eccdata.c 26 KB
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/* eccdata.c

   Generate compile time constant (but machine dependent) tables.

   Copyright (C) 2013 Niels Möller

   This file is part of GNU Nettle.

   GNU Nettle is free software: you can redistribute it and/or
   modify it under the terms of either:

     * the GNU Lesser General Public License as published by the Free
       Software Foundation; either version 3 of the License, or (at your
       option) any later version.

   or

     * the GNU General Public License as published by the Free
       Software Foundation; either version 2 of the License, or (at your
       option) any later version.

   or both in parallel, as here.

   GNU Nettle 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
   General Public License for more details.

   You should have received copies of the GNU General Public License and
   the GNU Lesser General Public License along with this program.  If
   not, see http://www.gnu.org/licenses/.
*/
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/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
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#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

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#include "mini-gmp.c"
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/* Affine coordinates, for simplicity. Infinity point represented as x
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   == y == 0. FIXME: Doesn't quite work for Montgomery curves, where
   (0,0) is a normal finite point. Shouldn't occur in these
   computations, though. */
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struct ecc_point
{
  mpz_t x;
  mpz_t y;
};

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enum ecc_type
  {
    /* y^2 = x^3 - 3x + b (mod p) */
    ECC_TYPE_WEIERSTRASS,
    /* y^2 = x^3 + b x^2 + x */
    ECC_TYPE_MONTGOMERY
  };
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struct ecc_curve
{
  unsigned bit_size;
  unsigned pippenger_k;
  unsigned pippenger_c;

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  enum ecc_type type;

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  /* Prime */
  mpz_t p;
  mpz_t b;

  /* Curve order */
  mpz_t q;
  struct ecc_point g;

  /* Table for pippenger's algorithm.
     Element

       i 2^c + j_0 + j_1 2 + j_2 2^2 + ... + j_{c-1} 2^{c-1}

     holds

       2^{ikc} ( j_0 + j_1 2^k + j_2 2^{2k} + ... + j_{c-1} 2^{(c-1)k}) g
   */
  mp_size_t table_size;
  struct ecc_point *table;

  /* If non-NULL, holds 2g, 3g, 4g */
  struct ecc_point *ref;
};

static void
ecc_init (struct ecc_point *p)
{
  mpz_init (p->x);
  mpz_init (p->y);
}

static void
ecc_clear (struct ecc_point *p)
{
  mpz_clear (p->x);
  mpz_clear (p->y);
}

static int
ecc_zero_p (const struct ecc_point *p)
{
  return mpz_sgn (p->x) == 0 && mpz_sgn (p->y) == 0;
}

static int
ecc_equal_p (const struct ecc_point *p, const struct ecc_point *q)
{
  return mpz_cmp (p->x, q->x) == 0 && mpz_cmp (p->y, q->y) == 0;
}

static void
ecc_set_zero (struct ecc_point *r)
{
  mpz_set_ui (r->x, 0);
  mpz_set_ui (r->y, 0);
}

static void
ecc_set (struct ecc_point *r, const struct ecc_point *p)
{
  mpz_set (r->x, p->x);
  mpz_set (r->y, p->y);
}

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/* Needs to support in-place operation. */
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static void
ecc_dup (const struct ecc_curve *ecc,
	 struct ecc_point *r, const struct ecc_point *p)
{
  if (ecc_zero_p (p))
    ecc_set_zero (r);

  else
    {
      mpz_t m, t, x, y;
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      mpz_init (m);
      mpz_init (t);
      mpz_init (x);
      mpz_init (y);

      /* m = (2 y)^-1 */
      mpz_mul_ui (m, p->y, 2);
      mpz_invert (m, m, ecc->p);

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      switch (ecc->type)
	{
	case ECC_TYPE_WEIERSTRASS:
	  /* t = 3 (x^2 - 1) * m */
	  mpz_mul (t, p->x, p->x);
	  mpz_mod (t, t, ecc->p);
	  mpz_sub_ui (t, t, 1);
	  mpz_mul_ui (t, t, 3);
	  break;
	case ECC_TYPE_MONTGOMERY:
	  /* t = (3 x^2 + 2 b x + 1) m = [x(3x+2b)+1] m */
	  mpz_mul_ui (t, ecc->b, 2);
	  mpz_addmul_ui (t, p->x, 3);
	  mpz_mul (t, t, p->x);
	  mpz_mod (t, t, ecc->p);
	  mpz_add_ui (t, t, 1);
	  break;
	}
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      mpz_mul (t, t, m);
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      mpz_mod (t, t, ecc->p);
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      /* x' = t^2 - 2 x */
      mpz_mul (x, t, t);
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      mpz_submul_ui (x, p->x, 2);
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      if (ecc->type == ECC_TYPE_MONTGOMERY)
	mpz_sub (x, x, ecc->b);

