path: root/ecc-secp224r1.c

/* ecc-secp224r1.c

   Compile time constant (but machine dependent) tables.

   Copyright (C) 2013, 2014 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/.
*/

/* Development of Nettle's ECC support was funded by the .SE Internet Fund. */

#if HAVE_CONFIG_H
# include "config.h"
#endif

#include <assert.h>

#include "ecc-internal.h"

#if HAVE_NATIVE_ecc_secp224r1_modp

#define USE_REDC 0
#define ecc_secp224r1_modp _nettle_ecc_secp224r1_modp
void
ecc_secp224r1_modp (const struct ecc_modulo *m, mp_limb_t *rp, mp_limb_t *xp);

#else
#define USE_REDC (ECC_REDC_SIZE != 0)
#define ecc_secp224r1_modp ecc_mod
#endif

#include "ecc-secp224r1.h"

#if ECC_REDC_SIZE < 0
# define ecc_secp224r1_redc ecc_pm1_redc
#elif ECC_REDC_SIZE == 0
# define ecc_secp224r1_redc NULL
#else
# error Configuration error
#endif

/* Computes a^{2^{127} - 1} mod m. Also produces the intermediate value a^{2^{96} - 1}.
   Needs 3*ECC_LIMB_SIZE scratch. */
static void
ecc_mod_pow_127m1 (const struct ecc_modulo *m,
		   mp_limb_t *rp, mp_limb_t *a96m1, const mp_limb_t *ap, mp_limb_t *scratch)
{
  /* Addition chain for 2^127 - 1:

       7           = 1 + 2 (2+1)                       2 S + 2 M
       2^{31} - 1  = 1 + 2 (2^{15} + 1)(1 + 2 (2^7 + 1) (1 + 2 (2^3+1) * 7))
                                                      28 S + 6 M
       2^{34} - 1  = 2^3 (2^{31} - 1) + 7              3 S +   M
       2^{65} - 1  = 2^{31}(2^{34} - 1) + 2^{31} - 1  31 S +   M
       2^{96} - 1  = 2^{31}(2^{65} - 1) + 2^{31} - 1  31 S +   M
       2^{127} - 1 = 2^{31}(2^{96} - 1) + 2^{31} - 1  31 S +   M

     This addition chain needs 126 squarings and 12 multiplies.
  */
#define a7 a96m1
#define t0 scratch
#define a31m1 t0
#define tp (scratch + ECC_LIMB_SIZE)

  ecc_mod_sqr        (m, rp, ap, tp);	        /* a^2 */
  ecc_mod_mul        (m, rp, rp, ap, tp);	/* a^3 */
  ecc_mod_sqr        (m, rp, rp, tp);		/* a^6 */
  ecc_mod_mul        (m, a7, rp, ap, tp);	/* a^{2^3-1} a7 */

  ecc_mod_pow_2kp1   (m, rp, a7, 3, tp);	/* a^{2^6 - 1} */
  ecc_mod_sqr        (m, rp, rp, tp);		/* a^{2^7 - 2} */
  ecc_mod_mul        (m, rp, rp, ap, tp);	/* a^{2^7 - 1} */
  ecc_mod_pow_2kp1   (m, t0, rp, 7, tp);	/* a^{2^14 - 1} */
  ecc_mod_sqr        (m, rp, t0, tp);		/* a^{2^15 - 2} */
  ecc_mod_mul        (m, rp, rp, ap, tp);	/* a^{2^15 - 1} */
  ecc_mod_pow_2kp1   (m, t0, rp, 15, tp);	/* a^{2^30 - 1} */
  ecc_mod_sqr        (m, rp, t0, tp);		/* a^{2^31 - 2} */
  ecc_mod_mul        (m, a31m1, rp, ap, tp);	/* a^{2^31 - 1} a7, a31m1 */

  ecc_mod_pow_2k_mul (m, rp, a31m1, 3, a7, tp); /* a^{2^34 - 1} a31m1 */
  ecc_mod_pow_2k_mul (m, rp, rp, 31, a31m1, tp); /* a^{2^65 - 1} a31m1 */
  ecc_mod_pow_2k_mul (m, a96m1, rp, 31, a31m1, tp); /* a^{2^96 - 1} a31m1, a96m1 */
  ecc_mod_pow_2k_mul (m, rp, a96m1, 31, a31m1, tp); /* a^{2^{127} - 1} a96m1 */
#undef a7
#undef t0
#undef a31m1
#undef tp
}

#define ECC_SECP224R1_INV_ITCH (4*ECC_LIMB_SIZE)

static void
ecc_secp224r1_inv (const struct ecc_modulo *p,
		   mp_limb_t *rp, const mp_limb_t *ap,
		   mp_limb_t *scratch)
{
#define a96m1 scratch
#define tp (scratch + ECC_LIMB_SIZE)

  /* Compute a^{p - 2}, with

       p-2 = 2^{224} - 2^{96} - 1
                   = 2^{97}(2^{127} - 1) + 2^{96} - 1

     This addition chain needs 97 squarings and one multiply in
     addition to ecc_mod_pow_127m1, for a total of 223 squarings and
     13 multiplies.
  */
  ecc_mod_pow_127m1 (p, rp, a96m1, ap, tp);
  ecc_mod_pow_2k_mul (p, rp, rp, 97, a96m1, tp); /* a^{2^{224} - 2^{96} - 1 */

#undef a96m1
#undef tp
}

#define ECC_SECP224R1_SQRT_ITCH (5*ECC_LIMB_SIZE)

static int
ecc_secp224r1_sqrt (const struct ecc_modulo *p,
		    mp_limb_t *xp,
		    const mp_limb_t *cp,
		    mp_limb_t *scratch)
{
  unsigned r;

#define bp scratch
#define yp (scratch + ECC_LIMB_SIZE)
#define t0 (scratch + 2*ECC_LIMB_SIZE)
#define tp (scratch + 3*ECC_LIMB_SIZE)

  /* Uses Tonnelli-Shanks' algorithm, and which isn't side-channel silent.

