Add libotr/etc sources

1 files changed, 1632 insertions, 0 deletions

diff --git a/libotr/libgcrypt-1.8.7/mpi/ec.c b/libotr/libgcrypt-1.8.7/mpi/ec.c
new file mode 100644
index 0000000..adb0260
--- /dev/null
+++ b/libotr/libgcrypt-1.8.7/mpi/ec.c
@@ -0,0 +1,1632 @@
+/* ec.c -  Elliptic Curve functions
+ * Copyright (C) 2007 Free Software Foundation, Inc.
+ * 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/>.
+ */
+
+#include <config.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <errno.h>
+
+#include "mpi-internal.h"
+#include "longlong.h"
+#include "g10lib.h"
+#include "context.h"
+#include "ec-context.h"
+#include "ec-internal.h"
+
+
+#define point_init(a)  _gcry_mpi_point_init ((a))
+#define point_free(a)  _gcry_mpi_point_free_parts ((a))
+
+
+/* Print a point using the log functions.  If CTX is not NULL affine
+   coordinates will be printed.  */
+void
+_gcry_mpi_point_log (const char *name, mpi_point_t point, mpi_ec_t ctx)
+{
+  gcry_mpi_t x, y;
+  char buf[100];
+
+  if (!point)
+    {
+      snprintf (buf, sizeof buf - 1, "%s.*", name);
+      log_mpidump (buf, NULL);
+      return;
+    }
+  snprintf (buf, sizeof buf - 1, "%s.X", name);
+
+  if (ctx)
+    {
+      x = mpi_new (0);
+      y = mpi_new (0);
+    }
+  if (!ctx || _gcry_mpi_ec_get_affine (x, y, point, ctx))
+    {
+      log_mpidump (buf, point->x);
+      buf[strlen(buf)-1] = 'Y';
+      log_mpidump (buf, point->y);
+      buf[strlen(buf)-1] = 'Z';
+      log_mpidump (buf, point->z);
+    }
+  else
+    {
+      buf[strlen(buf)-1] = 'x';
+      log_mpidump (buf, x);
+      buf[strlen(buf)-1] = 'y';
+      log_mpidump (buf, y);
+
+    }
+  if (ctx)
+    {
+      _gcry_mpi_release (x);
+      _gcry_mpi_release (y);
+    }
+}
+
+
+/* Create a new point option.  NBITS gives the size in bits of one
+   coordinate; it is only used to pre-allocate some resources and
+   might also be passed as 0 to use a default value.  */
+mpi_point_t
+_gcry_mpi_point_new (unsigned int nbits)
+{
+  mpi_point_t p;
+
+  (void)nbits;  /* Currently not used.  */
+
+  p = xmalloc (sizeof *p);
+  _gcry_mpi_point_init (p);
+  return p;
+}
+
+
+/* Release the point object P.  P may be NULL. */
+void
+_gcry_mpi_point_release (mpi_point_t p)
+{
+  if (p)
+    {
+      _gcry_mpi_point_free_parts (p);
+      xfree (p);
+    }
+}
+
+
+/* Initialize the fields of a point object.  gcry_mpi_point_free_parts
+   may be used to release the fields.  */
+void
+_gcry_mpi_point_init (mpi_point_t p)
+{
+  p->x = mpi_new (0);
+  p->y = mpi_new (0);
+  p->z = mpi_new (0);
+}
+
+
+/* Release the parts of a point object. */
+void
+_gcry_mpi_point_free_parts (mpi_point_t p)
+{
+  mpi_free (p->x); p->x = NULL;
+  mpi_free (p->y); p->y = NULL;
+  mpi_free (p->z); p->z = NULL;
+}
+
+
+/* Set the value from S into D.  */
+static void
+point_set (mpi_point_t d, mpi_point_t s)
+{
+  mpi_set (d->x, s->x);
+  mpi_set (d->y, s->y);
+  mpi_set (d->z, s->z);
+}
+
+
+/* Return a copy of POINT. */
+gcry_mpi_point_t
+_gcry_mpi_point_copy (gcry_mpi_point_t point)
+{
+  mpi_point_t newpoint;
+
+  newpoint = _gcry_mpi_point_new (0);
+  if (point)
+    point_set (newpoint, point);
+
+  return newpoint;
+}
+
+
+static void
+point_resize (mpi_point_t p, mpi_ec_t ctx)
+{
+  /*
+   * For now, we allocate enough limbs for our EC computation of ec_*.
+   * Once we will improve ec_* to be constant size (and constant
+   * time), NLIMBS can be ctx->p->nlimbs.
+   */
+  size_t nlimbs = 2*ctx->p->nlimbs+1;
+
+  mpi_resize (p->x, nlimbs);
+  if (ctx->model != MPI_EC_MONTGOMERY)
+    mpi_resize (p->y, nlimbs);
+  mpi_resize (p->z, nlimbs);
+}
+
+
+static void
+point_swap_cond (mpi_point_t d, mpi_point_t s, unsigned long swap,
+                 mpi_ec_t ctx)
+{
+  mpi_swap_cond (d->x, s->x, swap);
+  if (ctx->model != MPI_EC_MONTGOMERY)
+    mpi_swap_cond (d->y, s->y, swap);
+  mpi_swap_cond (d->z, s->z, swap);
+}
+
+
+/* Set the projective coordinates from POINT into X, Y, and Z.  If a
+   coordinate is not required, X, Y, or Z may be passed as NULL.  */
+void
+_gcry_mpi_point_get (gcry_mpi_t x, gcry_mpi_t y, gcry_mpi_t z,
+                     mpi_point_t point)
+{
+  if (x)
+    mpi_set (x, point->x);
+  if (y)
+    mpi_set (y, point->y);
+  if (z)
+    mpi_set (z, point->z);
+}
+
+
+/* Set the projective coordinates from POINT into X, Y, and Z and
+   release POINT.  If a coordinate is not required, X, Y, or Z may be
+   passed as NULL.  */
+void
+_gcry_mpi_point_snatch_get (gcry_mpi_t x, gcry_mpi_t y, gcry_mpi_t z,
+                            mpi_point_t point)
+{
+  mpi_snatch (x, point->x);
+  mpi_snatch (y, point->y);
+  mpi_snatch (z, point->z);
+  xfree (point);
+}
+
+
+/* Set the projective coordinates from X, Y, and Z into POINT.  If a
+   coordinate is given as NULL, the value 0 is stored into point.  If
+   POINT is given as NULL a new point object is allocated.  Returns
+   POINT or the newly allocated point object. */
+mpi_point_t
+_gcry_mpi_point_set (mpi_point_t point,
+                     gcry_mpi_t x, gcry_mpi_t y, gcry_mpi_t z)
+{
+  if (!point)
+    point = mpi_point_new (0);
+
+  if (x)
+    mpi_set (point->x, x);
+  else
+    mpi_clear (point->x);
