text: /*
   * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved.
   * Use is subject to license terms.
   *
   * This 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.
   *
   * This 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 this library; if not, write to the Free Software Foundation,
   * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
   *
   * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
   * or visit www.oracle.com if you need additional information or have any
   * questions.
   */
  
  /* *********************************************************************
   *
   * The Original Code is the elliptic curve math library for prime field curves.
   *
   * The Initial Developer of the Original Code is
   * Sun Microsystems, Inc.
   * Portions created by the Initial Developer are Copyright (C) 2003
   * the Initial Developer. All Rights Reserved.
   *
   * Contributor(s):
   *   Stephen Fung <fungstep@hotmail.com>, Sun Microsystems Laboratories
   *
   *********************************************************************** */
  
  #include "ecp.h"
  #include "ecl-priv.h"
  #include "mplogic.h"
  #ifndef _KERNEL
  #include <stdlib.h>
  #endif
  
  #define MAX_SCRATCH 6
  
  /* Computes R = 2P.  Elliptic curve points P and R can be identical.  Uses
   * Modified Jacobian coordinates.
   *
   * Assumes input is already field-encoded using field_enc, and returns
   * output that is still field-encoded.
   *
   */
  mp_err
  ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
                                   const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
                                   mp_int *raz4, mp_int scratch[], const ECGroup *group)
  {
          mp_err res = MP_OKAY;
          mp_int *t0, *t1, *M, *S;
  
          t0 = &scratch[0];
          t1 = &scratch[1];
          M = &scratch[2];
          S = &scratch[3];
  
  #if MAX_SCRATCH < 4
  #error "Scratch array defined too small "
  #endif
  
          /* Check for point at infinity */
          if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
                  /* Set r = pt at infinity by setting rz = 0 */
  
                  MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
                  goto CLEANUP;
          }
  
          /* M = 3 (px^2) + a*(pz^4) */
          MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
          MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
          MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
          MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
  
          /* rz = 2 * py * pz */
          MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
          MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
  
          /* t0 = 2y^2 , t1 = 8y^4 */
          MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
          MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
          MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
          MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
  
          /* S = 4 * px * py^2 = 2 * px * t0 */
          MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
          MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
  
  
          /* rx = M^2 - 2S */
          MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
          MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
          MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
  
          /* ry = M * (S - rx) - t1 */
          MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
          MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
          MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
  
          /* ra*z^4 = 2*t1*(apz4) */
          MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
          MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
  
  
    CLEANUP:
          return res;
  }
  
  /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
   * (qx, qy, 1).  Elliptic curve points P, Q, and R can all be identical.
   * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
   * already field-encoded using field_enc, and returns output that is still
   * field-encoded. */
  mp_err
  ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
                                           const mp_int *paz4, const mp_int *qx,
                                           const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
                                           mp_int *raz4, mp_int scratch[], const ECGroup *group)
  {
          mp_err res = MP_OKAY;
          mp_int *A, *B, *C, *D, *C2, *C3;
  
          A = &scratch[0];
          B = &scratch[1];
          C = &scratch[2];
          D = &scratch[3];
          C2 = &scratch[4];
          C3 = &scratch[5];
  
  #if MAX_SCRATCH < 6
  #error "Scratch array defined too small "
  #endif
  
          /* If either P or Q is the point at infinity, then return the other
           * point */
          if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
                  MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
                  MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
                  MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
                  MP_CHECKOK(group->meth->
                                     field_mul(raz4, &group->curvea, raz4, group->meth));
                  goto CLEANUP;
          }
          if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
                  MP_CHECKOK(mp_copy(px, rx));
                  MP_CHECKOK(mp_copy(py, ry));
                  MP_CHECKOK(mp_copy(pz, rz));
                  MP_CHECKOK(mp_copy(paz4, raz4));
                  goto CLEANUP;
          }
  
          /* A = qx * pz^2, B = qy * pz^3 */
          MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
          MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
          MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
          MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
  
          /* C = A - px, D = B - py */
          MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
          MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
  
          /* C2 = C^2, C3 = C^3 */
          MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
          MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
  
          /* rz = pz * C */
          MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
  
          /* C = px * C^2 */
          MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
          /* A = D^2 */
          MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
  
          /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
          MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
          MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
          MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
  
          /* C3 = py * C^3 */
          MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
  
          /* ry = D * (px * C^2 - rx) - py * C^3 */
          MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
          MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
          MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
  
          /* raz4 = a * rz^4 */
          MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
          MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
          MP_CHECKOK(group->meth->
                             field_mul(raz4, &group->curvea, raz4, group->meth));
  CLEANUP:
          return res;
  }
  