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      mpz_mod (x, x, ecc->p);

      /* y' = (x - x') * t - y */
      mpz_sub (y, p->x, x);
      mpz_mul (y, y, t);
      mpz_sub (y, y, p->y);
      mpz_mod (y, y, ecc->p);

      mpz_swap (x, r->x);
      mpz_swap (y, r->y);
  
      mpz_clear (m);
      mpz_clear (t);
      mpz_clear (x);
      mpz_clear (y);
    }
}

static void
ecc_add (const struct ecc_curve *ecc,
	 struct ecc_point *r, const struct ecc_point *p, const struct ecc_point *q)
{
  if (ecc_zero_p (p))
    ecc_set (r, q);

  else if (ecc_zero_p (q))
    ecc_set (r, p);

  else if (mpz_cmp (p->x, q->x) == 0)
    {
      if (mpz_cmp (p->y, q->y) == 0)
	ecc_dup (ecc, r, p);
      else
	ecc_set_zero (r);
    }
  else
    {
      mpz_t s, t, x, y;
      mpz_init (s);
      mpz_init (t);
      mpz_init (x);
      mpz_init (y);

      /* t = (q_y - p_y) / (q_x - p_x) */
      mpz_sub (t, q->x, p->x);
      mpz_invert (t, t, ecc->p);
      mpz_sub (s, q->y, p->y);
      mpz_mul (t, t, s);
      mpz_mod (t, t, ecc->p);

      /* x' = t^2 - p_x - q_x */
      mpz_mul (x, t, t);
      mpz_sub (x, x, p->x);
      mpz_sub (x, x, q->x);
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      /* This appears to be the only difference between formulas. */
      if (ecc->type == ECC_TYPE_MONTGOMERY)
	mpz_sub (x, x, ecc->b);
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      mpz_mod (x, x, ecc->p);

      /* y' = (x - x') * t - y */
      mpz_sub (y, p->x, x);
      mpz_mul (y, y, t);
      mpz_sub (y, y, p->y);
      mpz_mod (y, y, ecc->p);

      mpz_swap (x, r->x);
      mpz_swap (y, r->y);

      mpz_clear (s);
      mpz_clear (t);
      mpz_clear (x);
      mpz_clear (y);
    }
}

static void 
ecc_mul_binary (const struct ecc_curve *ecc,
		struct ecc_point *r, const mpz_t n, const struct ecc_point *p)
{
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  /* Avoid the mp_bitcnt_t type for compatibility with older GMP
     versions. */
  unsigned k;
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  assert (r != p);
  assert (mpz_sgn (n) > 0);

  ecc_set (r, p);

  /* Index of highest one bit */
  for (k = mpz_sizeinbase (n, 2) - 1; k-- > 0; )
    {
      ecc_dup (ecc, r, r);
      if (mpz_tstbit (n, k))
	ecc_add (ecc, r, r, p);
    }  
}

static struct ecc_point *
ecc_alloc (size_t n)
{
  struct ecc_point *p = malloc (n * sizeof(*p));
  size_t i;

  if (!p)
    {
      fprintf (stderr, "Virtual memory exhausted.\n");
      exit (EXIT_FAILURE);
    }
  for (i = 0; i < n; i++)
    ecc_init (&p[i]);

  return p;
}

static void
ecc_set_str (struct ecc_point *p,
	     const char *x, const char *y)
{
  mpz_set_str (p->x, x, 16);
  mpz_set_str (p->y, y, 16);  
}

static void
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ecc_curve_init_str (struct ecc_curve *ecc, enum ecc_type type,
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		    const char *p, const char *b, const char *q,
		    const char *gx, const char *gy)
{
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  ecc->type = type;

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  mpz_init_set_str (ecc->p, p, 16);
  mpz_init_set_str (ecc->b, b, 16);
  mpz_init_set_str (ecc->q, q, 16);
  ecc_init (&ecc->g);
  ecc_set_str (&ecc->g, gx, gy);

  ecc->pippenger_k = 0;
  ecc->pippenger_c = 0;
  ecc->table = NULL;

  ecc->ref = NULL;
}

static void
ecc_curve_init (struct ecc_curve *ecc, unsigned bit_size)
{
  switch (bit_size)
    {
    case 192:      
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      ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
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			  /* p = 2^{192} - 2^{64} - 1 */
			  "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE"
			  "FFFFFFFFFFFFFFFF",

