Integrate ecc_mul_g.

ChangeLog

 2013-02-15  Niels Möller  <nisse@lysator.liu.se>
 
+	Integrate ecc_mul_g.
+	* ecc.h: New file.
+	* ecc-j-to-a.c: New file.
+	* ecc-size.c: New file.
+	* ecc-add-jja.c: New file.
+	* ecc-dup-jj.c: New file.
+	* ecc-mul-g.c: New file.
+	* sec-tabselect.c: New file.
+	* Makefile.in (hogweed_SOURCES): Added new files.
+	(HEADERS): Added ecc.h
+	* testsuite/ecc-mul-g-test.c: New file.
+	* testsuite/Makefile.in (TS_HOGWEED_SOURCES): Added
+	ecc-mul-g-test.c.
+	* testsuite/testutils.c (xalloc_limbs): New function.
+	(test_mpn): New function.
+	(test_ecc_point): New function.
+	(test_ecc_mul_a): New function.
+	(test_ecc_mul_j): New function.
+	* testsuite/testutils.h: Corresponding declarations.
+
 	Integrate ECC internals.
 	* ecc-curve.h: New file.
 	* ecc-internal.h: New file.

Makefile.in

@@ -127,12 +127,14 @@ hogweed_SOURCES = sexp.c sexp-format.c \
 		  gmp-glue.c cnd-copy.c \
 		  ecc-mod.c ecc-generic-modp.c ecc-generic-modq.c \
 		  ecc-modp.c ecc-modq.c ecc-generic-redc.c \
-		  ecc-192.c ecc-224.c ecc-256.c ecc-384.c ecc-521.c
+		  ecc-192.c ecc-224.c ecc-256.c ecc-384.c ecc-521.c \
+		  ecc-size.c ecc-j-to-a.c ecc-dup-jj.c ecc-add-jja.c \
+		  ecc-mul-g.c
 
 HEADERS = aes.h arcfour.h arctwo.h asn1.h bignum.h blowfish.h \
 	  base16.h base64.h buffer.h camellia.h cast128.h \
 	  cbc.h ctr.h \
-	  des.h des-compat.h dsa.h ecc-curve.h \
+	  des.h des-compat.h dsa.h ecc-curve.h ecc.h \
 	  gcm.h gosthash94.h hmac.h \
 	  knuth-lfib.h \
 	  macros.h \

