Exemple #1
0
/* Do modular exponentiation using floating point multiply code. */
mp_err mp_exptmod_f(const mp_int *   montBase, 
                    const mp_int *   exponent, 
		    const mp_int *   modulus, 
		    mp_int *         result, 
		    mp_mont_modulus *mmm, 
		    int              nLen, 
		    mp_size          bits_in_exponent, 
		    mp_size          window_bits,
		    mp_size          odd_ints)
{
  mp_digit *mResult;
  double   *dBuf = 0, *dm1, *dn, *dSqr, *d16Tmp, *dTmp;
  double    dn0;
  mp_size   i;
  mp_err    res;
  int       expOff;
  int       dSize = 0, oddPowSize, dTmpSize;
  mp_int    accum1;
  double   *oddPowers[MAX_ODD_INTS];

  /* function for computing n0prime only works if n0 is odd */

  MP_DIGITS(&accum1) = 0;

  for (i = 0; i < MAX_ODD_INTS; ++i)
    oddPowers[i] = 0;

  MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );

  mp_set(&accum1, 1);
  MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
  MP_CHECKOK( s_mp_pad(&accum1, nLen) );

  oddPowSize = 2 * nLen + 1;
  dTmpSize   = 2 * oddPowSize;
  dSize = sizeof(double) * (nLen * 4 + 1 + 
			    ((odd_ints + 1) * oddPowSize) + dTmpSize);
  dBuf   = (double *)malloc(dSize);
  dm1    = dBuf;		/* array of d32 */
  dn     = dBuf   + nLen;	/* array of d32 */
  dSqr   = dn     + nLen;    	/* array of d32 */
  d16Tmp = dSqr   + nLen;	/* array of d16 */
  dTmp   = d16Tmp + oddPowSize;

  for (i = 0; i < odd_ints; ++i) {
      oddPowers[i] = dTmp;
      dTmp += oddPowSize;
  }
  mResult = (mp_digit *)(dTmp + dTmpSize);	/* size is nLen + 1 */

  /* Make dn and dn0 */
  conv_i32_to_d32(dn, MP_DIGITS(modulus), nLen);
  dn0 = (double)(mmm->n0prime & 0xffff);

  /* Make dSqr */
  conv_i32_to_d32_and_d16(dm1, oddPowers[0], MP_DIGITS(montBase), nLen);
  mont_mulf_noconv(mResult, dm1, oddPowers[0], 
		   dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
  conv_i32_to_d32(dSqr, mResult, nLen);

  for (i = 1; i < odd_ints; ++i) {
    mont_mulf_noconv(mResult, dSqr, oddPowers[i - 1], 
		     dTmp, dn, MP_DIGITS(modulus), nLen, dn0);
    conv_i32_to_d16(oddPowers[i], mResult, nLen);
  }

  s_mp_copy(MP_DIGITS(&accum1), mResult, nLen); /* from, to, len */

  for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
    mp_size smallExp;
    MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
    smallExp = (mp_size)res;

    if (window_bits == 1) {
      if (!smallExp) {
	SQR;
      } else if (smallExp & 1) {
	SQR; MUL(0); 
      } else {
	ABORT;
      }
    } else if (window_bits == 4) {
      if (!smallExp) {
	SQR; SQR; SQR; SQR;
      } else if (smallExp & 1) {
	SQR; SQR; SQR; SQR; MUL(smallExp/2); 
      } else if (smallExp & 2) {
	SQR; SQR; SQR; MUL(smallExp/4); SQR; 
      } else if (smallExp & 4) {
	SQR; SQR; MUL(smallExp/8); SQR; SQR; 
      } else if (smallExp & 8) {
	SQR; MUL(smallExp/16); SQR; SQR; SQR; 
      } else {
	ABORT;
      }
    } else if (window_bits == 5) {
      if (!smallExp) {
	SQR; SQR; SQR; SQR; SQR; 
      } else if (smallExp & 1) {
	SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2);
      } else if (smallExp & 2) {
	SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR;
      } else if (smallExp & 4) {
	SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR;
      } else if (smallExp & 8) {
	SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR;
      } else if (smallExp & 0x10) {
	SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR;
      } else {
	ABORT;
      }
    } else if (window_bits == 6) {
      if (!smallExp) {
	SQR; SQR; SQR; SQR; SQR; SQR;
      } else if (smallExp & 1) {
	SQR; SQR; SQR; SQR; SQR; SQR; MUL(smallExp/2); 
      } else if (smallExp & 2) {
	SQR; SQR; SQR; SQR; SQR; MUL(smallExp/4); SQR; 
      } else if (smallExp & 4) {
	SQR; SQR; SQR; SQR; MUL(smallExp/8); SQR; SQR; 
      } else if (smallExp & 8) {
	SQR; SQR; SQR; MUL(smallExp/16); SQR; SQR; SQR; 
      } else if (smallExp & 0x10) {
	SQR; SQR; MUL(smallExp/32); SQR; SQR; SQR; SQR; 
      } else if (smallExp & 0x20) {
	SQR; MUL(smallExp/64); SQR; SQR; SQR; SQR; SQR; 
      } else {
	ABORT;
      }
    } else {
      ABORT;
    }
  }