     We have p - 1 = 2^e q, with e = 2^{96} and q = 2^{128} - 1.

     Initially, we need b = c^q and x = c^{(q+1)/2}, and to get both,
     we start with

     c^{(q-1)/2} = a^{2^{127}-1}
  */

  /* Needs total 4 * ECC_LIMB_SIZE scratch space */
  ecc_mod_pow_127m1 (p, xp, scratch, cp, scratch + ECC_LIMB_SIZE);

  ecc_mod_sqr (p, bp, xp, tp);  /* b <-- c^{2^{128} - 2 */
  ecc_mod_mul (p, bp, bp, cp, tp);  /* b <-- c^{2^{128} - 1 */
  ecc_mod_mul (p, xp, xp, cp, tp);  /* x <-- c^{2^{127}} */

  mpn_copyi (yp, ecc_sqrt_z, p->size);
  r = ECC_SQRT_E;

  /* The algoritm maintains x^2 = c b; when b == 1, we are done. We
     also have the invariants b^{2^{r-1}} = 1 (assuming square root
     exists), and y^{2^{r-1}} = -1. */
  for (;;)
    {
      unsigned m;
      if (ecc_mod_equal_p (p, bp, ecc_unit, tp))
	return 1;

      ecc_mod_sqr (p, t0, bp, tp);
      for (m = 1;
	   m < r && !ecc_mod_equal_p (p, t0, ecc_unit, tp);
	   m++)
	ecc_mod_sqr (p, t0, t0, tp);

      if (m == r)
	{
	  /* We get here if there is no square root, or input is zero.
	     Will always be detected on first round in the outer
	     loop. */
	  assert (r == ECC_SQRT_E);
	  return ecc_mod_zero_p (p, xp);
	}

      if (m < r - 1)
	ecc_mod_pow_2k (p, yp, yp, r - m - 1, tp);

      r = m;
      ecc_mod_mul (p, xp, xp, yp, tp);	/* x' <-- x y^{2^{r-m-1} */
      ecc_mod_sqr (p, yp, yp, tp);	/* y' <-- y^{2^{r-m}} */
      ecc_mod_mul (p, bp, bp, yp, tp);	/* b' <-- b y^{2^{r-m}} */
    }
#undef bp
#undef yp
#undef tp
}

const struct ecc_curve _nettle_secp_224r1 =
{
  {
    224,
    ECC_LIMB_SIZE,    
    ECC_BMODP_SIZE,
    -ECC_REDC_SIZE,
    ECC_SECP224R1_INV_ITCH,
    ECC_SECP224R1_SQRT_ITCH,
    0,

    ecc_p,
    ecc_Bmodp,
    ecc_Bmodp_shifted,
    ecc_Bm2p,
    ecc_redc_ppm1,
    ecc_pp1h,

    ecc_secp224r1_modp,
    USE_REDC ? ecc_secp224r1_redc : ecc_secp224r1_modp,
    ecc_secp224r1_inv,
    ecc_secp224r1_sqrt,
    NULL,
  },
  {
    224,
    ECC_LIMB_SIZE,    
    ECC_BMODQ_SIZE,
    0,
    ECC_MOD_INV_ITCH (ECC_LIMB_SIZE),
    0,
    0,

    ecc_q,
    ecc_Bmodq,
    ecc_Bmodq_shifted,
    ecc_Bm2q,
    NULL,
    ecc_qp1h,

    ecc_mod,
    ecc_mod,
    ecc_mod_inv,
    NULL,
    NULL,
  },
  
  USE_REDC,
  ECC_PIPPENGER_K,
  ECC_PIPPENGER_C,

  ECC_ADD_JJA_ITCH (ECC_LIMB_SIZE),
  ECC_ADD_JJJ_ITCH (ECC_LIMB_SIZE),
  ECC_DUP_JJ_ITCH (ECC_LIMB_SIZE),
  ECC_MUL_A_ITCH (ECC_LIMB_SIZE),
  ECC_MUL_G_ITCH (ECC_LIMB_SIZE),
  ECC_J_TO_A_ITCH(ECC_LIMB_SIZE, ECC_SECP224R1_INV_ITCH),

  ecc_add_jja,
  ecc_add_jjj,
  ecc_dup_jj,
  ecc_mul_a,
  ecc_mul_g,
  ecc_j_to_a,

  ecc_b,
  ecc_unit,
  ecc_table
};

const struct ecc_curve *nettle_get_secp_224r1(void)
{
  return &_nettle_secp_224r1;
}