Integrate ecc_mul_a.

ChangeLog

 2013-02-15  Niels Möller  <nisse@lysator.liu.se>
 
+	Integrate ecc_mul_a.
+	* ecc-a-to-j.c: New file.
+	* ecc-add-jjj.c: New file.
+	* ecc-mul-a.c: New file.
+	* Makefile.in (hogweed_SOURCES): Added new files.
+	* testsuite/ecc-mul-a-test.c: New file.
+	* testsuite/Makefile.in (TS_HOGWEED_SOURCES): Added
+	ecc-mul-a-test.c.
+
 	* testsuite/testutils.c: Removed redundant includes.
 	(die): New function.
 

Makefile.in

@@ -128,8 +128,9 @@ hogweed_SOURCES = sexp.c sexp-format.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-size.c ecc-j-to-a.c ecc-dup-jj.c ecc-add-jja.c \
-		  ecc-mul-g.c
+		  ecc-size.c ecc-j-to-a.c ecc-a-to-j.c \
+		  ecc-dup-jj.c ecc-add-jja.c ecc-add-jjj.c \
+		  ecc-mul-g.c ecc-mul-a.c
 
 HEADERS = aes.h arcfour.h arctwo.h asn1.h bignum.h blowfish.h \
 	  base16.h base64.h buffer.h camellia.h cast128.h \

ecc-a-to-j.c

+/* ecc-a-to-j.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"
+
+void
+ecc_a_to_j (const struct ecc_curve *ecc,
+	    int initial,
+	    mp_limb_t *r, const mp_limb_t *p)
+{
+  if (ecc->use_redc && initial)
+    {
+      mpn_copyd (r + ecc->size, p, 2*ecc->size);
+
+      mpn_zero (r, ecc->size);
+      ecc->modp (ecc, r);
+
+      mpn_zero (r + ecc->size, ecc->size);
+      ecc->modp (ecc, r + ecc->size);
+    }
+  else if (r != p)
+    mpn_copyi (r, p, 2*ecc->size);
+
+  mpn_copyi (r + 2*ecc->size, ecc->unit, ecc->size);
+}

ecc-add-jjj.c

+/* ecc-add-jjj.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_add_jjj_itch (const struct ecc_curve *ecc)
+{
+  /* Needs 8 * ecc->size */
+  return ECC_ADD_JJJ_ITCH (ecc->size);
+}
+
+void
+ecc_add_jjj (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#addition-add-2007-bl:
+
+     Computation		Operation	Live variables
+
+      Z1Z1 = Z1^2		sqr		Z1Z1
+      Z2Z2 = Z2^2		sqr		Z1Z1, Z2Z2
+      U1 = X1*Z2Z2		mul		Z1Z1, Z2Z2, U1
+      U2 = X2*Z1Z1		mul		Z1Z1, Z2Z2, U1, U2
+      H = U2-U1					Z1Z1, Z2Z2, U1, H
+      Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H sqr, mul	Z1Z1, Z2Z2, U1, H
+      S1 = Y1*Z2*Z2Z2		mul, mul	Z1Z1, U1, H, S1
+      S2 = Y2*Z1*Z1Z1		mul, mul	U1, H, S1, S2
+      W = 2*(S2-S1)	(djb: r)		U1, H, S1, W
+      I = (2*H)^2		sqr		U1, H, S1, W, I
+      J = H*I			mul		U1, S1, W, J, V
+      V = U1*I			mul		S1, W, J, V
+      X3 = W^2-J-2*V		sqr		S1, W, J, V
+      Y3 = W*(V-X3)-2*S1*J	mul, mul
+  */
+  mp_limb_t *z1z1 = scratch;
+  mp_limb_t *z2z2 = scratch + ecc->size;
+  mp_limb_t *u1   = scratch + 2*ecc->size;
+  mp_limb_t *u2   = scratch + 3*ecc->size;
+  mp_limb_t *s1   = scratch; /* overlap z1z1 */
+  mp_limb_t *s2   = scratch + ecc->size; /* overlap z2z2 */
+  mp_limb_t *i    = scratch + 4*ecc->size;
+  mp_limb_t *j    = scratch + 5*ecc->size;
+  mp_limb_t *v    = scratch + 6*ecc->size;
+
+  /* z1^2, z2^2, u1 = x1 x2^2, u2 = x2 z1^2 - u1 */
+  ecc_modp_sqr (ecc, z1z1, p + 2*ecc->size);
+  ecc_modp_sqr (ecc, z2z2, q + 2*ecc->size);
+  ecc_modp_mul (ecc, u1, p, z2z2);
+  ecc_modp_mul (ecc, u2, q, z1z1);
+  ecc_modp_sub (ecc, u2, u2, u1);  /* Store h in u2 */
+
+  /* z3, use i, j, v as scratch, result at i. */
+  ecc_modp_add (ecc, i, p + 2*ecc->size, q + 2*ecc->size);
+  ecc_modp_sqr (ecc, v, i);
+  ecc_modp_sub (ecc, v, v, z1z1);
+  ecc_modp_sub (ecc, v, v, z2z2);
+  ecc_modp_mul (ecc, i, v, u2);
+  /* Delayed write, to support in-place operation. */
+
+  /* s1 = y1 z2^3, s2 = y2 z1^3, scratch at j and v */
+  ecc_modp_mul (ecc, j, z1z1, p + 2*ecc->size); /* z1^3 */
+  ecc_modp_mul (ecc, v, z2z2, q + 2*ecc->size); /* z2^3 */
+  ecc_modp_mul (ecc, s1, p + ecc->size, v);
+  ecc_modp_mul (ecc, v, j, q + ecc->size);
+  ecc_modp_sub (ecc, s2, v, s1);
+  ecc_modp_mul_1 (ecc, s2, s2, 2);
+
+  /* Store z3 */
+  mpn_copyi (r + 2*ecc->size, i, ecc->size);
+
+  /* i, j, v */
+  ecc_modp_sqr (ecc, i, u2);
+  ecc_modp_mul_1 (ecc, i, i, 4);
+  ecc_modp_mul (ecc, j, u2, i);
+  ecc_modp_mul (ecc, v, u1, i);
+
+  /* now, u1, u2 and i are free for reuse .*/
+  /* x3, use u1, u2 as scratch */
+  ecc_modp_sqr (ecc, u1, s2);
+  ecc_modp_sub (ecc, r, u1, j);
+  ecc_modp_submul_1 (ecc, r, v, 2);
+
+  /* y3 */
+  ecc_modp_mul (ecc, u1, s1, j); /* Frees j */
+  ecc_modp_sub (ecc, u2, v, r);  /* Frees v */
+  ecc_modp_mul (ecc, i, s2, u2);
+  ecc_modp_submul_1 (ecc, i, u1, 2);
+  mpn_copyi (r + ecc->size, i, ecc->size);
+}

