/* Copyright (c) 2018, Google Inc.

 *

 * Permission to use, copy, modify, and/or distribute this software for any

 * purpose with or without fee is hereby granted, provided that the above

 * copyright notice and this permission notice appear in all copies.

 *

 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES

 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF

 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY

 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES

 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION

 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN

 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */

#include <openssl/bn.h>

#include <assert.h>

#include "internal.h"

// The following functions use a Barrett reduction variant to avoid leaking the

// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html

//

// We use 32-bit numerator and 16-bit divisor for simplicity. This allows

// computing |m| and |q| without architecture-specific code.

// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see

// reference). For proof of correctness in Coq, see

// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v

// Note the Coq version of |mod_u16| additionally includes the computation of

// |p| and |m| from |bn_mod_u16_consttime| below.

static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) {

  // Compute floor(n/d) per steps 3 through 5.

  uint32_t q = ((uint64_t)m * n) >> 32;

  // Note there is a typo in the reference. We right-shift by one, not two.

  uint32_t t = ((n - q) >> 1) + q;

  t = t >> (p - 1);

  // Multiply and subtract to get the remainder.

  n -= d * t;

  declassify_assert(n < d);

  return n;

}

// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the

// "magic numbers" for |d| (see reference).

static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d,

                                      uint32_t p, uint32_t m) {

  // Incorporate |a| in two 16-bit chunks.

  uint32_t t = r;

  t <<= 16;

  t |= a >> 16;

  t = mod_u16(t, d, p, m);

  t <<= 16;

  t |= a & 0xffff;

  t = mod_u16(t, d, p, m);

  return t;

}

uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) {

  if (d <= 1) {

    return 0;

  }

  // Compute the "magic numbers" for |d|. See steps 1 and 2.

  // This computes p = ceil(log_2(d)).

  uint32_t p = BN_num_bits_word(d - 1);

  // This operation is not constant-time, but |p| and |d| are public values.

  // Note that |p| is at most 16, so the computation fits in |uint64_t|.

  assert(p <= 16);

  uint32_t m = (uint32_t)(((UINT64_C(1) << (32 + p)) + d - 1) / d);

  uint16_t ret = 0;

  for (int i = bn->width - 1; i >= 0; i--) {

#if BN_BITS2 == 32

    ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m);

#elif BN_BITS2 == 64

    ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m);

    ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m);

#else

#error "Unknown BN_ULONG size"

#endif

  }

  return ret;

}