			  "64210519e59c80e70fa7e9ab72243049"
			  "feb8deecc146b9b1", 

			  "ffffffffffffffffffffffff99def836"
			  "146bc9b1b4d22831",

			  "188da80eb03090f67cbf20eb43a18800"
			  "f4ff0afd82ff1012",

			  "07192b95ffc8da78631011ed6b24cdd5"
			  "73f977a11e794811");
      ecc->ref = ecc_alloc (3);
      ecc_set_str (&ecc->ref[0], /* 2 g */
		   "dafebf5828783f2ad35534631588a3f629a70fb16982a888",
		   "dd6bda0d993da0fa46b27bbc141b868f59331afa5c7e93ab");
      
      ecc_set_str (&ecc->ref[1], /* 3 g */
		   "76e32a2557599e6edcd283201fb2b9aadfd0d359cbb263da",
		   "782c37e372ba4520aa62e0fed121d49ef3b543660cfd05fd");

      ecc_set_str (&ecc->ref[2], /* 4 g */
		   "35433907297cc378b0015703374729d7a4fe46647084e4ba",
		   "a2649984f2135c301ea3acb0776cd4f125389b311db3be32");

      break;
    case 224:
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      ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
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			  /* p = 2^{224} - 2^{96} + 1 */
			  "ffffffffffffffffffffffffffffffff"
			  "000000000000000000000001",

			  "b4050a850c04b3abf54132565044b0b7"
			  "d7bfd8ba270b39432355ffb4",

			  "ffffffffffffffffffffffffffff16a2"
			  "e0b8f03e13dd29455c5c2a3d",

			  "b70e0cbd6bb4bf7f321390b94a03c1d3"
			  "56c21122343280d6115c1d21",

			  "bd376388b5f723fb4c22dfe6cd4375a0"
			  "5a07476444d5819985007e34");

      ecc->ref = ecc_alloc (3);
      ecc_set_str (&ecc->ref[0], /* 2 g */
		   "706a46dc76dcb76798e60e6d89474788d16dc18032d268fd1a704fa6",
		   "1c2b76a7bc25e7702a704fa986892849fca629487acf3709d2e4e8bb");
      
      ecc_set_str (&ecc->ref[1], /* 3 g */
		   "df1b1d66a551d0d31eff822558b9d2cc75c2180279fe0d08fd896d04",
		   "a3f7f03cadd0be444c0aa56830130ddf77d317344e1af3591981a925");

      ecc_set_str (&ecc->ref[2], /* 4 g */
		   "ae99feebb5d26945b54892092a8aee02912930fa41cd114e40447301",
		   "482580a0ec5bc47e88bc8c378632cd196cb3fa058a7114eb03054c9");

      break;
    case 256:
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      ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
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			  /* p = 2^{256} - 2^{224} + 2^{192} + 2^{96} - 1 */
			  "FFFFFFFF000000010000000000000000"
			  "00000000FFFFFFFFFFFFFFFFFFFFFFFF",

			  "5AC635D8AA3A93E7B3EBBD55769886BC"
			  "651D06B0CC53B0F63BCE3C3E27D2604B",

			  "FFFFFFFF00000000FFFFFFFFFFFFFFFF"
			  "BCE6FAADA7179E84F3B9CAC2FC632551",

			  "6B17D1F2E12C4247F8BCE6E563A440F2"
			  "77037D812DEB33A0F4A13945D898C296",

			  "4FE342E2FE1A7F9B8EE7EB4A7C0F9E16"
			  "2BCE33576B315ECECBB6406837BF51F5");

      ecc->ref = ecc_alloc (3);
      ecc_set_str (&ecc->ref[0], /* 2 g */
		   "7cf27b188d034f7e8a52380304b51ac3c08969e277f21b35a60b48fc47669978",
		   "7775510db8ed040293d9ac69f7430dbba7dade63ce982299e04b79d227873d1");
      
      ecc_set_str (&ecc->ref[1], /* 3 g */
		   "5ecbe4d1a6330a44c8f7ef951d4bf165e6c6b721efada985fb41661bc6e7fd6c",
		   "8734640c4998ff7e374b06ce1a64a2ecd82ab036384fb83d9a79b127a27d5032");

      ecc_set_str (&ecc->ref[2], /* 4 g */
		   "e2534a3532d08fbba02dde659ee62bd0031fe2db785596ef509302446b030852",
		   "e0f1575a4c633cc719dfee5fda862d764efc96c3f30ee0055c42c23f184ed8c6");

      break;
    case 384:
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      ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
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			  /* p = 2^{384} - 2^{128} - 2^{96} + 2^{32} - 1 */
			  "ffffffffffffffffffffffffffffffff"
			  "fffffffffffffffffffffffffffffffe"
			  "ffffffff0000000000000000ffffffff",
			  
