n");
gcry_mpi_set_ui (p, 1);
err = ec_p_new (&ctx, p, a);
if (!err || gpg_err_code (err) != GPG_ERR_EINVAL)
fail ("ec_p_new: bad parameter detection failed (2)\n");
gcry_mpi_release (p);
p = NULL;
err = ec_p_new (&ctx, p, a);
if (!err || gpg_err_code (err) != GPG_ERR_EINVAL)
fail ("ec_p_new: bad parameter detection failed (3)\n");
gcry_mpi_release (a);
a = NULL;
err = ec_p_new (&ctx, p, a);
if (!err || gpg_err_code (err) != GPG_ERR_EINVAL)
fail ("ec_p_new: bad parameter detection failed (4)\n");
}
static int
get_and_cmp_mpi (const char *name, const char *mpistring, const char *desc,
gcry_ctx_t ctx)
{
gcry_mpi_t mpi;
mpi = gcry_mpi_ec_get_mpi (name, ctx, 1);
if (!mpi)
{
fail ("error getting parameter '%s' of curve '%s'\n", name, desc);
return 1;
}
if (debug)
print_mpi (name, mpi);
if (cmp_mpihex (mpi, mpistring))
{
fail ("parameter '%s' of curve '%s' does not match\n", name, desc);
gcry_mpi_release (mpi);
return 1;
}
gcry_mpi_release (mpi);
return 0;
}
static int
get_and_cmp_point (const char *name,
const char *mpi_x_string, const char *mpi_y_string,
const char *desc, gcry_ctx_t ctx)
{
gcry_mpi_point_t point;
gcry_mpi_t x, y, z;
int result = 0;
point = gcry_mpi_ec_get_point (name, ctx, 1);
if (!point)
{
fail ("error getting point parameter '%s' of curve '%s'\n", name, desc);
return 1;
}
if (debug)
print_point (name, point);
x = gcry_mpi_new (0);
y = gcry_mpi_new (0);
z = gcry_mpi_new (0);
gcry_mpi_point_snatch_get (x, y, z, point);
if (cmp_mpihex (x, mpi_x_string))
{
fail ("x coordinate of '%s' of curve '%s' does not match\n", name, desc);
result = 1;
}
if (cmp_mpihex (y, mpi_y_string))
{
fail ("y coordinate of '%s' of curve '%s' does not match\n", name, desc);
result = 1;
}
if (cmp_mpihex (z, "01"))
{
fail ("z coordinate of '%s' of curve '%s' is not 1\n", name, desc);
result = 1;
}
gcry_mpi_release (x);
gcry_mpi_release (y);
gcry_mpi_release (z);
return result;
}
static void
context_param (void)
{
gpg_error_t err;
int idx;
gcry_ctx_t ctx = NULL;
gcry_mpi_t q, d;
gcry_sexp_t keyparam;
wherestr = "context_param";
show ("checking standard curves\n");
for (idx=0; test_curve[idx].desc; idx++)
{
gcry_ctx_release (ctx);
err = gcry_mpi_ec_new (&ctx, NULL, test_curve[idx].desc);
if (err)
{
fail ("can't create context for curve '%s': %s\n",
test_curve[idx].desc, gpg_strerror (err));
continue;
}
if (get_and_cmp_mpi ("p", test_curve[idx].p, test_curve[idx].desc, ctx))
continue;
if (get_and_cmp_mpi ("a", test_curve[idx].a, test_curve[idx].desc, ctx))
continue;
if (get_and_cmp_mpi ("b", test_curve[idx].b, test_curve[idx].desc, ctx))
continue;
if (get_and_cmp_mpi ("g.x",test_curve[idx].g_x, test_curve[idx].desc,ctx))
continue;
if (get_and_cmp_mpi ("g.y",test_curve[idx].g_y, test_curve[idx].desc,ctx))
continue;