ecc-mul-a.c

+/* ecc-mul-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 <assert.h>
+
+#include "ecc.h"
+#include "ecc-internal.h"
+
+mp_size_t
+ecc_mul_a_itch (const struct ecc_curve *ecc)
+{
+  /* Binary algorithm needs 6*ecc->size + scratch for ecc_add_jja.
+     Current total is 12 ecc->size, at most 864 bytes.
+
+     Window algorithm needs (3<<w) * ecc->size for the table,
+     3*ecc->size for a temporary point, and scratch for
+     ecc_add_jjj. */
+  return ECC_MUL_A_ITCH (ecc->size);
+}
+
+#if ECC_MUL_A_WBITS == 0
+void
+ecc_mul_a (const struct ecc_curve *ecc,
+	   int initial, mp_limb_t *r,
+	   const mp_limb_t *np, const mp_limb_t *p,
+	   mp_limb_t *scratch)
+{
+#define tp scratch
+#define pj (scratch + 3*ecc->size)
+#define scratch_out (scratch + 6*ecc->size)
+
+  int is_zero;
+
+  unsigned i;
+
+  ecc_a_to_j (ecc, initial, pj, p);
+  mpn_zero (r, 3*ecc->size);
+  
+  for (i = ecc->size, is_zero = 1; i-- > 0; )
+    {
+      mp_limb_t w = np[i];
+      mp_limb_t bit;
+
+      for (bit = (mp_limb_t) 1 << (GMP_NUMB_BITS - 1);
+	   bit > 0;
+	   bit >>= 1)
+	{
+	  int digit;
+
+	  ecc_dup_jj (ecc, r, r, scratch_out);
+	  ecc_add_jja (ecc, tp, r, pj, scratch_out);
+
+	  digit = (w & bit) > 0;
+	  /* If is_zero is set, r is the zero point,
+	     and ecc_add_jja produced garbage. */
+	  cnd_copy (is_zero, tp, pj, 3*ecc->size);
+	  is_zero &= ~digit;
+	  /* If we had a one-bit, use the sum. */
+	  cnd_copy (digit, r, tp, 3*ecc->size);
+	}
+    }
+}
+#else /* ECC_MUL_A_WBITS > 1 */
+
+#define TABLE_SIZE (1U << ECC_MUL_A_WBITS)
+#define TABLE_MASK (TABLE_SIZE - 1)
+
+#define TABLE(j) (table + (j) * 3*ecc->size)
+
+static void
+table_init (const struct ecc_curve *ecc,
+	    mp_limb_t *table, unsigned bits,
+	    int initial, const mp_limb_t *p,
+	    mp_limb_t *scratch)
+{
+  unsigned size = 1 << bits;
+  unsigned j;
+
+  mpn_zero (TABLE(0), 3*ecc->size);
+  ecc_a_to_j (ecc, initial, TABLE(1), p);
+
+  for (j = 2; j < size; j += 2)
+    {
+      ecc_dup_jj (ecc, TABLE(j), TABLE(j/2), scratch);
+      ecc_add_jja (ecc, TABLE(j+1), TABLE(j), TABLE(1), scratch);
+    }  
+}
+
+void
+ecc_mul_a (const struct ecc_curve *ecc,
+	   int initial, mp_limb_t *r,
+	   const mp_limb_t *np, const mp_limb_t *p,
+	   mp_limb_t *scratch)
+{
+#define tp scratch