+  if (y)
+    mpi_set (point->y, y);
+  else
+    mpi_clear (point->y);
+  if (z)
+    mpi_set (point->z, z);
+  else
+    mpi_clear (point->z);
+
+  return point;
+}
+
+
+/* Set the projective coordinates from X, Y, and Z into POINT.  If a
+   coordinate is given as NULL, the value 0 is stored into point.  If
+   POINT is given as NULL a new point object is allocated.  The
+   coordinates X, Y, and Z are released.  Returns POINT or the newly
+   allocated point object. */
+mpi_point_t
+_gcry_mpi_point_snatch_set (mpi_point_t point,
+                            gcry_mpi_t x, gcry_mpi_t y, gcry_mpi_t z)
+{
+  if (!point)
+    point = mpi_point_new (0);
+
+  if (x)
+    mpi_snatch (point->x, x);
+  else
+    mpi_clear (point->x);
+  if (y)
+    mpi_snatch (point->y, y);
+  else
+    mpi_clear (point->y);
+  if (z)
+    mpi_snatch (point->z, z);
+  else
+    mpi_clear (point->z);
+
+  return point;
+}
+
+
+/* W = W mod P.  */
+static void
+ec_mod (gcry_mpi_t w, mpi_ec_t ec)
+{
+  if (0 && ec->dialect == ECC_DIALECT_ED25519)
+    _gcry_mpi_ec_ed25519_mod (w);
+  else if (ec->t.p_barrett)
+    _gcry_mpi_mod_barrett (w, w, ec->t.p_barrett);
+  else
+    _gcry_mpi_mod (w, w, ec->p);
+}
+
+static void
+ec_addm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ctx)
+{
+  mpi_add (w, u, v);
+  ec_mod (w, ctx);
+}
+
+static void
+ec_subm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ec)
+{
+  mpi_sub (w, u, v);
+  while (w->sign)
+    mpi_add (w, w, ec->p);
+  /*ec_mod (w, ec);*/
+}
+
+static void
+ec_mulm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ctx)
+{
+  mpi_mul (w, u, v);
+  ec_mod (w, ctx);
+}
+
+/* W = 2 * U mod P.  */
+static void
+ec_mul2 (gcry_mpi_t w, gcry_mpi_t u, mpi_ec_t ctx)
+{
+  mpi_lshift (w, u, 1);
+  ec_mod (w, ctx);
+}
+
+static void
+ec_powm (gcry_mpi_t w, const gcry_mpi_t b, const gcry_mpi_t e,
+         mpi_ec_t ctx)
+{
+  mpi_powm (w, b, e, ctx->p);
+  /* _gcry_mpi_abs (w); */
+}
+
+
+/* Shortcut for
+     ec_powm (B, B, mpi_const (MPI_C_TWO), ctx);
+   for easier optimization.  */
+static void
+ec_pow2 (gcry_mpi_t w, const gcry_mpi_t b, mpi_ec_t ctx)
+{
+  /* Using mpi_mul is slightly faster (at least on amd64).  */
+  /* mpi_powm (w, b, mpi_const (MPI_C_TWO), ctx->p); */
+  ec_mulm (w, b, b, ctx);
+}
+
+
+/* Shortcut for
+     ec_powm (B, B, mpi_const (MPI_C_THREE), ctx);
+   for easier optimization.  */
+static void
+ec_pow3 (gcry_mpi_t w, const gcry_mpi_t b, mpi_ec_t ctx)
+{
+  mpi_powm (w, b, mpi_const (MPI_C_THREE), ctx->p);
+}
+
+
+static void
+ec_invm (gcry_mpi_t x, gcry_mpi_t a, mpi_ec_t ctx)
+{
+  if (!mpi_invm (x, a, ctx->p))
+    {
+      log_error ("ec_invm: inverse does not exist:\n");
+      log_mpidump ("  a", a);
+      log_mpidump ("  p", ctx->p);
+    }
+}
+
+
+/* Force recomputation of all helper variables.  */
+void
+_gcry_mpi_ec_get_reset (mpi_ec_t ec)
+{
+  ec->t.valid.a_is_pminus3 = 0;
+  ec->t.valid.two_inv_p = 0;
+}
+
+
+/* Accessor for helper variable.  */
+static int
+ec_get_a_is_pminus3 (mpi_ec_t ec)
+{
+  gcry_mpi_t tmp;
+
+  if (!ec->t.valid.a_is_pminus3)
+    {
+      ec->t.valid.a_is_pminus3 = 1;
+      tmp = mpi_alloc_like (ec->p);
+      mpi_sub_ui (tmp, ec->p, 3);
+      ec->t.a_is_pminus3 = !mpi_cmp (ec->a, tmp);
+      mpi_free (tmp);
+    }
+
+  return ec->t.a_is_pminus3;
+}
+
+
+/* Accessor for helper variable.  */
+static gcry_mpi_t
+ec_get_two_inv_p (mpi_ec_t ec)
+{
+  if (!ec->t.valid.two_inv_p)
+    {
+      ec->t.valid.two_inv_p = 1;
+      if (!ec->t.two_inv_p)
+        ec->t.two_inv_p = mpi_alloc (0);
+      ec_invm (ec->t.two_inv_p, mpi_const (MPI_C_TWO), ec);
+    }
+  return ec->t.two_inv_p;
+}
+
+
+static const char *curve25519_bad_points[] = {
+  "0x0000000000000000000000000000000000000000000000000000000000000000",
+  "0x0000000000000000000000000000000000000000000000000000000000000001",
+  "0x00b8495f16056286fdb1329ceb8d09da6ac49ff1fae35616aeb8413b7c7aebe0",
+  "0x57119fd0dd4e22d8868e1c58c45c44045bef839c55b1d0b1248c50a3bc959c5f",
+  "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec",
+  "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed",
+  "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffee",
+  NULL
+};
+
+static gcry_mpi_t
+scanval (const char *string)
+{
+  gpg_err_code_t rc;
+  gcry_mpi_t val;
+
+  rc = _gcry_mpi_scan (&val, GCRYMPI_FMT_HEX, string, 0, NULL);
+  if (rc)
+    log_fatal ("scanning ECC parameter failed: %s\n", gpg_strerror (rc));
+  return val;
+}
+
+
+/* This function initialized a context for elliptic curve based on the
+   field GF(p).  P is the prime specifying this field, A is the first
+   coefficient.  CTX is expected to be zeroized.  */
+static void
+ec_p_init (mpi_ec_t ctx, enum gcry_mpi_ec_models model,
+           enum ecc_dialects dialect,
+           int flags,
+           gcry_mpi_t p, gcry_mpi_t a, gcry_mpi_t b)
+{
+  int i;
+  static int use_barrett;
+
+  if (!use_barrett)
+    {
+      if (getenv ("GCRYPT_BARRETT"))
+        use_barrett = 1;
+      else
+        use_barrett = -1;
+    }
+
+  /* Fixme: Do we want to check some constraints? e.g.  a < p  */
+
+  ctx->model = model;
+  ctx->dialect = dialect;
+  ctx->flags = flags;
