Example #1
0
/**
 * Multiply the generator g of the elliptic curve by @a val
 * to obtain the point on the curve representing @a val.
 * Afterwards, point addition will correspond to integer
 * addition.  #GNUNET_CRYPTO_ecc_dlog() can be used to
 * convert a point back to an integer (as long as the
 * integer is smaller than the MAX of the @a edc context).
 *
 * @param edc calculation context for ECC operations
 * @param val value to encode into a point
 * @return representation of the value as an ECC point,
 *         must be freed using #GNUNET_CRYPTO_ecc_free()
 */
gcry_mpi_point_t
GNUNET_CRYPTO_ecc_dexp (struct GNUNET_CRYPTO_EccDlogContext *edc,
			int val)
{
  gcry_mpi_t fact;
  gcry_mpi_t n;
  gcry_mpi_point_t g;
  gcry_mpi_point_t r;

  g = gcry_mpi_ec_get_point ("g", edc->ctx, 0);
  GNUNET_assert (NULL != g);
  fact = gcry_mpi_new (0);
  if (val < 0)
  {
    n = gcry_mpi_ec_get_mpi ("n", edc->ctx, 1);
    gcry_mpi_set_ui (fact, - val);
    gcry_mpi_sub (fact, n, fact);
    gcry_mpi_release (n);
  }
  else
  {
    gcry_mpi_set_ui (fact, val);
  }
  r = gcry_mpi_point_new (0);
  gcry_mpi_ec_mul (r, fact, g, edc->ctx);
  gcry_mpi_release (fact);
  gcry_mpi_point_release (g);
  return r;
}
Example #2
0
/**
 * Obtain a random point on the curve and its
 * additive inverse. Both returned values
 * must be freed using #GNUNET_CRYPTO_ecc_free().
 *
 * @param edc calculation context for ECC operations
 * @param[out] r set to a random point on the curve
 * @param[out] r_inv set to the additive inverse of @a r
 */
void
GNUNET_CRYPTO_ecc_rnd (struct GNUNET_CRYPTO_EccDlogContext *edc,
		       gcry_mpi_point_t *r,
		       gcry_mpi_point_t *r_inv)
{
  gcry_mpi_t fact;
  gcry_mpi_t n;
  gcry_mpi_point_t g;

  fact = GNUNET_CRYPTO_ecc_random_mod_n (edc);

  /* calculate 'r' */
  g = gcry_mpi_ec_get_point ("g", edc->ctx, 0);
  GNUNET_assert (NULL != g);
  *r = gcry_mpi_point_new (0);
  gcry_mpi_ec_mul (*r, fact, g, edc->ctx);

  /* calculate 'r_inv' */
  n = gcry_mpi_ec_get_mpi ("n", edc->ctx, 1);
  gcry_mpi_sub (fact, n, fact); /* fact = n - fact = - fact */
  *r_inv = gcry_mpi_point_new (0);
  gcry_mpi_ec_mul (*r_inv, fact, g, edc->ctx);

  gcry_mpi_release (n);
  gcry_mpi_release (fact);
  gcry_mpi_point_release (g);
}
Example #3
0
/**
 * Do pre-calculation for ECC discrete logarithm for small factors.
 *
 * @param max maximum value the factor can be
 * @param mem memory to use (should be smaller than @a max), must not be zero.
 * @return @a max if dlog failed, otherwise the factor
 */
struct GNUNET_CRYPTO_EccDlogContext *
GNUNET_CRYPTO_ecc_dlog_prepare (unsigned int max,
				unsigned int mem)
{
  struct GNUNET_CRYPTO_EccDlogContext *edc;
  unsigned int K = ((max + (mem-1)) / mem);
  gcry_mpi_point_t g;
  struct GNUNET_PeerIdentity key;
  gcry_mpi_point_t gKi;
  gcry_mpi_t fact;
  gcry_mpi_t n;
  unsigned int i;

  GNUNET_assert (max < INT32_MAX);
  edc = GNUNET_new (struct GNUNET_CRYPTO_EccDlogContext);
  edc->max = max;
  edc->mem = mem;

  edc->map = GNUNET_CONTAINER_multipeermap_create (mem * 2,
						   GNUNET_NO);