  /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
   * curve points P and R can be identical. Uses mixed Modified-Jacobian
   * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
   * additions. Assumes input is already field-encoded using field_enc, and
   * returns output that is still field-encoded. Uses 5-bit window NAF
   * method (algorithm 11) for scalar-point multiplication from Brown,
   * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
   * Curves Over Prime Fields. */
  mp_err
  ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
                                            mp_int *rx, mp_int *ry, const ECGroup *group)
  {
          mp_err res = MP_OKAY;
          mp_int precomp[16][2], rz, tpx, tpy;
          mp_int raz4;
          mp_int scratch[MAX_SCRATCH];
          signed char *naf = NULL;
          int i, orderBitSize;
  
          MP_DIGITS(&rz) = 0;
          MP_DIGITS(&raz4) = 0;
          MP_DIGITS(&tpx) = 0;
          MP_DIGITS(&tpy) = 0;
          for (i = 0; i < 16; i++) {
                  MP_DIGITS(&precomp[i][0]) = 0;
                  MP_DIGITS(&precomp[i][1]) = 0;
          }
          for (i = 0; i < MAX_SCRATCH; i++) {
                  MP_DIGITS(&scratch[i]) = 0;
          }
  
          ARGCHK(group != NULL, MP_BADARG);
          ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
  
          /* initialize precomputation table */
          MP_CHECKOK(mp_init(&tpx, FLAG(n)));
          MP_CHECKOK(mp_init(&tpy, FLAG(n)));;
          MP_CHECKOK(mp_init(&rz, FLAG(n)));
          MP_CHECKOK(mp_init(&raz4, FLAG(n)));
  
          for (i = 0; i < 16; i++) {
                  MP_CHECKOK(mp_init(&precomp[i][0], FLAG(n)));
                  MP_CHECKOK(mp_init(&precomp[i][1], FLAG(n)));
          }
          for (i = 0; i < MAX_SCRATCH; i++) {
                  MP_CHECKOK(mp_init(&scratch[i], FLAG(n)));
          }
  
          /* Set out[8] = P */
          MP_CHECKOK(mp_copy(px, &precomp[8][0]));
          MP_CHECKOK(mp_copy(py, &precomp[8][1]));
  
          /* Set (tpx, tpy) = 2P */
          MP_CHECKOK(group->
                             point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
                                                   group));
  
          /* Set 3P, 5P, ..., 15P */
          for (i = 8; i < 15; i++) {
                  MP_CHECKOK(group->
                                     point_add(&precomp[i][0], &precomp[i][1], &tpx, &tpy,
                                                           &precomp[i + 1][0], &precomp[i + 1][1],
                                                           group));
          }
  
          /* Set -15P, -13P, ..., -P */
          for (i = 0; i < 8; i++) {
                  MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
                  MP_CHECKOK(group->meth->
                                     field_neg(&precomp[15 - i][1], &precomp[i][1],
                                                           group->meth));
          }
  
          /* R = inf */
          MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
  
          orderBitSize = mpl_significant_bits(&group->order);
  
          /* Allocate memory for NAF */
  #ifdef _KERNEL
          naf = (signed char *) kmem_alloc((orderBitSize + 1), FLAG(n));
  #else
          naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
          if (naf == NULL) {
                  res = MP_MEM;
                  goto CLEANUP;
          }
  #endif
  
          /* Compute 5NAF */
          ec_compute_wNAF(naf, orderBitSize, n, 5);
  
          /* wNAF method */
          for (i = orderBitSize; i >= 0; i--) {
                  /* R = 2R */
                  ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
                                               &raz4, scratch, group);
                  if (naf[i] != 0) {
                          ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
                                                                   &precomp[(naf[i] + 15) / 2][0],
                                                                   &precomp[(naf[i] + 15) / 2][1], rx, ry,
                                                                   &rz, &raz4, scratch, group);
                  }
          }
  
          /* convert result S to affine coordinates */
          MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
  
    CLEANUP:
          for (i = 0; i < MAX_SCRATCH; i++) {
                  mp_clear(&scratch[i]);
          }
          for (i = 0; i < 16; i++) {
                  mp_clear(&precomp[i][0]);
                  mp_clear(&precomp[i][1]);
          }
          mp_clear(&tpx);
          mp_clear(&tpy);
          mp_clear(&rz);
          mp_clear(&raz4);
  #ifdef _KERNEL
          kmem_free(naf, (orderBitSize + 1));
  #else
          free(naf);
  #endif
          return res;
  }
  