+#define table (scratch + 3*ecc->size)
+  mp_limb_t *scratch_out = table + (3*ecc->size << ECC_MUL_A_WBITS);
+  int is_zero = 0;
+
+  mp_bitcnt_t blocks = (ecc->bit_size + ECC_MUL_A_WBITS - 1) / ECC_MUL_A_WBITS;
+  mp_bitcnt_t bit_index = (blocks-1) * ECC_MUL_A_WBITS;
+
+  mp_size_t limb_index = bit_index / GMP_NUMB_BITS;
+  unsigned shift = bit_index % GMP_NUMB_BITS;
+  mp_limb_t w, bits;
+
+  table_init (ecc, table, ECC_MUL_A_WBITS, initial, p, scratch_out);
+
+  w = np[limb_index];
+  bits = w >> shift;
+  if (limb_index < ecc->size - 1)
+    bits |= np[limb_index + 1] << (GMP_NUMB_BITS - shift);
+
+  assert (bits < TABLE_SIZE);
+
+  sec_tabselect (r, 3*ecc->size, table, TABLE_SIZE, bits);
+  is_zero = (bits == 0);
+
+  for (;;)
+    {
+      unsigned j;
+      if (shift >= ECC_MUL_A_WBITS)
+	{
+	  shift -= ECC_MUL_A_WBITS;
+	  bits = w >> shift;
+	}
+      else
+	{
+	  if (limb_index == 0)
+	    {
+	      assert (shift == 0);
+	      break;
+	    }
+	  bits = w << (ECC_MUL_A_WBITS - shift);
+	  w = np[--limb_index];
+	  shift = shift + GMP_NUMB_BITS - ECC_MUL_A_WBITS;
+	  bits |= w >> shift;
+	}
+      for (j = 0; j < ECC_MUL_A_WBITS; j++)
+	ecc_dup_jj (ecc, r, r, scratch_out);
+
+      bits &= TABLE_MASK;
+      sec_tabselect (tp, 3*ecc->size, table, TABLE_SIZE, bits);
+      cnd_copy (is_zero, r, tp, 3*ecc->size);
+      ecc_add_jjj (ecc, tp, tp, r, 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 table
+#undef tp
+}
+
+#endif /* ECC_MUL_A_WBITS > 1 */

testsuite/.test-rules.make

@@ -172,6 +172,9 @@ ecc-redc-test$(EXEEXT): ecc-redc-test.$(OBJEXT)
 ecc-mul-g-test$(EXEEXT): ecc-mul-g-test.$(OBJEXT)
 	$(LINK) ecc-mul-g-test.$(OBJEXT) $(TEST_OBJS) -o ecc-mul-g-test$(EXEEXT)
 
+ecc-mul-a-test$(EXEEXT): ecc-mul-a-test.$(OBJEXT)
+	$(LINK) ecc-mul-a-test.$(OBJEXT) $(TEST_OBJS) -o ecc-mul-a-test$(EXEEXT)
+
 sha1-huge-test$(EXEEXT): sha1-huge-test.$(OBJEXT)
 	$(LINK) sha1-huge-test.$(OBJEXT) $(TEST_OBJS) -o sha1-huge-test$(EXEEXT)
 

testsuite/Makefile.in

@@ -36,7 +36,7 @@ TS_HOGWEED_SOURCES = sexp-test.c sexp-format-test.c \
 		     rsa-test.c rsa-encrypt-test.c rsa-keygen-test.c \
 		     dsa-test.c dsa-keygen-test.c \
 		     ecc-mod-test.c ecc-modinv-test.c ecc-redc-test.c \
-		     ecc-mul-g-test.c
+		     ecc-mul-g-test.c ecc-mul-a-test.c
 