+  if (dialect == ECC_DIALECT_ED25519)
+    ctx->nbits = 256;
+  else
+    ctx->nbits = mpi_get_nbits (p);
+  ctx->p = mpi_copy (p);
+  ctx->a = mpi_copy (a);
+  ctx->b = mpi_copy (b);
+
+  ctx->t.p_barrett = use_barrett > 0? _gcry_mpi_barrett_init (ctx->p, 0):NULL;
+
+  _gcry_mpi_ec_get_reset (ctx);
+
+  if (model == MPI_EC_MONTGOMERY)
+    {
+      for (i=0; i< DIM(ctx->t.scratch) && curve25519_bad_points[i]; i++)
+        ctx->t.scratch[i] = scanval (curve25519_bad_points[i]);
+    }
+  else
+    {
+      /* Allocate scratch variables.  */
+      for (i=0; i< DIM(ctx->t.scratch); i++)
+        ctx->t.scratch[i] = mpi_alloc_like (ctx->p);
+    }
+
+  /* Prepare for fast reduction.  */
+  /* FIXME: need a test for NIST values.  However it does not gain us
+     any real advantage, for 384 bits it is actually slower than using
+     mpi_mulm.  */
+/*   ctx->nist_nbits = mpi_get_nbits (ctx->p); */
+/*   if (ctx->nist_nbits == 192) */
+/*     { */
+/*       for (i=0; i < 4; i++) */
+/*         ctx->s[i] = mpi_new (192); */
+/*       ctx->c    = mpi_new (192*2); */
+/*     } */
+/*   else if (ctx->nist_nbits == 384) */
+/*     { */
+/*       for (i=0; i < 10; i++) */
+/*         ctx->s[i] = mpi_new (384); */
+/*       ctx->c    = mpi_new (384*2); */
+/*     } */
+}
+
+
+static void
+ec_deinit (void *opaque)
+{
+  mpi_ec_t ctx = opaque;
+  int i;
+
+  _gcry_mpi_barrett_free (ctx->t.p_barrett);
+
+  /* Domain parameter.  */
+  mpi_free (ctx->p);
+  mpi_free (ctx->a);
+  mpi_free (ctx->b);
+  _gcry_mpi_point_release (ctx->G);
+  mpi_free (ctx->n);
+  mpi_free (ctx->h);
+
+  /* The key.  */
+  _gcry_mpi_point_release (ctx->Q);
+  mpi_free (ctx->d);
+
+  /* Private data of ec.c.  */
+  mpi_free (ctx->t.two_inv_p);
+
+  for (i=0; i< DIM(ctx->t.scratch); i++)
+    mpi_free (ctx->t.scratch[i]);
+
+/*   if (ctx->nist_nbits == 192) */
+/*     { */
+/*       for (i=0; i < 4; i++) */
+/*         mpi_free (ctx->s[i]); */
+/*       mpi_free (ctx->c); */
+/*     } */
+/*   else if (ctx->nist_nbits == 384) */
+/*     { */
+/*       for (i=0; i < 10; i++) */
+/*         mpi_free (ctx->s[i]); */
+/*       mpi_free (ctx->c); */
+/*     } */
+}
+
+
+/* This function returns a new context for elliptic curve based on the
+   field GF(p).  P is the prime specifying this field, A is the first
+   coefficient, B is the second coefficient, and MODEL is the model
+   for the curve.  This function is only used within Libgcrypt and not
+   part of the public API.
+
+   This context needs to be released using _gcry_mpi_ec_free.  */
+mpi_ec_t
+_gcry_mpi_ec_p_internal_new (enum gcry_mpi_ec_models model,
+                             enum ecc_dialects dialect,
+                             int flags,
+                             gcry_mpi_t p, gcry_mpi_t a, gcry_mpi_t b)
+{
+  mpi_ec_t ctx;
+
+  ctx = xcalloc (1, sizeof *ctx);
+  ec_p_init (ctx, model, dialect, flags, p, a, b);
+
+  return ctx;
+}
+
+
+/* This is a variant of _gcry_mpi_ec_p_internal_new which returns an
+   public context and does some error checking on the supplied
+   arguments.  On success the new context is stored at R_CTX and 0 is
+   returned; on error NULL is stored at R_CTX and an error code is
+   returned.
+
+   The context needs to be released using gcry_ctx_release.  */
+gpg_err_code_t
+_gcry_mpi_ec_p_new (gcry_ctx_t *r_ctx,
+                    enum gcry_mpi_ec_models model,
+                    enum ecc_dialects dialect,
+                    int flags,
+                    gcry_mpi_t p, gcry_mpi_t a, gcry_mpi_t b)
+{
+  gcry_ctx_t ctx;
+  mpi_ec_t ec;
+
+  *r_ctx = NULL;
+  if (!p || !a)
+    return GPG_ERR_EINVAL;
+
+  ctx = _gcry_ctx_alloc (CONTEXT_TYPE_EC, sizeof *ec, ec_deinit);
+  if (!ctx)
+    return gpg_err_code_from_syserror ();
+  ec = _gcry_ctx_get_pointer (ctx, CONTEXT_TYPE_EC);
+  ec_p_init (ec, model, dialect, flags, p, a, b);
+
+  *r_ctx = ctx;
+  return 0;
+}
+
+
+void
+_gcry_mpi_ec_free (mpi_ec_t ctx)
+{
+  if (ctx)
+    {
+      ec_deinit (ctx);
+      xfree (ctx);
+    }
+}
+
+
+gcry_mpi_t
+_gcry_mpi_ec_get_mpi (const char *name, gcry_ctx_t ctx, int copy)
+{
+  mpi_ec_t ec = _gcry_ctx_get_pointer (ctx, CONTEXT_TYPE_EC);
+
+  return _gcry_ecc_get_mpi (name, ec, copy);
+}
+
+
+gcry_mpi_point_t
+_gcry_mpi_ec_get_point (const char *name, gcry_ctx_t ctx, int copy)
+{
+  mpi_ec_t ec = _gcry_ctx_get_pointer (ctx, CONTEXT_TYPE_EC);
+
+  (void)copy;  /* Not used.  */
+
+  return _gcry_ecc_get_point (name, ec);
+}
+
+
+gpg_err_code_t
+_gcry_mpi_ec_set_mpi (const char *name, gcry_mpi_t newvalue,
+                      gcry_ctx_t ctx)
+{
+  mpi_ec_t ec = _gcry_ctx_get_pointer (ctx, CONTEXT_TYPE_EC);
+
+  return _gcry_ecc_set_mpi (name, newvalue, ec);
+}
+
+
+gpg_err_code_t
+_gcry_mpi_ec_set_point (const char *name, gcry_mpi_point_t newvalue,
+                        gcry_ctx_t ctx)
+{
+  mpi_ec_t ec = _gcry_ctx_get_pointer (ctx, CONTEXT_TYPE_EC);
+
+  return _gcry_ecc_set_point (name, newvalue, ec);
+}
+
+
+/* Given an encoded point in the MPI VALUE and a context EC, decode
+ * the point according to the context and store it in RESULT.  On
+ * error an error code is return but RESULT might have been changed.