  s_mp_copy(mResult, MP_DIGITS(&accum1), nLen); /* from, to, len */

  res = s_mp_redc(&accum1, mmm);
  mp_exch(&accum1, result);

CLEANUP:
  mp_clear(&accum1);
  if (dBuf) {
    if (dSize)
      memset(dBuf, 0, dSize);
    free(dBuf);
  }

  return res;
}
Exemple #2
0
/* Do modular exponentiation using integer multiply code. */
mp_err mp_exptmod_i(const mp_int *   montBase, 
                    const mp_int *   exponent, 
		    const mp_int *   modulus, 
		    mp_int *         result, 
		    mp_mont_modulus *mmm, 
		    int              nLen, 
		    mp_size          bits_in_exponent, 
		    mp_size          window_bits,
		    mp_size          odd_ints)
{
  mp_int *pa1, *pa2, *ptmp;
  mp_size i;
  mp_err  res;
  int     expOff;
  mp_int  accum1, accum2, power2, oddPowers[MAX_ODD_INTS];

  /* power2 = base ** 2; oddPowers[i] = base ** (2*i + 1); */
  /* oddPowers[i] = base ** (2*i + 1); */

  MP_DIGITS(&accum1) = 0;
  MP_DIGITS(&accum2) = 0;
  MP_DIGITS(&power2) = 0;
  for (i = 0; i < MAX_ODD_INTS; ++i) {
    MP_DIGITS(oddPowers + i) = 0;
  }

  MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
  MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );

  MP_CHECKOK( mp_init_copy(&oddPowers[0], montBase) );

  mp_init_size(&power2, nLen + 2 * MP_USED(montBase) + 2);
  MP_CHECKOK( mp_sqr(montBase, &power2) );	/* power2 = montBase ** 2 */
  MP_CHECKOK( s_mp_redc(&power2, mmm) );

  for (i = 1; i < odd_ints; ++i) {
    mp_init_size(oddPowers + i, nLen + 2 * MP_USED(&power2) + 2);
    MP_CHECKOK( mp_mul(oddPowers + (i - 1), &power2, oddPowers + i) );
    MP_CHECKOK( s_mp_redc(oddPowers + i, mmm) );
  }

  /* set accumulator to montgomery residue of 1 */
  mp_set(&accum1, 1);
  MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
  pa1 = &accum1;
  pa2 = &accum2;

  for (expOff = bits_in_exponent - window_bits; expOff >= 0; expOff -= window_bits) {
    mp_size smallExp;
    MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
    smallExp = (mp_size)res;