  GNUNET_assert (0 == gcry_mpi_ec_new (&edc->ctx,
				       NULL,
				       CURVE));
  g = gcry_mpi_ec_get_point ("g", edc->ctx, 0);
  GNUNET_assert (NULL != g);
  fact = gcry_mpi_new (0);
  gKi = gcry_mpi_point_new (0);
  for (i=0;i<=mem;i++)
  {
    gcry_mpi_set_ui (fact, i * K);
    gcry_mpi_ec_mul (gKi, fact, g, edc->ctx);
    extract_pk (gKi, edc->ctx, &key);
    GNUNET_assert (GNUNET_OK ==
		   GNUNET_CONTAINER_multipeermap_put (edc->map,
						      &key,
						      (void*) (long) i + max,
						      GNUNET_CONTAINER_MULTIHASHMAPOPTION_UNIQUE_ONLY));
  }
  /* negative values */
  n = gcry_mpi_ec_get_mpi ("n", edc->ctx, 1);
  for (i=1;i<mem;i++)
  {
    gcry_mpi_set_ui (fact, i * K);
    gcry_mpi_sub (fact, n, fact);
    gcry_mpi_ec_mul (gKi, fact, g, edc->ctx);
    extract_pk (gKi, edc->ctx, &key);
    GNUNET_assert (GNUNET_OK ==
		   GNUNET_CONTAINER_multipeermap_put (edc->map,
						      &key,
						      (void*) (long) max - i,
						      GNUNET_CONTAINER_MULTIHASHMAPOPTION_UNIQUE_ONLY));
  }
  gcry_mpi_release (fact);
  gcry_mpi_release (n);
  gcry_mpi_point_release (gKi);
  gcry_mpi_point_release (g);
  return edc;
}
Example #4
0
/**
 * Do some DLOG operations for testing.
 *
 * @param edc context for ECC operations
 * @param do_dlog #GNUNET_YES if we want to actually do the bencharked operation
 */
static void
test_dlog (struct GNUNET_CRYPTO_EccDlogContext *edc, 
           int do_dlog)
{
  gcry_mpi_t fact;
  gcry_mpi_t n;
  gcry_ctx_t ctx;
  gcry_mpi_point_t q;
  gcry_mpi_point_t g;
  unsigned int i;
  int x;
  int iret;

  GNUNET_assert (0 == gcry_mpi_ec_new (&ctx, NULL, CURVE));
  g = gcry_mpi_ec_get_point ("g", ctx, 0);
  GNUNET_assert (NULL != g);
  n = gcry_mpi_ec_get_mpi ("n", ctx, 0);
  q = gcry_mpi_point_new (0);
  fact = gcry_mpi_new (0);
  for (i=0;i<TEST_ITER;i++)
  {
    fprintf (stderr, ".");
    x = GNUNET_CRYPTO_random_u32 (GNUNET_CRYPTO_QUALITY_WEAK,
				  MAX_FACT);
    if (0 == GNUNET_CRYPTO_random_u32 (GNUNET_CRYPTO_QUALITY_WEAK,
				       2))
    {
      gcry_mpi_set_ui (fact, x);
      gcry_mpi_sub (fact, n, fact);
      x = - x;
    }
    else 
    {
      gcry_mpi_set_ui (fact, x);
    }
    gcry_mpi_ec_mul (q, fact, g, ctx);
    if ( (GNUNET_YES == do_dlog) &&
	 (x !=
	  (iret = GNUNET_CRYPTO_ecc_dlog (edc,
					  q))) )
    {
      fprintf (stderr, 
	       "DLOG failed for value %d (%d)\n", 
	       x,
	       iret);
      GNUNET_assert (0);
    }
  }
  gcry_mpi_release (fact);
  gcry_mpi_release (n);
  gcry_mpi_point_release (g);
  gcry_mpi_point_release (q);
  gcry_ctx_release (ctx);
  fprintf (stderr, "\n");
}
Example #5
0
/**
 * Multiply the generator g of the elliptic curve by @a val
 * to obtain the point on the curve representing @a val.
 *
 * @param edc calculation context for ECC operations
 * @param val (positive) value to encode into a point
 * @return representation of the value as an ECC point,
 *         must be freed using #GNUNET_CRYPTO_ecc_free()
 */
gcry_mpi_point_t
GNUNET_CRYPTO_ecc_dexp_mpi (struct GNUNET_CRYPTO_EccDlogContext *edc,
			    gcry_mpi_t val)
{
  gcry_mpi_point_t g;
  gcry_mpi_point_t r;