ecc-add-jja.c

+/* ecc-dup-jj.c */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2013 Niels Möller
+ *  
+ * The nettle library 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.
+ * 
+ * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02111-1301, USA.
+ */
+
+/* Development of Nettle's ECC support was funded by Internetfonden. */
+
+#if HAVE_CONFIG_H
+# include "config.h"
+#endif
+
+#include "ecc.h"
+#include "ecc-internal.h"
+
+/* NOTE: Behaviour for corner cases:
+
+   + p = 0   ==>  r = 0 (invalid except if also q = 0)
+
+   + q = 0   ==>  r = invalid
+
+   + p = -q  ==>  r = 0, correct!
+
+   + p = q   ==>  r = 0, invalid
+*/
+
+mp_size_t
+ecc_add_jja_itch (const struct ecc_curve *ecc)
+{
+  return ECC_ADD_JJA_ITCH (ecc->size);
+}
+
+void
+ecc_add_jja (const struct ecc_curve *ecc,
+	     mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
+	     mp_limb_t *scratch)
+{
+  /* Formulas, from djb,
+     http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b):
+
+     Computation		Operation	Live variables
+     
+      ZZ = Z_1^2		sqr		ZZ
+      H = X_2*ZZ - X_1		mul (djb: U_2)	ZZ, H
+      HH = H^2			sqr		ZZ, H, HH
+      ZZZ = ZZ*Z_1		mul		ZZ, H, HH, ZZZ
+      Z_3 = (Z_1+H)^2-ZZ-HH	sqr		H, HH, ZZZ
+      W = 2 (Y_2*ZZZ - Y_1)	mul (djb: S_2)	H, HH, W
+      I = 4*HH					H, W, I
+      J = H*I			mul		W, I, J
+      V = X_1*I			mul		W, J, V
+      X_3 = W^2-J-2*V		sqr		W, J, V
+      Y_3 = W*(V-X_3)-2*Y_1*J	mul, mul
+  */
+#define zz  scratch
+#define h  (scratch + ecc->size)
+#define hh (scratch + 2*ecc->size)
+#define w  (scratch + 3*ecc->size)
+#define j  (scratch + 4*ecc->size)
+#define v   scratch
+
+#define x1  p
+#define y1 (p + ecc->size)
+#define z1 (p + 2*ecc->size)
+#define x2  q
+#define y2 (q + ecc->size)
+
+  /* zz */
+  ecc_modp_sqr (ecc, zz, z1);
+  /* h*/
+  ecc_modp_mul (ecc, h, x2, zz);
+  ecc_modp_sub (ecc, h, h, x1);
+  /* hh */
+  ecc_modp_sqr (ecc, hh, h);
+  /* Do z^3 early, store at w. */
+  ecc_modp_mul (ecc, w, zz, z1);
+  /* z_3, use j area for scratch */
+  ecc_modp_add (ecc, r + 2*ecc->size, p + 2*ecc->size, h);
+  ecc_modp_sqr (ecc, j, r + 2*ecc->size);
+  ecc_modp_sub (ecc, j, j, zz);
+  ecc_modp_sub (ecc, r + 2*ecc->size, j, hh);
+  
+  /* w */
+  ecc_modp_mul (ecc, j, y2, w);
+  ecc_modp_sub (ecc, w, j, y1);
+  ecc_modp_mul_1 (ecc, w, w, 2);
+  
+  /* i replaces hh, j */
+  ecc_modp_mul_1 (ecc, hh, hh, 4);
+  ecc_modp_mul (ecc, j, hh, h);
+
+  /* v */
+  ecc_modp_mul (ecc, v, x1, hh);
+
+  /* x_3, use (h, hh) as sqratch */  
+  ecc_modp_sqr (ecc, h, w);
+  ecc_modp_sub (ecc, r, h, j);
+  ecc_modp_submul_1 (ecc, r, v, 2);
+
+  /* y_3, use (h, hh) as sqratch */
+  ecc_modp_mul (ecc, h, y1, j); /* frees j */
+  ecc_modp_sub (ecc, r + ecc->size, v, r);
+  ecc_modp_mul (ecc, j, r + ecc->size, w);
+  ecc_modp_submul_1 (ecc, j, h, 2);
+  mpn_copyi (r + ecc->size, j, ecc->size);
+}

ecc-dup-jj.c

+/* ecc-dup-jj.c */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2013 Niels Möller
+ *  
+ * The nettle library 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.
+ * 
+ * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02111-1301, USA.
+ */
+
+/* Development of Nettle's ECC support was funded by Internetfonden. */
+
+#if HAVE_CONFIG_H
+# include "config.h"
+#endif
+
+#include "ecc.h"
+#include "ecc-internal.h"
+
+/* NOTE: Behaviour for corner cases:
+
+   + p = 0  ==>  r = 0, correct!
+*/
+mp_size_t
+ecc_dup_jj_itch (const struct ecc_curve *ecc)
+{
+  return ECC_DUP_JJ_ITCH (ecc->size);
+}
+
+void
+ecc_dup_jj (const struct ecc_curve *ecc,
+	    mp_limb_t *r, const mp_limb_t *p,
+	    mp_limb_t *scratch)
+{
+  /* Formulas (from djb,
+     http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b):
+
+     Computation			Operation	Live variables
+     delta = z^2			sqr		delta
+     gamma = y^2			sqr		delta, gamma
+     z' = (y+z)^2-gamma-delta		sqr		delta, gamma
+     alpha = 3*(x-delta)*(x+delta)	mul		gamma, beta, alpha
+     beta = x*gamma			mul		gamma, beta, alpha
+     x' = alpha^2-8*beta		sqr		gamma, beta, alpha
+     y' = alpha*(4*beta-x')-8*gamma^2	mul, sqr
+  */
+
+#define delta  scratch
+#define gamma (scratch + ecc->size)
+#define beta  (scratch + 2*ecc->size)
+#define g2    (scratch + 3*ecc->size)
+#define sum   (scratch + 4*ecc->size)
+#define alpha  scratch /* Overlap delta */
+  
+#define xp p
+#define yp (p + ecc->size)
+#define zp (p + 2*ecc->size)
+  
+  /* delta */
+  ecc_modp_sqr (ecc, delta, zp);
+
+  /* gamma */
+  ecc_modp_sqr (ecc, gamma, yp);
+
+  /* z'. Can use beta area as scratch. */
+  ecc_modp_add (ecc, r + 2*ecc->size, yp, zp);
+  ecc_modp_sqr (ecc, beta, r + 2*ecc->size);
+  ecc_modp_sub (ecc, beta, beta, gamma);
+  ecc_modp_sub (ecc, r + 2*ecc->size, beta, delta);
+  
+  /* alpha. Can use beta area as scratch, and overwrite delta. */
+  ecc_modp_add (ecc, sum, xp, delta);
+  ecc_modp_sub (ecc, delta, xp, delta);
+  ecc_modp_mul (ecc, beta, sum, delta);
+  ecc_modp_mul_1 (ecc, alpha, beta, 3);
+
+  /* beta */
+  ecc_modp_mul (ecc, beta, xp, gamma);
+
+  /* Do gamma^2 and 4*beta early, to get them out of the way. We can
+     then use the old area at gamma as scratch. */
+  ecc_modp_sqr (ecc, g2, gamma);
+  ecc_modp_mul_1 (ecc, sum, beta, 4);
+  
+  /* x' */
+  ecc_modp_sqr (ecc, gamma, alpha);   /* Overwrites gamma and beta */
+  ecc_modp_submul_1 (ecc, gamma, sum, 2);
+  mpn_copyi (r, gamma, ecc->size);
+
+  /* y' */
+  ecc_modp_sub (ecc, sum, sum, r);
+  ecc_modp_mul (ecc, gamma, sum, alpha);
+  ecc_modp_submul_1 (ecc, gamma, g2, 8);
+  mpn_copyi (r + ecc->size, gamma, ecc->size);
+}

