release/src/router/nettle/ecc-add-jjj.c

   1 /* ecc-add-jjj.c */
   2
   3 /* nettle, low-level cryptographics library
   4  *
   5  * Copyright (C) 2013 Niels Möller
   6  *
   7  * The nettle library is free software; you can redistribute it and/or modify
   8  * it under the terms of the GNU Lesser General Public License as published by
   9  * the Free Software Foundation; either version 2.1 of the License, or (at your
  10  * option) any later version.
  11  *
  12  * The nettle library is distributed in the hope that it will be useful, but
  13  * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  14  * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  15  * License for more details.
  16  *
  17  * You should have received a copy of the GNU Lesser General Public License
  18  * along with the nettle library; see the file COPYING.LIB.  If not, write to
  19  * the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
  20  * MA 02111-1301, USA.
  21  */
  22
  23 /* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
  24
  25 #if HAVE_CONFIG_H
  26 # include "config.h"
  27 #endif
  28
  29 #include "ecc.h"
  30 #include "ecc-internal.h"
  31
  32 mp_size_t
  33 ecc_add_jjj_itch (const struct ecc_curve *ecc)
  34 {
  35   /* Needs 8 * ecc->size */
  36   return ECC_ADD_JJJ_ITCH (ecc->size);
  37 }
  38
  39 void
  40 ecc_add_jjj (const struct ecc_curve *ecc,
  41              mp_limb_t *r, const mp_limb_t *p, const mp_limb_t *q,
  42              mp_limb_t *scratch)
  43 {
  44   /* Formulas, from djb,
  45      http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl:
  46
  47      Computation                Operation       Live variables
  48
  49       Z1Z1 = Z1^2               sqr             Z1Z1
  50       Z2Z2 = Z2^2               sqr             Z1Z1, Z2Z2
  51       U1 = X1*Z2Z2              mul             Z1Z1, Z2Z2, U1
  52       U2 = X2*Z1Z1              mul             Z1Z1, Z2Z2, U1, U2
  53       H = U2-U1                                 Z1Z1, Z2Z2, U1, H
  54       Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H sqr, mul     Z1Z1, Z2Z2, U1, H
  55       S1 = Y1*Z2*Z2Z2           mul, mul        Z1Z1, U1, H, S1
  56       S2 = Y2*Z1*Z1Z1           mul, mul        U1, H, S1, S2
  57       W = 2*(S2-S1)     (djb: r)                U1, H, S1, W
  58       I = (2*H)^2               sqr             U1, H, S1, W, I
  59       J = H*I                   mul             U1, S1, W, J, V
  60       V = U1*I                  mul             S1, W, J, V
  61       X3 = W^2-J-2*V            sqr             S1, W, J, V
  62       Y3 = W*(V-X3)-2*S1*J      mul, mul
  63   */
  64   mp_limb_t *z1z1 = scratch;
  65   mp_limb_t *z2z2 = scratch + ecc->size;
  66   mp_limb_t *u1   = scratch + 2*ecc->size;
  67   mp_limb_t *u2   = scratch + 3*ecc->size;
  68   mp_limb_t *s1   = scratch; /* overlap z1z1 */
  69   mp_limb_t *s2   = scratch + ecc->size; /* overlap z2z2 */
  70   mp_limb_t *i    = scratch + 4*ecc->size;
  71   mp_limb_t *j    = scratch + 5*ecc->size;
  72   mp_limb_t *v    = scratch + 6*ecc->size;
  73
  74   /* z1^2, z2^2, u1 = x1 x2^2, u2 = x2 z1^2 - u1 */
  75   ecc_modp_sqr (ecc, z1z1, p + 2*ecc->size);
  76   ecc_modp_sqr (ecc, z2z2, q + 2*ecc->size);
  77   ecc_modp_mul (ecc, u1, p, z2z2);
  78   ecc_modp_mul (ecc, u2, q, z1z1);
  79   ecc_modp_sub (ecc, u2, u2, u1);  /* Store h in u2 */
  80
  81   /* z3, use i, j, v as scratch, result at i. */
  82   ecc_modp_add (ecc, i, p + 2*ecc->size, q + 2*ecc->size);
  83   ecc_modp_sqr (ecc, v, i);
  84   ecc_modp_sub (ecc, v, v, z1z1);
  85   ecc_modp_sub (ecc, v, v, z2z2);
  86   ecc_modp_mul (ecc, i, v, u2);
  87   /* Delayed write, to support in-place operation. */
  88
  89   /* s1 = y1 z2^3, s2 = y2 z1^3, scratch at j and v */
  90   ecc_modp_mul (ecc, j, z1z1, p + 2*ecc->size); /* z1^3 */
  91   ecc_modp_mul (ecc, v, z2z2, q + 2*ecc->size); /* z2^3 */
  92   ecc_modp_mul (ecc, s1, p + ecc->size, v);
  93   ecc_modp_mul (ecc, v, j, q + ecc->size);
  94   ecc_modp_sub (ecc, s2, v, s1);
  95   ecc_modp_mul_1 (ecc, s2, s2, 2);
  96
  97   /* Store z3 */
  98   mpn_copyi (r + 2*ecc->size, i, ecc->size);
  99
 100   /* i, j, v */
 101   ecc_modp_sqr (ecc, i, u2);
 102   ecc_modp_mul_1 (ecc, i, i, 4);
 103   ecc_modp_mul (ecc, j, u2, i);
 104   ecc_modp_mul (ecc, v, u1, i);
 105
 106   /* now, u1, u2 and i are free for reuse .*/
 107   /* x3, use u1, u2 as scratch */
 108   ecc_modp_sqr (ecc, u1, s2);
 109   ecc_modp_sub (ecc, r, u1, j);
 110   ecc_modp_submul_1 (ecc, r, v, 2);
 111
 112   /* y3 */
 113   ecc_modp_mul (ecc, u1, s1, j); /* Frees j */
 114   ecc_modp_sub (ecc, u2, v, r);  /* Frees v */
 115   ecc_modp_mul (ecc, i, s2, u2);
 116   ecc_modp_submul_1 (ecc, i, u1, 2);
 117   mpn_copyi (r + ecc->size, i, ecc->size);
 118 }