  g = gcry_mpi_ec_get_point ("g", edc->ctx, 0);
  GNUNET_assert (NULL != g);
  r = gcry_mpi_point_new (0);
  gcry_mpi_ec_mul (r, val, g, edc->ctx);
  gcry_mpi_point_release (g);
  return r;
}
Example #6
0
/**
 * Calculate ECC discrete logarithm for small factors.
 *
 * @param edc precalculated values, determine range of factors
 * @param input point on the curve to factor
 * @return `edc->max` if dlog failed, otherwise the factor
 */
int
GNUNET_CRYPTO_ecc_dlog (struct GNUNET_CRYPTO_EccDlogContext *edc,
			gcry_mpi_point_t input)
{
  unsigned int K = ((edc->max + (edc->mem-1)) / edc->mem);
  gcry_mpi_point_t g;
  struct GNUNET_PeerIdentity key;
  gcry_mpi_point_t q;
  unsigned int i;
  int res;
  void *retp;

  g = gcry_mpi_ec_get_point ("g", edc->ctx, 0);
  GNUNET_assert (NULL != g);
  q = gcry_mpi_point_new (0);

  res = edc->max;
  for (i=0;i<=edc->max/edc->mem;i++)
  {
    if (0 == i)
      extract_pk (input, edc->ctx, &key);
    else
      extract_pk (q, edc->ctx, &key);
    retp = GNUNET_CONTAINER_multipeermap_get (edc->map,
					      &key);
    if (NULL != retp)
    {
      res = (((long) retp) - edc->max) * K - i;
      /* we continue the loop here to make the implementation
	 "constant-time". If we do not care about this, we could just
	 'break' here and do fewer operations... */
    }
    if (i == edc->max/edc->mem)
      break;
    /* q = q + g */
    if (0 == i)
      gcry_mpi_ec_add (q, input, g, edc->ctx);
    else
      gcry_mpi_ec_add (q, q, g, edc->ctx);
  }
  gcry_mpi_point_release (g);
  gcry_mpi_point_release (q);

  return res;
}
Example #7
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;
}
Example #8
0
File: gka.c Project: totakura/gotr
gcry_mpi_point_t deserialize_point(const struct gotr_point* data, const int len)
{
	gcry_sexp_t s;
	gcry_ctx_t ctx;
	gcry_mpi_point_t ret;
	gcry_error_t rc;

	rc = gcry_sexp_build(&s, NULL, "(public-key(ecc(curve " CURVE ")(q %b)))",
						 len, data);
	gotr_assert_gpgerr(rc);

	rc = gcry_mpi_ec_new(&ctx, s, NULL);
	gotr_assert_gpgerr(rc);
	gcry_sexp_release(s);

	ret = gcry_mpi_ec_get_point("q", ctx, 0);
	gotr_assert(ret);
	gcry_ctx_release(ctx);
	return ret;
}
Example #9
0
/**
 * Convert binary representation of a point to computational representation.
 *
 * @param edc calculation context for ECC operations
 * @param bin binary point representation
 * @return computational representation
 */
gcry_mpi_point_t
GNUNET_CRYPTO_ecc_bin_to_point (struct GNUNET_CRYPTO_EccDlogContext *edc,
                                const struct GNUNET_CRYPTO_EccPoint *bin)
{
  gcry_sexp_t pub_sexpr;
  gcry_ctx_t ctx;
  gcry_mpi_point_t q;