+ * If no context is given the function tries to decode VALUE by
+ * assuming a 0x04 prefixed uncompressed encoding.  */
+gpg_err_code_t
+_gcry_mpi_ec_decode_point (mpi_point_t result, gcry_mpi_t value, mpi_ec_t ec)
+{
+  gcry_err_code_t rc;
+
+  if (ec && ec->dialect == ECC_DIALECT_ED25519)
+    rc = _gcry_ecc_eddsa_decodepoint (value, ec, result, NULL, NULL);
+  else if (ec && ec->model == MPI_EC_MONTGOMERY)
+    rc = _gcry_ecc_mont_decodepoint (value, ec, result);
+  else
+    rc = _gcry_ecc_os2ec (result, value);
+
+  return rc;
+}
+
+
+/* Compute the affine coordinates from the projective coordinates in
+   POINT.  Set them into X and Y.  If one coordinate is not required,
+   X or Y may be passed as NULL.  CTX is the usual context. Returns: 0
+   on success or !0 if POINT is at infinity.  */
+int
+_gcry_mpi_ec_get_affine (gcry_mpi_t x, gcry_mpi_t y, mpi_point_t point,
+                         mpi_ec_t ctx)
+{
+  if (!mpi_cmp_ui (point->z, 0))
+    return -1;
+
+  switch (ctx->model)
+    {
+    case MPI_EC_WEIERSTRASS: /* Using Jacobian coordinates.  */
+      {
+        gcry_mpi_t z1, z2, z3;
+
+        z1 = mpi_new (0);
+        z2 = mpi_new (0);
+        ec_invm (z1, point->z, ctx);  /* z1 = z^(-1) mod p  */
+        ec_mulm (z2, z1, z1, ctx);    /* z2 = z^(-2) mod p  */
+
+        if (x)
+          ec_mulm (x, point->x, z2, ctx);
+
+        if (y)
+          {
+            z3 = mpi_new (0);
+            ec_mulm (z3, z2, z1, ctx);      /* z3 = z^(-3) mod p  */
+            ec_mulm (y, point->y, z3, ctx);
+            mpi_free (z3);
+          }
+
+        mpi_free (z2);
+        mpi_free (z1);
+      }
+      return 0;
+
+    case MPI_EC_MONTGOMERY:
+      {
+        if (x)
+          mpi_set (x, point->x);
+
+        if (y)
+          {
+            log_fatal ("%s: Getting Y-coordinate on %s is not supported\n",
+                       "_gcry_mpi_ec_get_affine", "Montgomery");
+            return -1;
+          }
+      }
+      return 0;
+
+    case MPI_EC_EDWARDS:
+      {
+        gcry_mpi_t z;
+
+        z = mpi_new (0);
+        ec_invm (z, point->z, ctx);
+
+        if (x)
+          ec_mulm (x, point->x, z, ctx);
+        if (y)
+          ec_mulm (y, point->y, z, ctx);
+
+        _gcry_mpi_release (z);
+      }
+      return 0;
+
+    default:
+      return -1;
+    }
+}
+
+
+
+/*  RESULT = 2 * POINT  (Weierstrass version). */
+static void
+dup_point_weierstrass (mpi_point_t result, mpi_point_t point, mpi_ec_t ctx)
+{
+#define x3 (result->x)
+#define y3 (result->y)
+#define z3 (result->z)
+#define t1 (ctx->t.scratch[0])
+#define t2 (ctx->t.scratch[1])
+#define t3 (ctx->t.scratch[2])
+#define l1 (ctx->t.scratch[3])
+#define l2 (ctx->t.scratch[4])
+#define l3 (ctx->t.scratch[5])
+
+  if (!mpi_cmp_ui (point->y, 0) || !mpi_cmp_ui (point->z, 0))
+    {
+      /* P_y == 0 || P_z == 0 => [1:1:0] */
+      mpi_set_ui (x3, 1);
+      mpi_set_ui (y3, 1);
+      mpi_set_ui (z3, 0);
+    }
+  else
+    {
+      if (ec_get_a_is_pminus3 (ctx))  /* Use the faster case.  */
+        {
+          /* L1 = 3(X - Z^2)(X + Z^2) */
+          /*                          T1: used for Z^2. */
+          /*                          T2: used for the right term.  */
+          ec_pow2 (t1, point->z, ctx);
+          ec_subm (l1, point->x, t1, ctx);
+          ec_mulm (l1, l1, mpi_const (MPI_C_THREE), ctx);
+          ec_addm (t2, point->x, t1, ctx);
+          ec_mulm (l1, l1, t2, ctx);
+        }
+      else /* Standard case. */
+        {
+          /* L1 = 3X^2 + aZ^4 */
+          /*                          T1: used for aZ^4. */
+          ec_pow2 (l1, point->x, ctx);
+          ec_mulm (l1, l1, mpi_const (MPI_C_THREE), ctx);
+          ec_powm (t1, point->z, mpi_const (MPI_C_FOUR), ctx);
+          ec_mulm (t1, t1, ctx->a, ctx);
+          ec_addm (l1, l1, t1, ctx);
+        }
+      /* Z3 = 2YZ */
+      ec_mulm (z3, point->y, point->z, ctx);
+      ec_mul2 (z3, z3, ctx);
+
+      /* L2 = 4XY^2 */
+      /*                              T2: used for Y2; required later. */
+      ec_pow2 (t2, point->y, ctx);
+      ec_mulm (l2, t2, point->x, ctx);
+      ec_mulm (l2, l2, mpi_const (MPI_C_FOUR), ctx);
+
+      /* X3 = L1^2 - 2L2 */
+      /*                              T1: used for L2^2. */
+      ec_pow2 (x3, l1, ctx);
+      ec_mul2 (t1, l2, ctx);
+      ec_subm (x3, x3, t1, ctx);
+
+      /* L3 = 8Y^4 */
+      /*                              T2: taken from above. */
+      ec_pow2 (t2, t2, ctx);
+      ec_mulm (l3, t2, mpi_const (MPI_C_EIGHT), ctx);
+
+      /* Y3 = L1(L2 - X3) - L3 */
+      ec_subm (y3, l2, x3, ctx);
+      ec_mulm (y3, y3, l1, ctx);
+      ec_subm (y3, y3, l3, ctx);
+    }
+
+#undef x3
+#undef y3
+#undef z3
+#undef t1
+#undef t2
+#undef t3
+#undef l1
+#undef l2
+#undef l3
+}
+
+
+/*  RESULT = 2 * POINT  (Montgomery version). */
+static void
+dup_point_montgomery (mpi_point_t result, mpi_point_t point, mpi_ec_t ctx)
+{
+  (void)result;
+  (void)point;
+  (void)ctx;
+  log_fatal ("%s: %s not yet supported\n",
+             "_gcry_mpi_ec_dup_point", "Montgomery");
+}
+
+
+/*  RESULT = 2 * POINT  (Twisted Edwards version). */
+static void
+dup_point_edwards (mpi_point_t result, mpi_point_t point, mpi_ec_t ctx)
+{
+#define X1 (point->x)
+#define Y1 (point->y)
+#define Z1 (point->z)
+#define X3 (result->x)
+#define Y3 (result->y)
+#define Z3 (result->z)
+#define B (ctx->t.scratch[0])