 TS_SOURCES = $(TS_NETTLE_SOURCES) $(TS_HOGWEED_SOURCES)
 CXX_SOURCES = cxx-test.cxx

testsuite/ecc-mul-a-test.c

+#include "testutils.h"
+
+void
+test_main (void)
+{
+  gmp_randstate_t state;
+  mpz_t r;
+  unsigned i;
+
+  gmp_randinit_default (state);
+  mpz_init (r);
+  
+  for (i = 0; ecc_curves[i]; i++)
+    {
+      const struct ecc_curve *ecc = ecc_curves[i];
+      mp_size_t size = ecc_size (ecc);
+      mp_limb_t *p = xalloc_limbs (ecc_size_j (ecc));
+      mp_limb_t *q = xalloc_limbs (ecc_size_j (ecc));
+      mp_limb_t *n = xalloc_limbs (size);
+      mp_limb_t *scratch = xalloc_limbs (ecc_mul_a_itch (ecc));
+      unsigned j;
+      
+      mpn_zero (n, size);
+
+      n[0] = 1;
+      ecc_mul_a (ecc, 1, p, n, ecc->g, scratch);
+      ecc_j_to_a (ecc, 1, p, p, scratch);
+
+      if (mpn_cmp (p, ecc->g, 2*size != 0))
+	die ("curve %d: ecc_mul_a with n = 1 failed.\n", ecc->bit_size);
+
+      if (ecc->use_redc)
+	{
+	  ecc_mul_a (ecc, 0, p, n, ecc->redc_g, scratch);
+	  ecc_j_to_a (ecc, 1, p, p, scratch);
+
+	  if (mpn_cmp (p, ecc->g, 2*size != 0))
+	    die ("curve %d: ecc_mul_a with n = 1 and redc failed.\n", ecc->bit_size);
+	}
+      for (n[0] = 2; n[0] <= 4; n[0]++)
+	{
+	  ecc_mul_a (ecc, 1, p, n, ecc->g, scratch);
+	  test_ecc_mul_j (i, n[0], p);
+	  if (ecc->use_redc)
+	    {
+	      ecc_mul_a (ecc, 0, p, n, ecc->redc_g, scratch);
+	      test_ecc_mul_j (i, n[0], p);
+	    }
+	}
+
+      /* (order - 1) * g = - g */
+      mpn_sub_1 (n, ecc->q, size, 1);
+      ecc_mul_a (ecc, 1, p, n, ecc->g, scratch);
+      ecc_j_to_a (ecc, 1, p, p, scratch);
+      mpn_sub_n (p + size, ecc->p, p + size, size);
+      if (mpn_cmp (p, ecc->g, 2*size) != 0)
+	{
+	  fprintf (stderr, "ecc_mul_a with n = order - 1 failed.\n");
+	  abort ();
+	}
+
+      mpn_zero (n, size);
+
+      for (j = 0; j < 100; j++)
+	{
+	  if (j & 1)
+	    mpz_rrandomb (r, state, size * GMP_NUMB_BITS);
+	  else
+	    mpz_urandomb (r, state, size * GMP_NUMB_BITS);
+
+	  /* Reduce so that (almost surely) n < q */
+	  _mpz_copy_limbs (n, r, size);
+	  n[size - 1] %= ecc->q[size - 1];
+
+	  ecc_mul_a (ecc, 1, p, n, ecc->g, scratch);
+	  ecc_j_to_a (ecc, 1, p, p, scratch);
+
+	  ecc_mul_g (ecc, q, n, scratch);
+	  ecc_j_to_a (ecc, 1, q, q, scratch);
+
+	  if (mpn_cmp (p, q, 2*size))
+	    {
+	      gmp_fprintf (stderr,
+			   "Different results from ecc_mul_a and ecc_mul_g.\n"
+			   " bits = %u\n"
+			   " n = %Nx\n",
+			   ecc->bit_size, n, size);
+	      gmp_fprintf (stderr, "p = %Nx,\n    %Nx\n",
+			   p, size, p + size, size);
+	      gmp_fprintf (stderr, "q = %Nx,\n    %Nx\n",
+			   q, size, q + size, size);
+	      abort ();
+	    }
+	}
+      free (n);
+      free (p);
+      free (q);
+      free (scratch);
+    }
+  mpz_clear (r); 
+  gmp_randclear (state);
+}