			  "b3312fa7e23ee7e4988e056be3f82d19"
			  "181d9c6efe8141120314088f5013875a"
			  "c656398d8a2ed19d2a85c8edd3ec2aef",
			  
			  "ffffffffffffffffffffffffffffffff"
			  "ffffffffffffffffc7634d81f4372ddf"
			  "581a0db248b0a77aecec196accc52973",
			  
			  "aa87ca22be8b05378eb1c71ef320ad74"
			  "6e1d3b628ba79b9859f741e082542a38"
			  "5502f25dbf55296c3a545e3872760ab7",
			  
			  "3617de4a96262c6f5d9e98bf9292dc29"
			  "f8f41dbd289a147ce9da3113b5f0b8c0"
			  "0a60b1ce1d7e819d7a431d7c90ea0e5f");

      ecc->ref = ecc_alloc (3);
      ecc_set_str (&ecc->ref[0], /* 2 g */
		   "8d999057ba3d2d969260045c55b97f089025959a6f434d651d207d19fb96e9e4fe0e86ebe0e64f85b96a9c75295df61",
		   "8e80f1fa5b1b3cedb7bfe8dffd6dba74b275d875bc6cc43e904e505f256ab4255ffd43e94d39e22d61501e700a940e80");

      ecc_set_str (&ecc->ref[1], /* 3 g */
		   "77a41d4606ffa1464793c7e5fdc7d98cb9d3910202dcd06bea4f240d3566da6b408bbae5026580d02d7e5c70500c831",
		   "c995f7ca0b0c42837d0bbe9602a9fc998520b41c85115aa5f7684c0edc111eacc24abd6be4b5d298b65f28600a2f1df1");

      ecc_set_str (&ecc->ref[2], /* 4 g */
		   "138251cd52ac9298c1c8aad977321deb97e709bd0b4ca0aca55dc8ad51dcfc9d1589a1597e3a5120e1efd631c63e1835",
		   "cacae29869a62e1631e8a28181ab56616dc45d918abc09f3ab0e63cf792aa4dced7387be37bba569549f1c02b270ed67");

      break;
    case 521:
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      ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
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			  "1ff" /* p = 2^{521} - 1 */
			  "ffffffffffffffffffffffffffffffff"
			  "ffffffffffffffffffffffffffffffff"
			  "ffffffffffffffffffffffffffffffff"
			  "ffffffffffffffffffffffffffffffff",

			  "051"
			  "953eb9618e1c9a1f929a21a0b68540ee"
			  "a2da725b99b315f3b8b489918ef109e1"
			  "56193951ec7e937b1652c0bd3bb1bf07"
			  "3573df883d2c34f1ef451fd46b503f00",

			  "1ff"
			  "ffffffffffffffffffffffffffffffff"
			  "fffffffffffffffffffffffffffffffa"
			  "51868783bf2f966b7fcc0148f709a5d0"
			  "3bb5c9b8899c47aebb6fb71e91386409",

			  "c6"
			  "858e06b70404e9cd9e3ecb662395b442"
			  "9c648139053fb521f828af606b4d3dba"
			  "a14b5e77efe75928fe1dc127a2ffa8de"
			  "3348b3c1856a429bf97e7e31c2e5bd66",

			  "118"
			  "39296a789a3bc0045c8a5fb42c7d1bd9"
			  "98f54449579b446817afbd17273e662c"
			  "97ee72995ef42640c550b9013fad0761"
			  "353c7086a272c24088be94769fd16650");

      ecc->ref = ecc_alloc (3);
      ecc_set_str (&ecc->ref[0], /* 2 g */
		   "433c219024277e7e682fcb288148c282747403279b1ccc06352c6e5505d769be97b3b204da6ef55507aa104a3a35c5af41cf2fa364d60fd967f43e3933ba6d783d",
		   "f4bb8cc7f86db26700a7f3eceeeed3f0b5c6b5107c4da97740ab21a29906c42dbbb3e377de9f251f6b93937fa99a3248f4eafcbe95edc0f4f71be356d661f41b02");
      
      ecc_set_str (&ecc->ref[1], /* 3 g */
		   "1a73d352443de29195dd91d6a64b5959479b52a6e5b123d9ab9e5ad7a112d7a8dd1ad3f164a3a4832051da6bd16b59fe21baeb490862c32ea05a5919d2ede37ad7d",
		   "13e9b03b97dfa62ddd9979f86c6cab814f2f1557fa82a9d0317d2f8ab1fa355ceec2e2dd4cf8dc575b02d5aced1dec3c70cf105c9bc93a590425f588ca1ee86c0e5");

      ecc_set_str (&ecc->ref[2], /* 4 g */
		   "35b5df64ae2ac204c354b483487c9070cdc61c891c5ff39afc06c5d55541d3ceac8659e24afe3d0750e8b88e9f078af066a1d5025b08e5a5e2fbc87412871902f3",
		   "82096f84261279d2b673e0178eb0b4abb65521aef6e6e32e1b5ae63fe2f19907f279f283e54ba385405224f750a95b85eebb7faef04699d1d9e21f47fc346e4d0d");

      break;
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    case 255:
      /* curve25519, y^2 = x^3 + 486662 x^2 + x (mod p), with p = 2^{255} - 19.