+#define C (ctx->t.scratch[1])
+#define D (ctx->t.scratch[2])
+#define E (ctx->t.scratch[3])
+#define F (ctx->t.scratch[4])
+#define H (ctx->t.scratch[5])
+#define J (ctx->t.scratch[6])
+
+  /* Compute: (X_3 : Y_3 : Z_3) = 2( X_1 : Y_1 : Z_1 ) */
+
+  /* B = (X_1 + Y_1)^2  */
+  ec_addm (B, X1, Y1, ctx);
+  ec_pow2 (B, B, ctx);
+
+  /* C = X_1^2 */
+  /* D = Y_1^2 */
+  ec_pow2 (C, X1, ctx);
+  ec_pow2 (D, Y1, ctx);
+
+  /* E = aC */
+  if (ctx->dialect == ECC_DIALECT_ED25519)
+    mpi_sub (E, ctx->p, C);
+  else
+    ec_mulm (E, ctx->a, C, ctx);
+
+  /* F = E + D */
+  ec_addm (F, E, D, ctx);
+
+  /* H = Z_1^2 */
+  ec_pow2 (H, Z1, ctx);
+
+  /* J = F - 2H */
+  ec_mul2 (J, H, ctx);
+  ec_subm (J, F, J, ctx);
+
+  /* X_3 = (B - C - D) · J */
+  ec_subm (X3, B, C, ctx);
+  ec_subm (X3, X3, D, ctx);
+  ec_mulm (X3, X3, J, ctx);
+
+  /* Y_3 = F · (E - D) */
+  ec_subm (Y3, E, D, ctx);
+  ec_mulm (Y3, Y3, F, ctx);
+
+  /* Z_3 = F · J */
+  ec_mulm (Z3, F, J, ctx);
+
+#undef X1
+#undef Y1
+#undef Z1
+#undef X3
+#undef Y3
+#undef Z3
+#undef B
+#undef C
+#undef D
+#undef E
+#undef F
+#undef H
+#undef J
+}
+
+
+/*  RESULT = 2 * POINT  */
+void
+_gcry_mpi_ec_dup_point (mpi_point_t result, mpi_point_t point, mpi_ec_t ctx)
+{
+  switch (ctx->model)
+    {
+    case MPI_EC_WEIERSTRASS:
+      dup_point_weierstrass (result, point, ctx);
+      break;
+    case MPI_EC_MONTGOMERY:
+      dup_point_montgomery (result, point, ctx);
+      break;
+    case MPI_EC_EDWARDS:
+      dup_point_edwards (result, point, ctx);
+      break;
+    }
+}
+
+
+/* RESULT = P1 + P2  (Weierstrass version).*/
+static void
+add_points_weierstrass (mpi_point_t result,
+                        mpi_point_t p1, mpi_point_t p2,
+                        mpi_ec_t ctx)
+{
+#define x1 (p1->x    )
+#define y1 (p1->y    )
+#define z1 (p1->z    )
+#define x2 (p2->x    )
+#define y2 (p2->y    )
+#define z2 (p2->z    )
+#define x3 (result->x)
+#define y3 (result->y)
+#define z3 (result->z)
+#define l1 (ctx->t.scratch[0])
+#define l2 (ctx->t.scratch[1])
+#define l3 (ctx->t.scratch[2])
+#define l4 (ctx->t.scratch[3])
+#define l5 (ctx->t.scratch[4])
+#define l6 (ctx->t.scratch[5])
+#define l7 (ctx->t.scratch[6])
+#define l8 (ctx->t.scratch[7])
+#define l9 (ctx->t.scratch[8])
+#define t1 (ctx->t.scratch[9])
+#define t2 (ctx->t.scratch[10])
+
+  if ( (!mpi_cmp (x1, x2)) && (!mpi_cmp (y1, y2)) && (!mpi_cmp (z1, z2)) )
+    {
+      /* Same point; need to call the duplicate function.  */
+      _gcry_mpi_ec_dup_point (result, p1, ctx);
+    }
+  else if (!mpi_cmp_ui (z1, 0))
+    {
+      /* P1 is at infinity.  */
+      mpi_set (x3, p2->x);
+      mpi_set (y3, p2->y);
+      mpi_set (z3, p2->z);
+    }
+  else if (!mpi_cmp_ui (z2, 0))
+    {
+      /* P2 is at infinity.  */
+      mpi_set (x3, p1->x);
+      mpi_set (y3, p1->y);
+      mpi_set (z3, p1->z);
+    }
+  else
+    {
+      int z1_is_one = !mpi_cmp_ui (z1, 1);
+      int z2_is_one = !mpi_cmp_ui (z2, 1);
+
+      /* l1 = x1 z2^2  */
+      /* l2 = x2 z1^2  */
+      if (z2_is_one)
+        mpi_set (l1, x1);
+      else
+        {
+          ec_pow2 (l1, z2, ctx);
+          ec_mulm (l1, l1, x1, ctx);
+        }
+      if (z1_is_one)
+        mpi_set (l2, x2);
+      else
+        {
+          ec_pow2 (l2, z1, ctx);
+          ec_mulm (l2, l2, x2, ctx);
+        }
+      /* l3 = l1 - l2 */
+      ec_subm (l3, l1, l2, ctx);
+      /* l4 = y1 z2^3  */
+      ec_powm (l4, z2, mpi_const (MPI_C_THREE), ctx);
+      ec_mulm (l4, l4, y1, ctx);
+      /* l5 = y2 z1^3  */
+      ec_powm (l5, z1, mpi_const (MPI_C_THREE), ctx);
+      ec_mulm (l5, l5, y2, ctx);
+      /* l6 = l4 - l5  */
+      ec_subm (l6, l4, l5, ctx);
+
+      if (!mpi_cmp_ui (l3, 0))
+        {
+          if (!mpi_cmp_ui (l6, 0))
+            {
+              /* P1 and P2 are the same - use duplicate function.  */
+              _gcry_mpi_ec_dup_point (result, p1, ctx);
+            }
+          else
+            {
+              /* P1 is the inverse of P2.  */
+              mpi_set_ui (x3, 1);
+              mpi_set_ui (y3, 1);
+              mpi_set_ui (z3, 0);
+            }
+        }
+      else
+        {
+          /* l7 = l1 + l2  */
+          ec_addm (l7, l1, l2, ctx);
+          /* l8 = l4 + l5  */
+          ec_addm (l8, l4, l5, ctx);
+          /* z3 = z1 z2 l3  */
+          ec_mulm (z3, z1, z2, ctx);
+          ec_mulm (z3, z3, l3, ctx);
+          /* x3 = l6^2 - l7 l3^2  */
+          ec_pow2 (t1, l6, ctx);
+          ec_pow2 (t2, l3, ctx);
+          ec_mulm (t2, t2, l7, ctx);
+          ec_subm (x3, t1, t2, ctx);
+          /* l9 = l7 l3^2 - 2 x3  */
+          ec_mul2 (t1, x3, ctx);
+          ec_subm (l9, t2, t1, ctx);
+          /* y3 = (l9 l6 - l8 l3^3)/2  */
+          ec_mulm (l9, l9, l6, ctx);
+          ec_powm (t1, l3, mpi_const (MPI_C_THREE), ctx); /* fixme: Use saved value*/
+          ec_mulm (t1, t1, l8, ctx);
+          ec_subm (y3, l9, t1, ctx);
+          ec_mulm (y3, y3, ec_get_two_inv_p (ctx), ctx);
+        }
+    }
+
+#undef x1
+#undef y1
+#undef z1
+#undef x2
+#undef y2
+#undef z2
+#undef x3
+#undef y3
+#undef z3
+#undef l1
+#undef l2
+#undef l3
+#undef l4
+#undef l5
+#undef l6
+#undef l7
+#undef l8
+#undef l9
+#undef t1
+#undef t2
+}
+
+
+/* RESULT = P1 + P2  (Montgomery version).*/
+static void
+add_points_montgomery (mpi_point_t result,
+                       mpi_point_t p1, mpi_point_t p2,