ecc-j-to-a.c

+/* ecc-j-to-a.c */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2013 Niels Möller
+ *  
+ * The nettle library 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.
+ * 
+ * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02111-1301, USA.
+ */
+
+/* Development of Nettle's ECC support was funded by Internetfonden. */
+
+#if HAVE_CONFIG_H
+# include "config.h"
+#endif
+
+#include "ecc.h"
+#include "ecc-internal.h"
+
+mp_size_t
+ecc_j_to_a_itch (const struct ecc_curve *ecc)
+{
+  /* Needs 2*ecc->size + scratch for ecc_modq_inv */
+  return ECC_J_TO_A_ITCH (ecc->size);
+}
+
+void
+ecc_j_to_a (const struct ecc_curve *ecc,
+	    int flags,
+	    mp_limb_t *r, const mp_limb_t *p,
+	    mp_limb_t *scratch)
+{
+#define izp   scratch
+#define up   (scratch + ecc->size)
+#define iz2p (scratch + ecc->size)
+#define iz3p (scratch + 2*ecc->size)
+#define tp    scratch
+
+  mp_limb_t cy;
+
+  if (ecc->use_redc)
+    {
+      /* Set v = (r_z / B^2)^-1,
+
+	 r_x = p_x v^2 / B^3 =  ((v/B * v)/B * p_x)/B
+	 r_y = p_y v^3 / B^4 = (((v/B * v)/B * v)/B * p_x)/B
+
+	 Skip the first redc, if we want to stay in Montgomery
+	 representation.
+      */
+
+      mpn_copyi (up, p + 2*ecc->size, ecc->size);
+      mpn_zero (up + ecc->size, ecc->size);
+      ecc->redc (ecc, up);
+      mpn_zero (up + ecc->size, ecc->size);
+      ecc->redc (ecc, up);
+
+      ecc_modp_inv (ecc, izp, up, up + ecc->size);
+
+      if (flags & 1)
+	{
+	  /* Divide this common factor by B */
+	  mpn_copyi (iz3p, izp, ecc->size);
+	  mpn_zero (iz3p + ecc->size, ecc->size);
+	  ecc->redc (ecc, iz3p);
+      
+	  ecc_modp_mul (ecc, iz2p, izp, iz3p);
+	}
+      else
+	ecc_modp_sqr (ecc, iz2p, izp);	
+    }
+  else
+    {
+      /* Set s = p_z^{-1}, r_x = p_x s^2, r_y = p_y s^3 */
+
+      mpn_copyi (up, p+2*ecc->size, ecc->size); /* p_z */
+      ecc_modp_inv (ecc, izp, up, up + ecc->size);
+
+      ecc_modp_sqr (ecc, iz2p, izp);
+    }
+
+  ecc_modp_mul (ecc, iz3p, iz2p, p);
+  /* ecc_modp (and ecc_modp_mul) may return a value up to 2p - 1, so
+     do a conditional subtraction. */
+  cy = mpn_sub_n (r, iz3p, ecc->p, ecc->size);
+  cnd_copy (cy, r, iz3p, ecc->size);
+
+  if (flags & 2)
+    /* Skip y coordinate */
+    return;
+
+  ecc_modp_mul (ecc, iz3p, iz2p, izp);
+  ecc_modp_mul (ecc, tp, iz3p, p + ecc->size);
+  /* And a similar subtraction. */
+  cy = mpn_sub_n (r + ecc->size, tp, ecc->p, ecc->size);
+  cnd_copy (cy, r + ecc->size, tp, ecc->size);
+
+#undef izp
+#undef up
+#undef iz2p
+#undef iz3p
+#undef tp
+}

