text: /* LibTomCrypt, modular cryptographic library -- Tom St Denis
   *
   * LibTomCrypt is a library that provides various cryptographic
   * algorithms in a highly modular and flexible manner.
   *
   * The library is free for all purposes without any express
   * guarantee it works.
   *
   * Tom St Denis, tomstdenis@gmail.com, http://libtomcrypt.com
   */
  
  /* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
   *
   * All curves taken from NIST recommendation paper of July 1999
   * Available at http://csrc.nist.gov/cryptval/dss.htm
   */
  #include "tomcrypt.h"
  
  /**
    @file ltc_ecc_projective_add_point.c
    ECC Crypto, Tom St Denis
  */  
  
  #if defined(MECC) && (!defined(MECC_ACCEL) || defined(LTM_DESC))
  
  /**
     Add two ECC points
     @param P        The point to add
     @param Q        The point to add
     @param R        [out] The destination of the double
     @param modulus  The modulus of the field the ECC curve is in
     @param mp       The "b" value from montgomery_setup()
     @return CRYPT_OK on success
  */
  int ltc_ecc_projective_add_point(ecc_point *P, ecc_point *Q, ecc_point *R, void *modulus, void *mp)
  {
     void  *t1, *t2, *x, *y, *z;
     int err;
  
     LTC_ARGCHK(P       != NULL);
     LTC_ARGCHK(Q       != NULL);
     LTC_ARGCHK(R       != NULL);
     LTC_ARGCHK(modulus != NULL);
     LTC_ARGCHK(mp      != NULL);
  
     if ((err = mp_init_multi(&t1, &t2, &x, &y, &z, NULL)) != CRYPT_OK) {
        return err;
     }
     
     /* should we dbl instead? */
     if ((err = mp_sub(modulus, Q->y, t1)) != CRYPT_OK)                          { goto done; }
  
     if ( (mp_cmp(P->x, Q->x) == LTC_MP_EQ) && 
          (Q->z != NULL && mp_cmp(P->z, Q->z) == LTC_MP_EQ) &&
          (mp_cmp(P->y, Q->y) == LTC_MP_EQ || mp_cmp(P->y, t1) == LTC_MP_EQ)) {
          mp_clear_multi(t1, t2, x, y, z, NULL);
          return ltc_ecc_projective_dbl_point(P, R, modulus, mp);
     }
  
     if ((err = mp_copy(P->x, x)) != CRYPT_OK)                                   { goto done; }
     if ((err = mp_copy(P->y, y)) != CRYPT_OK)                                   { goto done; }
     if ((err = mp_copy(P->z, z)) != CRYPT_OK)                                   { goto done; }
  
     /* if Z is one then these are no-operations */
     if (Q->z != NULL) {
        /* T1 = Z' * Z' */
        if ((err = mp_sqr(Q->z, t1)) != CRYPT_OK)                                { goto done; }
        if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)           { goto done; }
        /* X = X * T1 */
        if ((err = mp_mul(t1, x, x)) != CRYPT_OK)                                { goto done; }
        if ((err = mp_montgomery_reduce(x, modulus, mp)) != CRYPT_OK)            { goto done; }
        /* T1 = Z' * T1 */
        if ((err = mp_mul(Q->z, t1, t1)) != CRYPT_OK)                            { goto done; }
        if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)           { goto done; }
        /* Y = Y * T1 */
        if ((err = mp_mul(t1, y, y)) != CRYPT_OK)                                { goto done; }
        if ((err = mp_montgomery_reduce(y, modulus, mp)) != CRYPT_OK)            { goto done; }
     }
  
     /* T1 = Z*Z */
     if ((err = mp_sqr(z, t1)) != CRYPT_OK)                                      { goto done; }
     if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)              { goto done; }
     /* T2 = X' * T1 */
     if ((err = mp_mul(Q->x, t1, t2)) != CRYPT_OK)                               { goto done; }
     if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK)              { goto done; }
     /* T1 = Z * T1 */
     if ((err = mp_mul(z, t1, t1)) != CRYPT_OK)                                  { goto done; }
     if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)              { goto done; }
     /* T1 = Y' * T1 */
     if ((err = mp_mul(Q->y, t1, t1)) != CRYPT_OK)                               { goto done; }
     if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)              { goto done; }
  