+                       mpi_ec_t ctx)
+{
+  (void)result;
+  (void)p1;
+  (void)p2;
+  (void)ctx;
+  log_fatal ("%s: %s not yet supported\n",
+             "_gcry_mpi_ec_add_points", "Montgomery");
+}
+
+
+/* RESULT = P1 + P2  (Twisted Edwards version).*/
+static void
+add_points_edwards (mpi_point_t result,
+                    mpi_point_t p1, mpi_point_t p2,
+                    mpi_ec_t ctx)
+{
+#define X1 (p1->x)
+#define Y1 (p1->y)
+#define Z1 (p1->z)
+#define X2 (p2->x)
+#define Y2 (p2->y)
+#define Z2 (p2->z)
+#define X3 (result->x)
+#define Y3 (result->y)
+#define Z3 (result->z)
+#define A (ctx->t.scratch[0])
+#define B (ctx->t.scratch[1])
+#define C (ctx->t.scratch[2])
+#define D (ctx->t.scratch[3])
+#define E (ctx->t.scratch[4])
+#define F (ctx->t.scratch[5])
+#define G (ctx->t.scratch[6])
+#define tmp (ctx->t.scratch[7])
+
+  /* Compute: (X_3 : Y_3 : Z_3) = (X_1 : Y_1 : Z_1) + (X_2 : Y_2 : Z_3)  */
+
+  /* A = Z1 · Z2 */
+  ec_mulm (A, Z1, Z2, ctx);
+
+  /* B = A^2 */
+  ec_pow2 (B, A, ctx);
+
+  /* C = X1 · X2 */
+  ec_mulm (C, X1, X2, ctx);
+
+  /* D = Y1 · Y2 */
+  ec_mulm (D, Y1, Y2, ctx);
+
+  /* E = d · C · D */
+  ec_mulm (E, ctx->b, C, ctx);
+  ec_mulm (E, E, D, ctx);
+
+  /* F = B - E */
+  ec_subm (F, B, E, ctx);
+
+  /* G = B + E */
+  ec_addm (G, B, E, ctx);
+
+  /* X_3 = A · F · ((X_1 + Y_1) · (X_2 + Y_2) - C - D) */
+  ec_addm (tmp, X1, Y1, ctx);
+  ec_addm (X3, X2, Y2, ctx);
+  ec_mulm (X3, X3, tmp, ctx);
+  ec_subm (X3, X3, C, ctx);
+  ec_subm (X3, X3, D, ctx);
+  ec_mulm (X3, X3, F, ctx);
+  ec_mulm (X3, X3, A, ctx);
+
+  /* Y_3 = A · G · (D - aC) */
+  if (ctx->dialect == ECC_DIALECT_ED25519)
+    {
+      ec_addm (Y3, D, C, ctx);
+    }
+  else
+    {
+      ec_mulm (Y3, ctx->a, C, ctx);
+      ec_subm (Y3, D, Y3, ctx);
+    }
+  ec_mulm (Y3, Y3, G, ctx);
+  ec_mulm (Y3, Y3, A, ctx);
+
+  /* Z_3 = F · G */
+  ec_mulm (Z3, F, G, ctx);
+
+
+#undef X1
+#undef Y1
+#undef Z1
+#undef X2
+#undef Y2
+#undef Z2
+#undef X3
+#undef Y3
+#undef Z3
+#undef A
+#undef B
+#undef C
+#undef D
+#undef E
+#undef F
+#undef G
+#undef tmp
+}
+
+
+/* Compute a step of Montgomery Ladder (only use X and Z in the point).
+   Inputs:  P1, P2, and x-coordinate of DIF = P1 - P1.
+   Outputs: PRD = 2 * P1 and  SUM = P1 + P2. */
+static void
+montgomery_ladder (mpi_point_t prd, mpi_point_t sum,
+                   mpi_point_t p1, mpi_point_t p2, gcry_mpi_t dif_x,
+                   mpi_ec_t ctx)
+{
+  ec_addm (sum->x, p2->x, p2->z, ctx);
+  ec_subm (p2->z, p2->x, p2->z, ctx);
+  ec_addm (prd->x, p1->x, p1->z, ctx);
+  ec_subm (p1->z, p1->x, p1->z, ctx);
+  ec_mulm (p2->x, p1->z, sum->x, ctx);
+  ec_mulm (p2->z, prd->x, p2->z, ctx);
+  ec_pow2 (p1->x, prd->x, ctx);
+  ec_pow2 (p1->z, p1->z, ctx);
+  ec_addm (sum->x, p2->x, p2->z, ctx);
+  ec_subm (p2->z, p2->x, p2->z, ctx);
+  ec_mulm (prd->x, p1->x, p1->z, ctx);
+  ec_subm (p1->z, p1->x, p1->z, ctx);
+  ec_pow2 (sum->x, sum->x, ctx);
+  ec_pow2 (sum->z, p2->z, ctx);
+  ec_mulm (prd->z, p1->z, ctx->a, ctx); /* CTX->A: (a-2)/4 */
+  ec_mulm (sum->z, sum->z, dif_x, ctx);
+  ec_addm (prd->z, p1->x, prd->z, ctx);
+  ec_mulm (prd->z, prd->z, p1->z, ctx);
+}
+
+
+/* RESULT = P1 + P2 */
+void
+_gcry_mpi_ec_add_points (mpi_point_t result,
+                         mpi_point_t p1, mpi_point_t p2,
+                         mpi_ec_t ctx)
+{
+  switch (ctx->model)
+    {
+    case MPI_EC_WEIERSTRASS:
+      add_points_weierstrass (result, p1, p2, ctx);
+      break;
+    case MPI_EC_MONTGOMERY:
+      add_points_montgomery (result, p1, p2, ctx);
+      break;
+    case MPI_EC_EDWARDS:
+      add_points_edwards (result, p1, p2, ctx);
+      break;
+    }
+}
+
+
+/* RESULT = P1 - P2  (Weierstrass version).*/
+static void
+sub_points_weierstrass (mpi_point_t result,
+                        mpi_point_t p1, mpi_point_t p2,
+                        mpi_ec_t ctx)
+{
+  (void)result;
+  (void)p1;
+  (void)p2;
+  (void)ctx;
+  log_fatal ("%s: %s not yet supported\n",
+             "_gcry_mpi_ec_sub_points", "Weierstrass");
+}
+
+
+/* RESULT = P1 - P2  (Montgomery version).*/
+static void
+sub_points_montgomery (mpi_point_t result,
+                       mpi_point_t p1, mpi_point_t p2,
+                       mpi_ec_t ctx)
+{
+  (void)result;
+  (void)p1;
+  (void)p2;
+  (void)ctx;
+  log_fatal ("%s: %s not yet supported\n",
+             "_gcry_mpi_ec_sub_points", "Montgomery");
+}
+
+
+/* RESULT = P1 - P2  (Twisted Edwards version).*/
+static void
+sub_points_edwards (mpi_point_t result,
+                    mpi_point_t p1, mpi_point_t p2,
+                    mpi_ec_t ctx)
+{
+  mpi_point_t p2i = _gcry_mpi_point_new (0);
+  point_set (p2i, p2);
+  mpi_sub (p2i->x, ctx->p, p2i->x);
+  add_points_edwards (result, p1, p2i, ctx);
+  _gcry_mpi_point_release (p2i);
+}
+
+
+/* RESULT = P1 - P2 */
+void
+_gcry_mpi_ec_sub_points (mpi_point_t result,
+                         mpi_point_t p1, mpi_point_t p2,
+                         mpi_ec_t ctx)
+{
+  switch (ctx->model)
+    {
+    case MPI_EC_WEIERSTRASS:
+      sub_points_weierstrass (result, p1, p2, ctx);
+      break;
+    case MPI_EC_MONTGOMERY:
+      sub_points_montgomery (result, p1, p2, ctx);
+      break;
+    case MPI_EC_EDWARDS:
+      sub_points_edwards (result, p1, p2, ctx);
+      break;
+    }
+}
+
+
+/* Scalar point multiplication - the main function for ECC.  If takes
+   an integer SCALAR and a POINT as well as the usual context CTX.