	 Acccording to http://cr.yp.to/papers.html#newelliptic, this
	 is birationally equivalent to the Edwards curve

	   x^2 + y^2 = 1 + (121665/121666) x^2 y^2 (mod p).

	 And since the constant is not a square, the Edwards formulas
	 should be "complete", with no special cases needed for
	 doubling, neutral element, negatives, etc.

	 Generator is x = 9, with y coordinate
	 14781619447589544791020593568409986887264606134616475288964881837755586237401,
	 according to

	   x = Mod(9, 2^255-19); sqrt(x^3 + 486662*x^2 + x)

	 in PARI/GP. Also, in PARI notation,

	   curve25519 = Mod([0, 486662, 0, 1, 0], 2^255-19)
       */
      ecc_curve_init_str (ecc, ECC_TYPE_MONTGOMERY,
			  "7fffffffffffffffffffffffffffffff"
			  "ffffffffffffffffffffffffffffffed",
			  "76d06",
			  /* Order of the subgroup is 2^252 +
			     27742317777372353535851937790883648493 */
			  "10000000000000000000000000000000"
			  "14def9dea2f79cd65812631a5cf5d3ed",
			  "9",
			  /* y coordinate from PARI/GP
			     x = Mod(9, 2^255-19); sqrt(x^3 + 486662*x^2 + x)
			  */
			  "20ae19a1b8a086b4e01edd2c7748d14c"
			  "923d4d7e6d7c61b229e9c5a27eced3d9");
      ecc->ref = ecc_alloc (3);
      ecc_set_str (&ecc->ref[0], /* 2 g */
		   "20d342d51873f1b7d9750c687d157114"
		   "8f3f5ced1e350b5c5cae469cdd684efb",
		   "13b57e011700e8ae050a00945d2ba2f3"
		   "77659eb28d8d391ebcd70465c72df563");
      ecc_set_str (&ecc->ref[1], /* 3 g */
		   "1c12bc1a6d57abe645534d91c21bba64"
		   "f8824e67621c0859c00a03affb713c12",
		   "2986855cbe387eaeaceea446532c338c"
		   "536af570f71ef7cf75c665019c41222b");

      ecc_set_str (&ecc->ref[2], /* 4 g */
		   "79ce98b7e0689d7de7d1d074a15b315f"
		   "fe1805dfcd5d2a230fee85e4550013ef",
		   "75af5bf4ebdc75c8fe26873427d275d7"
		   "3c0fb13da361077a565539f46de1c30");

      break;

562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649
    default:
      fprintf (stderr, "No known curve for size %d\n", bit_size);
      exit(EXIT_FAILURE);     
    }
  ecc->bit_size = bit_size;
}

static void
ecc_pippenger_precompute (struct ecc_curve *ecc, unsigned k, unsigned c)
{
  unsigned p = (ecc->bit_size + k-1) / k;
  unsigned M = (p + c-1)/c;
  unsigned i, j;

  ecc->pippenger_k = k;
  ecc->pippenger_c = c;
  ecc->table_size = M << c;
  ecc->table = ecc_alloc (ecc->table_size);
  
  /* Compute the first 2^c entries */
  ecc_set_zero (&ecc->table[0]);
  ecc_set (&ecc->table[1], &ecc->g);

  for (j = 2; j < (1U<<c); j <<= 1)
    {
      /* T[j] = 2^k T[j/2] */
      ecc_dup (ecc, &ecc->table[j], &ecc->table[j/2]);
      for (i = 1; i < k; i++)
	ecc_dup (ecc, &ecc->table[j], &ecc->table[j]);

      for (i = 1; i < j; i++)
	ecc_add (ecc, &ecc->table[j + i], &ecc->table[j], &ecc->table[i]);
    }
  for (j = 1<<c; j < ecc->table_size; j++)
    {
      /* T[j] = 2^{kc} T[j-2^c] */
      ecc_dup (ecc, &ecc->table[j], &ecc->table[j - (1<<c)]);
      for (i = 1; i < k*c; i++)
	ecc_dup (ecc, &ecc->table[j], &ecc->table[j]);
    }
}