     /* Y = Y - T1 */
     if ((err = mp_sub(y, t1, y)) != CRYPT_OK)                                   { goto done; }
     if (mp_cmp_d(y, 0) == LTC_MP_LT) {
        if ((err = mp_add(y, modulus, y)) != CRYPT_OK)                           { goto done; }
     }
     /* T1 = 2T1 */
     if ((err = mp_add(t1, t1, t1)) != CRYPT_OK)                                 { goto done; }
     if (mp_cmp(t1, modulus) != LTC_MP_LT) {
        if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK)                         { goto done; }
     }
     /* T1 = Y + T1 */
     if ((err = mp_add(t1, y, t1)) != CRYPT_OK)                                  { goto done; }
     if (mp_cmp(t1, modulus) != LTC_MP_LT) {
        if ((err = mp_sub(t1, modulus, t1)) != CRYPT_OK)                         { goto done; }
     }
     /* X = X - T2 */
     if ((err = mp_sub(x, t2, x)) != CRYPT_OK)                                   { goto done; }
     if (mp_cmp_d(x, 0) == LTC_MP_LT) {
        if ((err = mp_add(x, modulus, x)) != CRYPT_OK)                           { goto done; }
     }
     /* T2 = 2T2 */
     if ((err = mp_add(t2, t2, t2)) != CRYPT_OK)                                 { goto done; }
     if (mp_cmp(t2, modulus) != LTC_MP_LT) {
        if ((err = mp_sub(t2, modulus, t2)) != CRYPT_OK)                         { goto done; }
     }
     /* T2 = X + T2 */
     if ((err = mp_add(t2, x, t2)) != CRYPT_OK)                                  { goto done; }
     if (mp_cmp(t2, modulus) != LTC_MP_LT) {
        if ((err = mp_sub(t2, modulus, t2)) != CRYPT_OK)                         { goto done; }
     }
  
     /* if Z' != 1 */
     if (Q->z != NULL) {
        /* Z = Z * Z' */
        if ((err = mp_mul(z, Q->z, z)) != CRYPT_OK)                              { goto done; }
        if ((err = mp_montgomery_reduce(z, modulus, mp)) != CRYPT_OK)            { goto done; }
     }
  
     /* Z = Z * X */
     if ((err = mp_mul(z, x, z)) != CRYPT_OK)                                    { goto done; }
     if ((err = mp_montgomery_reduce(z, modulus, mp)) != CRYPT_OK)               { goto done; }
  
     /* T1 = T1 * X  */
     if ((err = mp_mul(t1, x, t1)) != CRYPT_OK)                                  { goto done; }
     if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)              { goto done; }
     /* X = X * X */
     if ((err = mp_sqr(x, x)) != CRYPT_OK)                                       { goto done; }
     if ((err = mp_montgomery_reduce(x, modulus, mp)) != CRYPT_OK)               { goto done; }
     /* T2 = T2 * x */
     if ((err = mp_mul(t2, x, t2)) != CRYPT_OK)                                  { goto done; }
     if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK)              { goto done; }
     /* T1 = T1 * X  */
     if ((err = mp_mul(t1, x, t1)) != CRYPT_OK)                                  { goto done; }
     if ((err = mp_montgomery_reduce(t1, modulus, mp)) != CRYPT_OK)              { goto done; }
   
     /* X = Y*Y */
     if ((err = mp_sqr(y, x)) != CRYPT_OK)                                       { goto done; }
     if ((err = mp_montgomery_reduce(x, modulus, mp)) != CRYPT_OK)               { goto done; }
     /* X = X - T2 */
     if ((err = mp_sub(x, t2, x)) != CRYPT_OK)                                   { goto done; }
     if (mp_cmp_d(x, 0) == LTC_MP_LT) {
        if ((err = mp_add(x, modulus, x)) != CRYPT_OK)                           { goto done; }
     }
  
     /* T2 = T2 - X */
     if ((err = mp_sub(t2, x, t2)) != CRYPT_OK)                                  { goto done; }
     if (mp_cmp_d(t2, 0) == LTC_MP_LT) {
        if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK)                         { goto done; }
     } 
     /* T2 = T2 - X */
     if ((err = mp_sub(t2, x, t2)) != CRYPT_OK)                                  { goto done; }
     if (mp_cmp_d(t2, 0) == LTC_MP_LT) {
        if ((err = mp_add(t2, modulus, t2)) != CRYPT_OK)                         { goto done; }
     }
     /* T2 = T2 * Y */
     if ((err = mp_mul(t2, y, t2)) != CRYPT_OK)                                  { goto done; }
     if ((err = mp_montgomery_reduce(t2, modulus, mp)) != CRYPT_OK)              { goto done; }
     /* Y = T2 - T1 */
     if ((err = mp_sub(t2, t1, y)) != CRYPT_OK)                                  { goto done; }
     if (mp_cmp_d(y, 0) == LTC_MP_LT) {
        if ((err = mp_add(y, modulus, y)) != CRYPT_OK)                           { goto done; }
     }
     /* Y = Y/2 */
     if (mp_isodd(y)) {
        if ((err = mp_add(y, modulus, y)) != CRYPT_OK)                           { goto done; }
     }
     if ((err = mp_div_2(y, y)) != CRYPT_OK)                                     { goto done; }
  
     if ((err = mp_copy(x, R->x)) != CRYPT_OK)                                   { goto done; }
     if ((err = mp_copy(y, R->y)) != CRYPT_OK)                                   { goto done; }
     if ((err = mp_copy(z, R->z)) != CRYPT_OK)                                   { goto done; }
  
     err = CRYPT_OK;
     goto done;
  done:
     mp_clear_multi(t1, t2, x, y, z, NULL);
     return err;
  }
  
  #endif
  
  /* $Source: /cvs/libtom/libtomcrypt/src/pk/ecc/ltc_ecc_projective_add_point.c,v $ */
  /* $Revision: 1.11 $ */
  /* $Date: 2006/06/09 21:46:17 $ */
  
  