    if (window_bits == 1) {
      if (!smallExp) {
	SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 1) {
	SQR(pa1,pa2); MUL(0,pa2,pa1);
      } else {
	ABORT;
      }
    } else if (window_bits == 4) {
      if (!smallExp) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
      } else if (smallExp & 1) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	MUL(smallExp/2, pa1,pa2); SWAPPA;
      } else if (smallExp & 2) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); 
	MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 4) {
	SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/8,pa1,pa2); 
	SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 8) {
	SQR(pa1,pa2); MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2); 
	SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else {
	ABORT;
      }
    } else if (window_bits == 5) {
      if (!smallExp) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 1) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); MUL(smallExp/2,pa2,pa1);
      } else if (smallExp & 2) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	MUL(smallExp/4,pa1,pa2); SQR(pa2,pa1);
      } else if (smallExp & 4) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); 
	MUL(smallExp/8,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
      } else if (smallExp & 8) {
	SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/16,pa1,pa2); 
	SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
      } else if (smallExp & 0x10) {
	SQR(pa1,pa2); MUL(smallExp/32,pa2,pa1); SQR(pa1,pa2); 
	SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
      } else {
	ABORT;
      }
    } else if (window_bits == 6) {
      if (!smallExp) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); SQR(pa2,pa1);
      } else if (smallExp & 1) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/2,pa1,pa2); SWAPPA;
      } else if (smallExp & 2) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); MUL(smallExp/4,pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 4) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	MUL(smallExp/8,pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 8) {
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); 
	MUL(smallExp/16,pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 0x10) {
	SQR(pa1,pa2); SQR(pa2,pa1); MUL(smallExp/32,pa1,pa2); 
	SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else if (smallExp & 0x20) {
	SQR(pa1,pa2); MUL(smallExp/64,pa2,pa1); SQR(pa1,pa2); 
	SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SWAPPA;
      } else {
	ABORT;
      }
    } else {
      ABORT;
    }
  }

  res = s_mp_redc(pa1, mmm);
  mp_exch(pa1, result);

CLEANUP:
  mp_clear(&accum1);
  mp_clear(&accum2);
  mp_clear(&power2);
  for (i = 0; i < odd_ints; ++i) {
    mp_clear(oddPowers + i);
  }
  return res;
}
Exemple #3
0
/* Do modular exponentiation using integer multiply code. */
mp_err mp_exptmod_safe_i(const mp_int *   montBase, 
                    const mp_int *   exponent, 
		    const mp_int *   modulus, 
		    mp_int *         result, 
		    mp_mont_modulus *mmm, 
		    int              nLen, 
		    mp_size          bits_in_exponent, 
		    mp_size          window_bits,
		    mp_size          num_powers)
{
  mp_int *pa1, *pa2, *ptmp;
  mp_size i;
  mp_size first_window;
  mp_err  res;
  int     expOff;
  mp_int  accum1, accum2, accum[WEAVE_WORD_SIZE];
  mp_int  tmp;
  unsigned char *powersArray;
  unsigned char *powers;

  MP_DIGITS(&accum1) = 0;
  MP_DIGITS(&accum2) = 0;
  MP_DIGITS(&accum[0]) = 0;
  MP_DIGITS(&accum[1]) = 0;
  MP_DIGITS(&accum[2]) = 0;
  MP_DIGITS(&accum[3]) = 0;
  MP_DIGITS(&tmp) = 0;

  powersArray = (unsigned char *)malloc(num_powers*(nLen*sizeof(mp_digit)+1));
  if (powersArray == NULL) {
    res = MP_MEM;
    goto CLEANUP;
  }

  /* powers[i] = base ** (i); */
  powers = (unsigned char *)MP_ALIGN(powersArray,num_powers);

  /* grab the first window value. This allows us to preload accumulator1
   * and save a conversion, some squares and a multiple*/
  MP_CHECKOK( mpl_get_bits(exponent, 
				bits_in_exponent-window_bits, window_bits) );
  first_window = (mp_size)res;

  MP_CHECKOK( mp_init_size(&accum1, 3 * nLen + 2) );
  MP_CHECKOK( mp_init_size(&accum2, 3 * nLen + 2) );
  MP_CHECKOK( mp_init_size(&tmp, 3 * nLen + 2) );

  /* build the first WEAVE_WORD powers inline */
  /* if WEAVE_WORD_SIZE is not 4, this code will have to change */
  if (num_powers > 2) {
    MP_CHECKOK( mp_init_size(&accum[0], 3 * nLen + 2) );
    MP_CHECKOK( mp_init_size(&accum[1], 3 * nLen + 2) );
    MP_CHECKOK( mp_init_size(&accum[2], 3 * nLen + 2) );
    MP_CHECKOK( mp_init_size(&accum[3], 3 * nLen + 2) );
    mp_set(&accum[0], 1);
    MP_CHECKOK( s_mp_to_mont(&accum[0], mmm, &accum[0]) );
    MP_CHECKOK( mp_copy(montBase, &accum[1]) );
    SQR(montBase, &accum[2]);
    MUL_NOWEAVE(montBase, &accum[2], &accum[3]);
    MP_CHECKOK( mpi_to_weave(accum, powers, nLen, num_powers) );
    if (first_window < 4) {
      MP_CHECKOK( mp_copy(&accum[first_window], &accum1) );
      first_window = num_powers;
    }
  } else {
      if (first_window == 0) {
        mp_set(&accum1, 1);
        MP_CHECKOK( s_mp_to_mont(&accum1, mmm, &accum1) );
      } else {
        /* assert first_window == 1? */
        MP_CHECKOK( mp_copy(montBase, &accum1) );
      }
  }