  if (0 != gcry_sexp_build (&pub_sexpr, NULL,
                            "(public-key(ecc(curve " CURVE ")(q %b)))",
                            (int) sizeof (bin->q_y),
                            bin->q_y))
  {
    GNUNET_break (0);
    return NULL;
  }
  GNUNET_assert (0 == gcry_mpi_ec_new (&ctx, pub_sexpr, NULL));
  gcry_sexp_release (pub_sexpr);
  q = gcry_mpi_ec_get_point ("q", ctx, 0);
  gcry_ctx_release (ctx);
  return q;
}
Example #10
0
/* This is the same as basic_ec_math but uses more advanced
   features.  */
static void
basic_ec_math_simplified (void)
{
  gpg_error_t err;
  gcry_ctx_t ctx;
  gcry_mpi_point_t G, Q;
  gcry_mpi_t d;
  gcry_mpi_t x, y, z;
  gcry_sexp_t sexp;

  wherestr = "basic_ec_math_simplified";
  show ("checking basic math functions for EC (variant)\n");

  d = hex2mpi ("D4EF27E32F8AD8E2A1C6DDEBB1D235A69E3CEF9BCE90273D");
  Q = gcry_mpi_point_new (0);

  err = gcry_mpi_ec_new (&ctx, NULL, "NIST P-192");
  if (err)
    die ("gcry_mpi_ec_new failed: %s\n", gpg_strerror (err));
  G = gcry_mpi_ec_get_point ("g", ctx, 1);
  if (!G)
    die ("gcry_mpi_ec_get_point(G) failed\n");
  gcry_mpi_ec_mul (Q, d, G, ctx);

  x = gcry_mpi_new (0);
  y = gcry_mpi_new (0);
  z = gcry_mpi_new (0);
  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);

  /* Let us also check wheer we can update the context.  */
  err = gcry_mpi_ec_set_point ("g", G, ctx);
  if (err)
    die ("gcry_mpi_ec_set_point(G) failed\n");
  err = gcry_mpi_ec_set_mpi ("d", d, ctx);
  if (err)
    die ("gcry_mpi_ec_set_mpi(d) failed\n");

  /* FIXME: Below we need to check that the returned S-expression is
     as requested.  For now we use manual inspection using --debug.  */

  /* Does get_sexp return the private key?  */
  err = gcry_pubkey_get_sexp (&sexp, 0, ctx);
  if (err)
    fail ("gcry_pubkey_get_sexp(0) failed: %s\n", gpg_strerror (err));
  else if (verbose)
    print_sexp ("Result of gcry_pubkey_get_sexp (0):\n", sexp);
  gcry_sexp_release (sexp);

  /* Does get_sexp return the public key if requested?  */
  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 (verbose)
    print_sexp ("Result of gcry_pubkey_get_sexp (GET_PUBKEY):\n", sexp);
  gcry_sexp_release (sexp);

  /* Does get_sexp return the public key if after d has been deleted?  */
  err = gcry_mpi_ec_set_mpi ("d", NULL, ctx);
  if (err)
    die ("gcry_mpi_ec_set_mpi(d=NULL) failed\n");
  err = gcry_pubkey_get_sexp (&sexp, 0, ctx);
  if (err)
    fail ("gcry_pubkey_get_sexp(0 w/o d) failed: %s\n", gpg_strerror (err));
  else if (verbose)
    print_sexp ("Result of gcry_pubkey_get_sexp (0 w/o d):\n", sexp);
  gcry_sexp_release (sexp);

  /* Does get_sexp return an error after d has been deleted?  */
  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);

  /* Does get_sexp return an error after d and Q have been deleted?  */
  err = gcry_mpi_ec_set_point ("q", NULL, ctx);
  if (err)
    die ("gcry_mpi_ec_set_point(q=NULL) failed\n");
  err = gcry_pubkey_get_sexp (&sexp, 0, ctx);
  if (gpg_err_code (err) != GPG_ERR_BAD_CRYPT_CTX)
    fail ("gcry_pubkey_get_sexp(0 w/o Q,d) returned wrong error: %s\n",
          gpg_strerror (err));
  gcry_sexp_release (sexp);


  gcry_mpi_point_release (Q);
  gcry_mpi_release (d);
  gcry_mpi_point_release (G);
  gcry_ctx_release (ctx);
}
Example #11
0
/* 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);
}