static void
ecc_mul_pippenger (const struct ecc_curve *ecc,
		   struct ecc_point *r, const mpz_t n_input)
{
  mpz_t n;
  unsigned k, c;
  unsigned i, j;
  unsigned bit_rows;

  mpz_init (n);
  
  mpz_mod (n, n_input, ecc->q);
  ecc_set_zero (r);

  k = ecc->pippenger_k;
  c = ecc->pippenger_c;

  bit_rows = (ecc->bit_size + k - 1) / k;

  for (i = k; i-- > 0; )
    {
      ecc_dup (ecc, r, r);
      for (j = 0; j * c < bit_rows; j++)
	{
	  unsigned bits;
	  mp_size_t bit_index;
	  
	  /* Extract c bits of the exponent, 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; )
	    {
	      bit_index -= k;
	      bits = (bits << 1) | mpz_tstbit (n, bit_index);
	    }

	  ecc_add (ecc, r, r, &ecc->table[(j << c) | bits]);
	}
    }
  mpz_clear (n);
}

#define ASSERT_EQUAL(p, q) do {						\
    if (!ecc_equal_p (p, q))						\
      {									\
	fprintf (stderr, "%s:%d: ASSERT_EQUAL (%s, %s) failed.\n",	\
		 __FILE__, __LINE__, #p, #q);				\
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	fprintf (stderr, "p = (");					\
	mpz_out_str (stderr, 16, (p)->x);				\
	fprintf (stderr, ",\n     ");					\
	mpz_out_str (stderr, 16, (p)->y);				\
	fprintf (stderr, ")\nq = (");					\
	mpz_out_str (stderr, 16, (q)->x);				\
	fprintf (stderr, ",\n     ");					\
	mpz_out_str (stderr, 16, (q)->y);				\
	fprintf (stderr, ")\n");					\
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	abort();							\
      }									\
  } while (0)

#define ASSERT_ZERO(p) do {						\
    if (!ecc_zero_p (p))						\
      {									\
	fprintf (stderr, "%s:%d: ASSERT_ZERO (%s) failed.\n",		\
		 __FILE__, __LINE__, #p);				\
668 669 670 671 672
	fprintf (stderr, "p = (");					\
	mpz_out_str (stderr, 16, (p)->x);				\
	fprintf (stderr, ",\n     ");					\
	mpz_out_str (stderr, 16, (p)->y);				\
	fprintf (stderr, ")\n");					\
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	abort();							\
      }									\
  } while (0)

static void
ecc_curve_check (const struct ecc_curve *ecc)
{
  struct ecc_point p, q;
  mpz_t n;

  ecc_init (&p);
  ecc_init (&q);
  mpz_init (n);

  ecc_dup (ecc, &p, &ecc->g);
  if (ecc->ref)
    ASSERT_EQUAL (&p, &ecc->ref[0]);
  else
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    {
      fprintf (stderr, "g2 = ");
      mpz_out_str (stderr, 16, p.x);
      fprintf (stderr, "\n     ");
      mpz_out_str (stderr, 16, p.y);
      fprintf (stderr, "\n");
    }
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  ecc_add (ecc, &q, &p, &ecc->g);
  if (ecc->ref)
    ASSERT_EQUAL (&q, &ecc->ref[1]);
  else
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    {
      fprintf (stderr, "g3 = ");
      mpz_out_str (stderr, 16, q.x);
      fprintf (stderr, "\n     ");
      mpz_out_str (stderr, 16, q.y);
      fprintf (stderr, "\n");
    }
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  ecc_add (ecc, &q, &q, &ecc->g);
  if (ecc->ref)
    ASSERT_EQUAL (&q, &ecc->ref[2]);
  else
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    {
      fprintf (stderr, "g4 = ");
      mpz_out_str (stderr, 16, q.x);
      fprintf (stderr, "\n     ");
      mpz_out_str (stderr, 16, q.y);
      fprintf (stderr, "\n");
    }
721 722 723 724 725

  ecc_dup (ecc, &q, &p);
  if (ecc->ref)
    ASSERT_EQUAL (&q, &ecc->ref[2]);
  else
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    {
      fprintf (stderr, "g4 = ");
      mpz_out_str (stderr, 16, q.x);
      fprintf (stderr, "\n     ");
      mpz_out_str (stderr, 16, q.y);
      fprintf (stderr, "\n");
    }
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  ecc_mul_binary (ecc, &p, ecc->q, &ecc->g);
  ASSERT_ZERO (&p);