ecc-mul-g.c

+/* ecc-mul-g.c */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2013 Niels Möller
+ *
+ * The nettle library 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.
+ *
+ * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02111-1301, USA.
+ */
+
+/* Development of Nettle's ECC support was funded by Internetfonden. */
+
+#if HAVE_CONFIG_H
+# include "config.h"
+#endif
+
+#include <assert.h>
+
+#include "ecc.h"
+#include "ecc-internal.h"
+
+mp_size_t
+ecc_mul_g_itch (const struct ecc_curve *ecc)
+{
+  /* Needs 3*ecc->size + scratch for ecc_add_jja. */
+  return ECC_MUL_G_ITCH (ecc->size);
+}
+
+void
+ecc_mul_g (const struct ecc_curve *ecc, mp_limb_t *r,
+	   const mp_limb_t *np, mp_limb_t *scratch)
+{
+  /* Scratch need determined by the ecc_add_jja call. Current total is
+     9 * ecc->size, at most 648 bytes. */
+#define tp scratch
+#define scratch_out (scratch + 3*ecc->size)
+
+  unsigned k, c;
+  unsigned i, j;
+  unsigned bit_rows;
+
+  int is_zero;
+
+  k = ecc->pippenger_k;
+  c = ecc->pippenger_c;
+
+  bit_rows = (ecc->bit_size + k - 1) / k;
+  
+  mpn_zero (r, 3*ecc->size);
+  
+  for (i = k, is_zero = 1; i-- > 0; )
+    {
+      ecc_dup_jj (ecc, r, r, scratch);
+      for (j = 0; j * c < bit_rows; j++)
+	{
+	  unsigned bits;
+	  mp_bitcnt_t bit_index;
+	  
+	  /* Extract c bits from n, stride k, starting at i + kcj,
+	     ending at i + k (cj + c - 1)*/
+	  for (bits = 0, bit_index = i + k*(c*j+c); bit_index > i + k*c*j; )
+	    {
+	      mp_size_t limb_index;
+	      unsigned shift;
+	      
+	      bit_index -= k;
+
+	      limb_index = bit_index / GMP_NUMB_BITS;
+	      if (limb_index >= ecc->size)
+		continue;
+
+	      shift = bit_index % GMP_NUMB_BITS;
+	      bits = (bits << 1) | ((np[limb_index] >> shift) & 1);
+	    }
+	  sec_tabselect (tp, 2*ecc->size,
+			 (ecc->pippenger_table
+			  + (2*ecc->size * (mp_size_t) j << c)),
+			 1<<c, bits);
+	  cnd_copy (is_zero, r, tp, 2*ecc->size);
+	  cnd_copy (is_zero, r + 2*ecc->size, ecc->unit, ecc->size);
+	  
+	  ecc_add_jja (ecc, tp, r, tp, scratch_out);
+	  /* Use the sum when valid. ecc_add_jja produced garbage if
+	     is_zero != 0 or bits == 0, . */	  
+	  cnd_copy (bits & (is_zero - 1), r, tp, 3*ecc->size);
+	  is_zero &= (bits == 0);
+	}
+    }
+#undef tp
+#undef scratch_out
+}