if (get_and_cmp_mpi ("n", test_curve[idx].n, test_curve[idx].desc, ctx))
continue;
if (get_and_cmp_point ("g", test_curve[idx].g_x, test_curve[idx].g_y,
test_curve[idx].desc, ctx))
continue;
}
show ("checking sample public key (nistp256)\n");
q = hex2mpi (sample_p256_q);
err = gcry_sexp_build (&keyparam, NULL,
"(public-key(ecc(curve %s)(q %m)))",
"NIST P-256", q);
if (err)
die ("gcry_sexp_build failed: %s\n", gpg_strerror (err));
gcry_mpi_release (q);
/* We can't call gcry_pk_testkey because it is only implemented for
private keys. */
/* err = gcry_pk_testkey (keyparam); */
/* if (err) */
/* fail ("gcry_pk_testkey failed for sample public key: %s\n", */
/* gpg_strerror (err)); */
gcry_ctx_release (ctx);
err = gcry_mpi_ec_new (&ctx, keyparam, NULL);
if (err)
fail ("gcry_mpi_ec_new failed for sample public key (nistp256): %s\n",
gpg_strerror (err));
else
{
gcry_sexp_t sexp;
get_and_cmp_mpi ("q", sample_p256_q, "nistp256", ctx);
get_and_cmp_point ("q", sample_p256_q_x, sample_p256_q_y, "nistp256",
ctx);
/* Delete Q. */
err = gcry_mpi_ec_set_mpi ("q", NULL, ctx);
if (err)
fail ("clearing Q for nistp256 failed: %s\n", gpg_strerror (err));
if (gcry_mpi_ec_get_mpi ("q", ctx, 0))
fail ("clearing Q for nistp256 did not work\n");
/* Set Q again. */
q = hex2mpi (sample_p256_q);
err = gcry_mpi_ec_set_mpi ("q", q, ctx);
if (err)
fail ("setting Q for nistp256 failed: %s\n", gpg_strerror (err));
get_and_cmp_mpi ("q", sample_p256_q, "nistp256(2)", ctx);
gcry_mpi_release (q);
/* Get as s-expression. */
err = gcry_pubkey_get_sexp (&sexp, 0, ctx);
if (err)
fail ("gcry_pubkey_get_sexp(0) failed: %s\n", gpg_strerror (err));
else if (debug)
print_sexp ("Result of gcry_pubkey_get_sexp (0):\n", sexp);
gcry_sexp_release (sexp);
err = gcry_pubkey_get_sexp (&sexp, GCRY_PK_GET_PUBKEY, ctx);
if (err)
fail ("gcry_pubkey_get_sexp(GET_PUBKEY) failed: %s\n",
gpg_strerror (err));
else if (debug)
print_sexp ("Result of gcry_pubkey_get_sexp (GET_PUBKEY):\n", sexp);
gcry_sexp_release (sexp);
err = gcry_pubkey_get_sexp (&sexp, GCRY_PK_GET_SECKEY, ctx);
if (gpg_err_code (err) != GPG_ERR_NO_SECKEY)
fail ("gcry_pubkey_get_sexp(GET_SECKEY) returned wrong error: %s\n",
gpg_strerror (err));
gcry_sexp_release (sexp);
}
show ("checking sample public key (Ed25519)\n");
q = hex2mpi (sample_ed25519_q);
gcry_sexp_release (keyparam);
err = gcry_sexp_build (&keyparam, NULL,
"(public-key(ecc(curve %s)(flags eddsa)(q %m)))",
"Ed25519", q);
if (err)
die ("gcry_sexp_build failed: %s\n", gpg_strerror (err));
gcry_mpi_release (q);
/* We can't call gcry_pk_testkey because it is only implemented for
private keys. */
/* err = gcry_pk_testkey (keyparam); */
/* if (err) */
/* fail ("gcry_pk_testkey failed for sample public key: %s\n", */
/* gpg_strerror (err)); */
gcry_ctx_release (ctx);