  ecc_mul_pippenger (ecc, &q, ecc->q);
  ASSERT_ZERO (&q);

  ecc_clear (&p);
  ecc_clear (&q);
  mpz_clear (n);
}

static void
output_digits (const mpz_t x,
	       unsigned size, unsigned bits_per_limb)
{  
  mpz_t t;
  mpz_t mask;
  mpz_t limb;
  unsigned i;
  const char *suffix;

  mpz_init (t);
  mpz_init (mask);
  mpz_init (limb);

  mpz_setbit (mask, bits_per_limb);
  mpz_sub_ui (mask, mask, 1);

  suffix = bits_per_limb > 32 ? "ULL" : "UL";

  mpz_init_set (t, x);

  for (i = 0; i < size; i++)
    {
      if ( (i % 8) == 0)
	printf("\n ");
      
      mpz_and (limb, mask, t);
772 773 774
      printf (" 0x");
      mpz_out_str (stdout, 16, limb);
      printf ("%s,", suffix);
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      mpz_tdiv_q_2exp (t, t, bits_per_limb);
    }

  mpz_clear (t);
  mpz_clear (mask);
  mpz_clear (limb);
}

static void
output_bignum (const char *name, const mpz_t x,
	       unsigned size, unsigned bits_per_limb)
{  
  printf ("static const mp_limb_t %s[%d] = {", name, size);
  output_digits (x, size, bits_per_limb);
  printf("\n};\n");
}

static void
output_point (const char *name, const struct ecc_point *p,
	      unsigned size, unsigned bits_per_limb)
{
  if (name)
    printf("static const mp_limb_t %s[%u] = {", name, 2*size);

  output_digits (p->x, size, bits_per_limb);
  output_digits (p->y, size, bits_per_limb);

  if (name)
    printf("\n};\n");
}

static void
output_point_redc (const char *name, const struct ecc_curve *ecc,
		   const struct ecc_point *p,
		   unsigned size, unsigned bits_per_limb)
{
  mpz_t t;
  mpz_init (t);

  if (name)
    printf("static const mp_limb_t %s[%u] = {", name, 2*size);
    
  mpz_mul_2exp (t, p->x, size * bits_per_limb);
  mpz_mod (t, t, ecc->p);
      
  output_digits (t, size, bits_per_limb);

  mpz_mul_2exp (t, p->y, size * bits_per_limb);
  mpz_mod (t, t, ecc->p);
      
  output_digits (t, size, bits_per_limb);

  if (name)
    printf("\n};\n");

  mpz_clear (t);
}

static unsigned
output_modulo (const char *name, const mpz_t x,
	       unsigned size, unsigned bits_per_limb)
{
  mpz_t mod;
  unsigned bits;

  mpz_init (mod);

  mpz_setbit (mod, bits_per_limb * size);
  mpz_mod (mod, mod, x);

  bits = mpz_sizeinbase (mod, 2);
  output_bignum (name, mod, size, bits_per_limb);
  
  mpz_clear (mod);
  return bits;
}

static void
output_curve (const struct ecc_curve *ecc, unsigned bits_per_limb)
{
  unsigned limb_size = (ecc->bit_size + bits_per_limb - 1)/bits_per_limb;
  unsigned i;
  unsigned bits;
  int redc_limbs;
  mpz_t t;

  mpz_init (t);

  printf ("/* For NULL. */\n#include <stddef.h>\n");

  printf ("#define ECC_LIMB_SIZE %u\n", limb_size);
  printf ("#define ECC_PIPPENGER_K %u\n", ecc->pippenger_k);
  printf ("#define ECC_PIPPENGER_C %u\n", ecc->pippenger_c);

  output_bignum ("ecc_p", ecc->p, limb_size, bits_per_limb);
  output_bignum ("ecc_b", ecc->b, limb_size, bits_per_limb);
  output_bignum ("ecc_q", ecc->q, limb_size, bits_per_limb);
  output_point ("ecc_g", &ecc->g, limb_size, bits_per_limb);
  output_point_redc ("ecc_redc_g", ecc, &ecc->g, limb_size, bits_per_limb);
  
  bits = output_modulo ("ecc_Bmodp", ecc->p, limb_size, bits_per_limb);
  printf ("#define ECC_BMODP_SIZE %u\n",
	  (bits + bits_per_limb - 1) / bits_per_limb);
  bits = output_modulo ("ecc_Bmodq", ecc->q, limb_size, bits_per_limb);
  printf ("#define ECC_BMODQ_SIZE %u\n",
	  (bits + bits_per_limb - 1) / bits_per_limb);

  if (ecc->bit_size < limb_size * bits_per_limb)
    {
      int shift;

      mpz_set_ui (t, 0);
      mpz_setbit (t, ecc->bit_size);
      mpz_sub (t, t, ecc->p);      
      output_bignum ("ecc_Bmodp_shifted", t, limb_size, bits_per_limb);

      shift = limb_size * bits_per_limb - ecc->bit_size;
      if (shift > 0)
	{
	  /* Check condition for reducing hi limbs. If s is the
	     normalization shift and n is the bit size (so that s + n
	     = limb_size * bite_per_limb), then we need