+   RESULT will be set to the resulting point. */
+void
+_gcry_mpi_ec_mul_point (mpi_point_t result,
+                        gcry_mpi_t scalar, mpi_point_t point,
+                        mpi_ec_t ctx)
+{
+  gcry_mpi_t x1, y1, z1, k, h, yy;
+  unsigned int i, loops;
+  mpi_point_struct p1, p2, p1inv;
+
+  if (ctx->model == MPI_EC_EDWARDS
+      || (ctx->model == MPI_EC_WEIERSTRASS
+          && mpi_is_secure (scalar)))
+    {
+      /* Simple left to right binary method.  Algorithm 3.27 from
+       * {author={Hankerson, Darrel and Menezes, Alfred J. and Vanstone, Scott},
+       *  title = {Guide to Elliptic Curve Cryptography},
+       *  year = {2003}, isbn = {038795273X},
+       *  url = {http://www.cacr.math.uwaterloo.ca/ecc/},
+       *  publisher = {Springer-Verlag New York, Inc.}} */
+      unsigned int nbits;
+      int j;
+
+      if (mpi_cmp (scalar, ctx->p) >= 0)
+        nbits = mpi_get_nbits (scalar);
+      else
+        nbits = mpi_get_nbits (ctx->p);
+
+      if (ctx->model == MPI_EC_WEIERSTRASS)
+        {
+          mpi_set_ui (result->x, 1);
+          mpi_set_ui (result->y, 1);
+          mpi_set_ui (result->z, 0);
+        }
+      else
+        {
+          mpi_set_ui (result->x, 0);
+          mpi_set_ui (result->y, 1);
+          mpi_set_ui (result->z, 1);
+        }
+
+      if (mpi_is_secure (scalar))
+        {
+          /* If SCALAR is in secure memory we assume that it is the
+             secret key we use constant time operation.  */
+          mpi_point_struct tmppnt;
+
+          point_init (&tmppnt);
+          point_resize (result, ctx);
+          point_resize (&tmppnt, ctx);
+          for (j=nbits-1; j >= 0; j--)
+            {
+              _gcry_mpi_ec_dup_point (result, result, ctx);
+              _gcry_mpi_ec_add_points (&tmppnt, result, point, ctx);
+              point_swap_cond (result, &tmppnt, mpi_test_bit (scalar, j), ctx);
+            }
+          point_free (&tmppnt);
+        }
+      else
+        {
+          for (j=nbits-1; j >= 0; j--)
+            {
+              _gcry_mpi_ec_dup_point (result, result, ctx);
+              if (mpi_test_bit (scalar, j))
+                _gcry_mpi_ec_add_points (result, result, point, ctx);
+            }
+        }
+      return;
+    }
+  else if (ctx->model == MPI_EC_MONTGOMERY)
+    {
+      unsigned int nbits;
+      int j;
+      mpi_point_struct p1_, p2_;
+      mpi_point_t q1, q2, prd, sum;
+      unsigned long sw;
+
+      /* Compute scalar point multiplication with Montgomery Ladder.
+         Note that we don't use Y-coordinate in the points at all.
+         RESULT->Y will be filled by zero.  */
+
+      nbits = mpi_get_nbits (scalar);
+      point_init (&p1);
+      point_init (&p2);
+      point_init (&p1_);
+      point_init (&p2_);
+      mpi_set_ui (p1.x, 1);
+      mpi_free (p2.x);
+      p2.x  = mpi_copy (point->x);
+      mpi_set_ui (p2.z, 1);
+
+      point_resize (&p1, ctx);
+      point_resize (&p2, ctx);
+      point_resize (&p1_, ctx);
+      point_resize (&p2_, ctx);
+
+      q1 = &p1;
+      q2 = &p2;
+      prd = &p1_;
+      sum = &p2_;
+
+      for (j=nbits-1; j >= 0; j--)
+        {
+          mpi_point_t t;
+
+          sw = mpi_test_bit (scalar, j);
+          point_swap_cond (q1, q2, sw, ctx);
+          montgomery_ladder (prd, sum, q1, q2, point->x, ctx);
+          point_swap_cond (prd, sum, sw, ctx);
+          t = q1;  q1 = prd;  prd = t;
+          t = q2;  q2 = sum;  sum = t;
+        }
+
+      mpi_clear (result->y);
+      sw = (nbits & 1);
+      point_swap_cond (&p1, &p1_, sw, ctx);
+
+      if (p1.z->nlimbs == 0)
+        {
+          mpi_set_ui (result->x, 1);
+          mpi_set_ui (result->z, 0);
+        }
+      else
+        {
+          z1 = mpi_new (0);
+          ec_invm (z1, p1.z, ctx);
+          ec_mulm (result->x, p1.x, z1, ctx);
+          mpi_set_ui (result->z, 1);
+          mpi_free (z1);
+        }
+
+      point_free (&p1);
+      point_free (&p2);
+      point_free (&p1_);
+      point_free (&p2_);
+      return;
+    }
+
+  x1 = mpi_alloc_like (ctx->p);
+  y1 = mpi_alloc_like (ctx->p);
+  h  = mpi_alloc_like (ctx->p);
+  k  = mpi_copy (scalar);
+  yy = mpi_copy (point->y);
+
+  if ( mpi_has_sign (k) )
+    {
+      k->sign = 0;
+      ec_invm (yy, yy, ctx);
+    }
+
+  if (!mpi_cmp_ui (point->z, 1))
+    {
+      mpi_set (x1, point->x);
+      mpi_set (y1, yy);
+    }
+  else
+    {
+      gcry_mpi_t z2, z3;
+
+      z2 = mpi_alloc_like (ctx->p);
+      z3 = mpi_alloc_like (ctx->p);
+      ec_mulm (z2, point->z, point->z, ctx);
+      ec_mulm (z3, point->z, z2, ctx);
+      ec_invm (z2, z2, ctx);
+      ec_mulm (x1, point->x, z2, ctx);