err = gcry_mpi_ec_new (&ctx, keyparam, NULL);
if (err)
fail ("gcry_mpi_ec_new failed for sample public key: %s\n",
gpg_strerror (err));
else
{
gcry_sexp_t sexp;
get_and_cmp_mpi ("q", sample_ed25519_q, "Ed25519", ctx);
get_and_cmp_point ("q", sample_ed25519_q_x, sample_ed25519_q_y,
"Ed25519", ctx);
get_and_cmp_mpi ("q@eddsa", sample_ed25519_q_eddsa, "Ed25519", ctx);
/* Set d to see whether Q is correctly re-computed. */
d = hex2mpi (sample_ed25519_d);
err = gcry_mpi_ec_set_mpi ("d", d, ctx);
if (err)
fail ("setting d for Ed25519 failed: %s\n", gpg_strerror (err));
gcry_mpi_release (d);
get_and_cmp_mpi ("q", sample_ed25519_q, "Ed25519(recompute Q)", ctx);
/* Delete Q by setting d and then clearing d. The clearing is
required so that we can check whether Q has been cleared and
because further tests only expect a public key. */
d = hex2mpi (sample_ed25519_d);
err = gcry_mpi_ec_set_mpi ("d", d, ctx);
if (err)
fail ("setting d for Ed25519 failed: %s\n", gpg_strerror (err));
gcry_mpi_release (d);
err = gcry_mpi_ec_set_mpi ("d", NULL, ctx);
if (err)
fail ("setting d for Ed25519 failed(2): %s\n", gpg_strerror (err));
if (gcry_mpi_ec_get_mpi ("q", ctx, 0))
fail ("setting d for Ed25519 did not reset Q\n");
/* Set Q again. We need to use an opaque MPI here because
sample_ed25519_q is in uncompressed format which can only be
auto-detected if passed opaque. */
q = hex2mpiopa (sample_ed25519_q);
err = gcry_mpi_ec_set_mpi ("q", q, ctx);
if (err)
fail ("setting Q for Ed25519 failed: %s\n", gpg_strerror (err));
gcry_mpi_release (q);
get_and_cmp_mpi ("q", sample_ed25519_q, "Ed25519(2)", ctx);
/* Get as s-expression. */
err = gcry_pubkey_get_sexp (&sexp, 0, ctx);
if (err)
fail ("gcry_pubkey_get_sexp(0) failed: %s\n", gpg_strerror (err));
else if (debug)
print_sexp ("Result of gcry_pubkey_get_sexp (0):\n", sexp);
gcry_sexp_release (sexp);
err = gcry_pubkey_get_sexp (&sexp, GCRY_PK_GET_PUBKEY, ctx);
if (err)
fail ("gcry_pubkey_get_sexp(GET_PUBKEY) failed: %s\n",
gpg_strerror (err));
else if (debug)
print_sexp ("Result of gcry_pubkey_get_sexp (GET_PUBKEY):\n", sexp);
gcry_sexp_release (sexp);
err = gcry_pubkey_get_sexp (&sexp, GCRY_PK_GET_SECKEY, ctx);
if (gpg_err_code (err) != GPG_ERR_NO_SECKEY)
fail ("gcry_pubkey_get_sexp(GET_SECKEY) returned wrong error: %s\n",
gpg_strerror (err));
gcry_sexp_release (sexp);
}
gcry_ctx_release (ctx);
gcry_sexp_release (keyparam);
}
/* Create a new point from (X,Y,Z) given as hex strings. */
gcry_mpi_point_t
make_point (const char *x, const char *y, const char *z)
{
gcry_mpi_point_t point;
point = gcry_mpi_point_new (0);
gcry_mpi_point_snatch_set (point, hex2mpi (x), hex2mpi (y), hex2mpi (z));
return point;
}
/* This tests checks that the low-level EC API yields the same result
as using the high level API. The values have been taken from a