	       (2^n - 1) + (2^s - 1) (2^n - p) < 2p

	     or equivalently,

	       2^s (2^n - p) <= p

	     To a allow a carry limb to be added in at the same time,
	     substitute s+1 for s.
	  */
	  /* FIXME: For ecdsa verify, we actually need the stricter
	     inequality < 2 q. */
	  mpz_mul_2exp (t, t, shift + 1);
	  if (mpz_cmp (t, ecc->p) > 0)
	    {
	      fprintf (stderr, "Reduction condition failed for %u-bit curve.\n",
		       ecc->bit_size);
	      exit (EXIT_FAILURE);
	    }
	}
      mpz_set_ui (t, 0);
      mpz_setbit (t, ecc->bit_size);
      mpz_sub (t, t, ecc->q);      
      output_bignum ("ecc_Bmodq_shifted", t, limb_size, bits_per_limb);      
    }
  else
    {
      printf ("#define ecc_Bmodp_shifted ecc_Bmodp\n");
      printf ("#define ecc_Bmodq_shifted ecc_Bmodq\n");
    }

  mpz_add_ui (t, ecc->p, 1);
  mpz_fdiv_q_2exp (t, t, 1);
  output_bignum ("ecc_pp1h", t, limb_size, bits_per_limb);      

  mpz_add_ui (t, ecc->q, 1);
  mpz_fdiv_q_2exp (t, t, 1);
  output_bignum ("ecc_qp1h", t, limb_size, bits_per_limb);  
  
  /* Trailing zeros in p+1 correspond to trailing ones in p. */
  redc_limbs = mpz_scan0 (ecc->p, 0) / bits_per_limb;
  if (redc_limbs > 0)
    {
      mpz_add_ui (t, ecc->p, 1);
      mpz_fdiv_q_2exp (t, t, redc_limbs * bits_per_limb);
      output_bignum ("ecc_redc_ppm1", t, limb_size - redc_limbs, bits_per_limb);
    }
  else
    {    
      /* Trailing zeros in p-1 correspond to zeros just above the low
	 bit of p */
      redc_limbs = mpz_scan1 (ecc->p, 1) / bits_per_limb;
      if (redc_limbs > 0)
	{
	  printf ("#define ecc_redc_ppm1 (ecc_p + %d)\n",
		  redc_limbs);
	  redc_limbs = -redc_limbs;
	}
      else
	printf ("#define ecc_redc_ppm1 NULL\n");
    }
  printf ("#define ECC_REDC_SIZE %d\n", redc_limbs);

  printf ("#if USE_REDC\n");
  printf ("#define ecc_unit ecc_Bmodp\n");

  printf ("static const mp_limb_t ecc_table[%lu] = {",
	 (unsigned long) (2*ecc->table_size * limb_size));
  for (i = 0; i < ecc->table_size; i++)
    output_point_redc (NULL, ecc, &ecc->table[i], limb_size, bits_per_limb);

  printf("\n};\n");

  printf ("#else\n");

  mpz_init_set_ui (t, 1);
  output_bignum ("ecc_unit", t, limb_size, bits_per_limb);
  
  printf ("static const mp_limb_t ecc_table[%lu] = {",
	 (unsigned long) (2*ecc->table_size * limb_size));
  for (i = 0; i < ecc->table_size; i++)
    output_point (NULL, &ecc->table[i], limb_size, bits_per_limb);

  printf("\n};\n");
  printf ("#endif\n");
  
  mpz_clear (t);
}

int
main (int argc, char **argv)
{
  struct ecc_curve ecc;

  if (argc < 4)
    {
      fprintf (stderr, "Usage: %s CURVE-BITS K C [BITS-PER-LIMB]\n", argv[0]);
      return EXIT_FAILURE;
    }

  ecc_curve_init (&ecc, atoi(argv[1]));

  ecc_pippenger_precompute (&ecc, atoi(argv[2]), atoi(argv[3]));

  fprintf (stderr, "Table size: %lu entries\n",
	   (unsigned long) ecc.table_size);

  ecc_curve_check (&ecc);

  if (argc > 4)
    output_curve (&ecc, atoi(argv[4]));

  return EXIT_SUCCESS;
}