+      ec_invm (z3, z3, ctx);
+      ec_mulm (y1, yy, z3, ctx);
+      mpi_free (z2);
+      mpi_free (z3);
+    }
+  z1 = mpi_copy (mpi_const (MPI_C_ONE));
+
+  mpi_mul (h, k, mpi_const (MPI_C_THREE)); /* h = 3k */
+  loops = mpi_get_nbits (h);
+  if (loops < 2)
+    {
+      /* If SCALAR is zero, the above mpi_mul sets H to zero and thus
+         LOOPs will be zero.  To avoid an underflow of I in the main
+         loop we set LOOP to 2 and the result to (0,0,0).  */
+      loops = 2;
+      mpi_clear (result->x);
+      mpi_clear (result->y);
+      mpi_clear (result->z);
+    }
+  else
+    {
+      mpi_set (result->x, point->x);
+      mpi_set (result->y, yy);
+      mpi_set (result->z, point->z);
+    }
+  mpi_free (yy); yy = NULL;
+
+  p1.x = x1; x1 = NULL;
+  p1.y = y1; y1 = NULL;
+  p1.z = z1; z1 = NULL;
+  point_init (&p2);
+  point_init (&p1inv);
+
+  /* Invert point: y = p - y mod p  */
+  point_set (&p1inv, &p1);
+  ec_subm (p1inv.y, ctx->p, p1inv.y, ctx);
+
+  for (i=loops-2; i > 0; i--)
+    {
+      _gcry_mpi_ec_dup_point (result, result, ctx);
+      if (mpi_test_bit (h, i) == 1 && mpi_test_bit (k, i) == 0)
+        {
+          point_set (&p2, result);
+          _gcry_mpi_ec_add_points (result, &p2, &p1, ctx);
+        }
+      if (mpi_test_bit (h, i) == 0 && mpi_test_bit (k, i) == 1)
+        {
+          point_set (&p2, result);
+          _gcry_mpi_ec_add_points (result, &p2, &p1inv, ctx);
+        }
+    }
+
+  point_free (&p1);
+  point_free (&p2);
+  point_free (&p1inv);
+  mpi_free (h);
+  mpi_free (k);
+}
+
+
+/* Return true if POINT is on the curve described by CTX.  */
+int
+_gcry_mpi_ec_curve_point (gcry_mpi_point_t point, mpi_ec_t ctx)
+{
+  int res = 0;
+  gcry_mpi_t x, y, w;
+
+  x = mpi_new (0);
+  y = mpi_new (0);
+  w = mpi_new (0);
+
+  /* Check that the point is in range.  This needs to be done here and
+   * not after conversion to affine coordinates.  */
+  if (mpi_cmpabs (point->x, ctx->p) >= 0)
+    goto leave;
+  if (mpi_cmpabs (point->y, ctx->p) >= 0)
+    goto leave;
+  if (mpi_cmpabs (point->z, ctx->p) >= 0)
+    goto leave;
+
+  switch (ctx->model)
+    {
+    case MPI_EC_WEIERSTRASS:
+      {
+        gcry_mpi_t xxx;
+
+        if (_gcry_mpi_ec_get_affine (x, y, point, ctx))
+          goto leave;
+
+        xxx = mpi_new (0);
+
+        /* y^2 == x^3 + a·x + b */
+        ec_pow2 (y, y, ctx);
+
+        ec_pow3 (xxx, x, ctx);
+        ec_mulm (w, ctx->a, x, ctx);
+        ec_addm (w, w, ctx->b, ctx);
+        ec_addm (w, w, xxx, ctx);
+
+        if (!mpi_cmp (y, w))
+          res = 1;
+
+        _gcry_mpi_release (xxx);
+      }
+      break;
+    case MPI_EC_MONTGOMERY:
+      {
+#define xx y
+        /* With Montgomery curve, only X-coordinate is valid.  */
+        if (_gcry_mpi_ec_get_affine (x, NULL, point, ctx))
+          goto leave;
+
+        /* The equation is: b * y^2 == x^3 + a · x^2 + x */
+        /* We check if right hand is quadratic residue or not by
+           Euler's criterion.  */
+        /* CTX->A has (a-2)/4 and CTX->B has b^-1 */
+        ec_mulm (w, ctx->a, mpi_const (MPI_C_FOUR), ctx);
+        ec_addm (w, w, mpi_const (MPI_C_TWO), ctx);
+        ec_mulm (w, w, x, ctx);
+        ec_pow2 (xx, x, ctx);
+        ec_addm (w, w, xx, ctx);
+        ec_addm (w, w, mpi_const (MPI_C_ONE), ctx);
+        ec_mulm (w, w, x, ctx);
+        ec_mulm (w, w, ctx->b, ctx);
+#undef xx
+        /* Compute Euler's criterion: w^(p-1)/2 */
+#define p_minus1 y
+        ec_subm (p_minus1, ctx->p, mpi_const (MPI_C_ONE), ctx);
+        mpi_rshift (p_minus1, p_minus1, 1);
+        ec_powm (w, w, p_minus1, ctx);
+
+        res = !mpi_cmp_ui (w, 1);
+#undef p_minus1
+      }
+      break;
+    case MPI_EC_EDWARDS:
+      {
+        if (_gcry_mpi_ec_get_affine (x, y, point, ctx))
+          goto leave;
+
+        /* a · x^2 + y^2 - 1 - b · x^2 · y^2 == 0 */
+        ec_pow2 (x, x, ctx);
+        ec_pow2 (y, y, ctx);
+        if (ctx->dialect == ECC_DIALECT_ED25519)
+          mpi_sub (w, ctx->p, x);
+        else
+          ec_mulm (w, ctx->a, x, ctx);
+        ec_addm (w, w, y, ctx);
+        ec_subm (w, w, mpi_const (MPI_C_ONE), ctx);
+        ec_mulm (x, x, y, ctx);
+        ec_mulm (x, x, ctx->b, ctx);
+        ec_subm (w, w, x, ctx);
+        if (!mpi_cmp_ui (w, 0))
+          res = 1;
+      }
+      break;
+    }
+
+ leave:
+  _gcry_mpi_release (w);
+  _gcry_mpi_release (x);
+  _gcry_mpi_release (y);
+
+  return res;
+}
+
+
+int
+_gcry_mpi_ec_bad_point (gcry_mpi_point_t point, mpi_ec_t ctx)
+{
+  int i;
+  gcry_mpi_t x_bad;
+
+  for (i = 0; (x_bad = ctx->t.scratch[i]); i++)
+    if (!mpi_cmp (point->x, x_bad))
+      return 1;
+
+  return 0;
+}