ecc-size.c

+/* ecc-size.c */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2013 Niels Möller
+ *  
+ * The nettle library 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.
+ * 
+ * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02111-1301, USA.
+ */
+
+/* Development of Nettle's ECC support was funded by Internetfonden. */
+
+#if HAVE_CONFIG_H
+# include "config.h"
+#endif
+
+#include "ecc.h"
+#include "ecc-internal.h"
+
+mp_size_t
+ecc_size (const struct ecc_curve *ecc)
+{
+  return ecc->size;
+}
+
+mp_size_t
+ecc_size_a (const struct ecc_curve *ecc)
+{
+  return 2*ecc->size;
+}
+
+mp_size_t
+ecc_size_j (const struct ecc_curve *ecc)
+{
+  return 3*ecc->size;
+}

ecc.h

+/* ecc.h */
+
+/* nettle, low-level cryptographics library
+ *
+ * Copyright (C) 2013 Niels Möller
+ *  
+ * The nettle library 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.
+ * 
+ * The nettle library 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 the nettle library; see the file COPYING.LIB.  If not, write to
+ * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
+ * MA 02111-1301, USA.
+ */
+
+/* Development of Nettle's ECC support was funded by Internetfonden. */
+
+#ifndef NETTLE_ECC_H_INCLUDED
+#define NETTLE_ECC_H_INCLUDED
+
+#include <stdint.h>
+
+#include <gmp.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Name mangling */
+#define ecc_size nettle_ecc_size
+#define ecc_size_a nettle_ecc_size_a
+#define ecc_size_j nettle_ecc_size_j
+#define ecc_a_to_a_itch nettle_ecc_a_to_a_itch
+#define ecc_a_to_a nettle_ecc_a_to_a
+#define ecc_a_to_j nettle_ecc_a_to_j
+#define ecc_j_to_a_itch nettle_ecc_j_to_a_itch
+#define ecc_j_to_a nettle_ecc_j_to_a
+#define ecc_dup_ja_itch nettle_ecc_dup_ja_itch
+#define ecc_dup_ja nettle_ecc_dup_ja
+#define ecc_dup_jj_itch nettle_ecc_dup_jj_itch
+#define ecc_dup_jj nettle_ecc_dup_jj
+#define ecc_add_jja_itch nettle_ecc_add_jja_itch
+#define ecc_add_jja nettle_ecc_add_jja
+#define ecc_add_jjj_itch nettle_ecc_add_jjj_itch
+#define ecc_add_jjj nettle_ecc_add_jjj
+#define ecc_mul_g_itch nettle_ecc_mul_g_itch
+#define ecc_mul_g nettle_ecc_mul_g
+#define ecc_mul_a_itch nettle_ecc_mul_a_itch
+#define ecc_mul_a nettle_ecc_mul_a
+
+struct ecc_curve;
+
+/* Points on a curve are represented as arrays of mp_limb_t. For some
+   curves, point coordinates are represented in montgomery form. We
+   use either affine coordinates x,y, or Jacobian coordinates X, Y, Z,
+   where x = X/Z^2 and y = X/Z^2.
+
+   Since we use additive notation for the groups, the infinity point
+   on the curve is denoted 0. The infinity point can be represented
+   with x = y = 0 in affine coordinates, and Z = 0 in Jacobian
+   coordinates. However, note that most of the ECC functions do *not*
+   support infinity as an input or output.
+*/
+
+/* FIXME: Also provided some compile time constants? */
+
+/* Returns the size of a single coordinate. */
+mp_size_t
+ecc_size (const struct ecc_curve *ecc);
+
+/* Size of a point, using affine coordinates x, y. */
+mp_size_t
+ecc_size_a (const struct ecc_curve *ecc);
+
+/* Size of a point, using jacobian coordinates X, Y and Z. */
+mp_size_t
+ecc_size_j (const struct ecc_curve *ecc);
+
+/* FIXME: Rename the low-level (and side-channel silent) functions to
+   _ecc_*, and provide public ecc_* functions which handle the
+   infinity points properly? */
+
+/* Converts the affine coordinates of a point into montgomery form, if
+   used for this curve. */
+mp_size_t
+ecc_a_to_a_itch (const struct ecc_curve *ecc);
+void
+ecc_a_to_a (const struct ecc_curve *ecc,
+	    mp_limb_t *r, const mp_limb_t *p,
+	    mp_limb_t *scratch);
+
+/* Converts a point P in affine coordinates into a point R in jacobian
+   coordinates. If INITIAL is non-zero, and the curve uses montgomery