  /*
   * calculate all the powers in the powers array.
   * this adds 2**(k-1)-2 square operations over just calculating the
   * odd powers where k is the window size in the two other mp_modexpt
   * implementations in this file. We will get some of that
   * back by not needing the first 'k' squares and one multiply for the 
   * first window */ 
  for (i = WEAVE_WORD_SIZE; i < num_powers; i++) {
    int acc_index = i & (WEAVE_WORD_SIZE-1); /* i % WEAVE_WORD_SIZE */
    if ( i & 1 ) {
      MUL_NOWEAVE(montBase, &accum[acc_index-1] , &accum[acc_index]);
      /* we've filled the array do our 'per array' processing */
      if (acc_index == (WEAVE_WORD_SIZE-1)) {
        MP_CHECKOK( mpi_to_weave(accum, powers + i - (WEAVE_WORD_SIZE-1),
							 nLen, num_powers) );

        if (first_window <= i) {
          MP_CHECKOK( mp_copy(&accum[first_window & (WEAVE_WORD_SIZE-1)], 
								&accum1) );
          first_window = num_powers;
        }
      }
    } else {
      /* up to 8 we can find 2^i-1 in the accum array, but at 8 we our source
       * and target are the same so we need to copy.. After that, the
       * value is overwritten, so we need to fetch it from the stored
       * weave array */
      if (i > 2* WEAVE_WORD_SIZE) {
        MP_CHECKOK(weave_to_mpi(&accum2, powers+i/2, nLen, num_powers));
        SQR(&accum2, &accum[acc_index]);
      } else {
	int half_power_index = (i/2) & (WEAVE_WORD_SIZE-1);
	if (half_power_index == acc_index) {
	   /* copy is cheaper than weave_to_mpi */
	   MP_CHECKOK(mp_copy(&accum[half_power_index], &accum2));
	   SQR(&accum2,&accum[acc_index]);
	} else {
	   SQR(&accum[half_power_index],&accum[acc_index]);
	}
      }
    }
  }
  /* if the accum1 isn't set, Then there is something wrong with our logic 
   * above and is an internal programming error. 
   */
#if MP_ARGCHK == 2
  assert(MP_USED(&accum1) != 0);
#endif

  /* set accumulator to montgomery residue of 1 */
  pa1 = &accum1;
  pa2 = &accum2;

  for (expOff = bits_in_exponent - window_bits*2; expOff >= 0; expOff -= window_bits) {
    mp_size smallExp;
    MP_CHECKOK( mpl_get_bits(exponent, expOff, window_bits) );
    smallExp = (mp_size)res;

    /* handle unroll the loops */
    switch (window_bits) {
    case 1:
	if (!smallExp) {
	    SQR(pa1,pa2); SWAPPA;
	} else if (smallExp & 1) {
	    SQR(pa1,pa2); MUL_NOWEAVE(montBase,pa2,pa1);
	} else {
	    abort();
	}
	break;
    case 6:
	SQR(pa1,pa2); SQR(pa2,pa1); 
	/* fall through */
    case 4:
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1);
	MUL(smallExp, pa1,pa2); SWAPPA;
	break;
    case 5:
	SQR(pa1,pa2); SQR(pa2,pa1); SQR(pa1,pa2); SQR(pa2,pa1); 
	SQR(pa1,pa2); MUL(smallExp,pa2,pa1);
	break;
    default:
	abort(); /* could do a loop? */
    }
  }

  res = s_mp_redc(pa1, mmm);
  mp_exch(pa1, result);

CLEANUP:
  mp_clear(&accum1);
  mp_clear(&accum2);
  mp_clear(&accum[0]);
  mp_clear(&accum[1]);
  mp_clear(&accum[2]);
  mp_clear(&accum[3]);
  mp_clear(&tmp);
  /* PORT_Memset(powers,0,num_powers*nLen*sizeof(mp_digit)); */
  free(powersArray);
  return res;
}