test run using the high level API. */
static void
basic_ec_math (void)
{
gpg_error_t err;
gcry_ctx_t ctx;
gcry_mpi_t P, A;
gcry_mpi_point_t G, Q;
gcry_mpi_t d;
gcry_mpi_t x, y, z;
wherestr = "basic_ec_math";
show ("checking basic math functions for EC\n");
P = hex2mpi ("0xfffffffffffffffffffffffffffffffeffffffffffffffff");
A = hex2mpi ("0xfffffffffffffffffffffffffffffffefffffffffffffffc");
G = make_point ("188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
"7192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
"1");
d = hex2mpi ("D4EF27E32F8AD8E2A1C6DDEBB1D235A69E3CEF9BCE90273D");
Q = gcry_mpi_point_new (0);
err = ec_p_new (&ctx, P, A);
if (err)
die ("ec_p_new failed: %s\n", gpg_strerror (err));
x = gcry_mpi_new (0);
y = gcry_mpi_new (0);
z = gcry_mpi_new (0);
{
/* A quick check that multiply by zero works. */
gcry_mpi_t tmp;
tmp = gcry_mpi_new (0);
gcry_mpi_ec_mul (Q, tmp, G, ctx);
gcry_mpi_release (tmp);
gcry_mpi_point_get (x, y, z, Q);
if (gcry_mpi_cmp_ui (x, 0) || gcry_mpi_cmp_ui (y, 0)
|| gcry_mpi_cmp_ui (z, 0))
fail ("multiply a point by zero failed\n");
}
gcry_mpi_ec_mul (Q, d, G, ctx);
gcry_mpi_point_get (x, y, z, Q);
if (cmp_mpihex (x, "222D9EC717C89D047E0898C9185B033CD11C0A981EE6DC66")
|| cmp_mpihex (y, "605DE0A82D70D3E0F84A127D0739ED33D657DF0D054BFDE8")
|| cmp_mpihex (z, "00B06B519071BC536999AC8F2D3934B3C1FC9EACCD0A31F88F"))
fail ("computed public key does not match\n");
if (debug)
{
print_mpi ("Q.x", x);
print_mpi ("Q.y", y);
print_mpi ("Q.z", z);
}
if (gcry_mpi_ec_get_affine (x, y, Q, ctx))
fail ("failed to get affine coordinates\n");
if (cmp_mpihex (x, "008532093BA023F4D55C0424FA3AF9367E05F309DC34CDC3FE")
|| cmp_mpihex (y, "00C13CA9E617C6C8487BFF6A726E3C4F277913D97117939966"))
fail ("computed affine coordinates of public key do not match\n");
if (debug)
{
print_mpi ("q.x", x);
print_mpi ("q.y", y);
}
gcry_mpi_release (z);
gcry_mpi_release (y);
gcry_mpi_release (x);
gcry_mpi_point_release (Q);
gcry_mpi_release (d);
gcry_mpi_point_release (G);
gcry_mpi_release (A);
gcry_mpi_release (P);
gcry_ctx_release (ctx);
}
/* 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);
}
int
main (int argc, char **argv)
{
if (argc > 1 && !strcmp (argv[1], "--verbose"))
verbose = 1;
else if (argc > 1 && !strcmp (argv[1], "--debug"))
verbose = debug = 1;
if (!gcry_check_version (GCRYPT_VERSION))
die ("version mismatch\n");
gcry_control (GCRYCTL_DISABLE_SECMEM, 0);
gcry_control (GCRYCTL_ENABLE_QUICK_RANDOM, 0);
if (debug)
gcry_control (GCRYCTL_SET_DEBUG_FLAGS, 1u, 0);
gcry_control (GCRYCTL_INITIALIZATION_FINISHED, 0);
set_get_point ();
context_alloc ();
context_param ();
basic_ec_math ();
twistededwards_math ();
show ("All tests completed. Errors: %d\n", error_count);
return error_count ? 1 : 0;
}