/*

 * Copyright (c) 2018 Thomas Pornin <pornin@bolet.org>

 *

 * Permission is hereby granted, free of charge, to any person obtaining 

 * a copy of this software and associated documentation files (the

 * "Software"), to deal in the Software without restriction, including

 * without limitation the rights to use, copy, modify, merge, publish,

 * distribute, sublicense, and/or sell copies of the Software, and to

 * permit persons to whom the Software is furnished to do so, subject to

 * the following conditions:

 *

 * The above copyright notice and this permission notice shall be 

 * included in all copies or substantial portions of the Software.

 *

 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 

 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF

 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 

 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS

 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN

 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN

 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

 * SOFTWARE.

 */

#include "inner.h"

#if BR_INT128 || BR_UMUL128

#if BR_UMUL128

#include <intrin.h>

#endif

static const unsigned char GEN[] = {

  0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,

  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00

};

static const unsigned char ORDER[] = {

  0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,

  0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF

};

static const unsigned char *

api_generator(int curve, size_t *len)

{

  (void)curve;

  *len = 32;

  return GEN;

}

static const unsigned char *

api_order(int curve, size_t *len)

{

  (void)curve;

  *len = 32;

  return ORDER;

}

static size_t

api_xoff(int curve, size_t *len)

{

  (void)curve;

  *len = 32;

  return 0;

}

/*

 * A field element is encoded as five 64-bit integers, in basis 2^51.

 * Limbs may be occasionally larger than 2^51, to save on carry

 * propagation costs.

 */

#define MASK51   (((uint64_t)1 << 51) - (uint64_t)1)

/*

 * Swap two field elements, conditionally on a flag.

 */

static inline void

f255_cswap(uint64_t *a, uint64_t *b, uint32_t ctl)

{

  uint64_t m, w;

  m = -(uint64_t)ctl;

  w = m & (a[0] ^ b[0]); a[0] ^= w; b[0] ^= w;

  w = m & (a[1] ^ b[1]); a[1] ^= w; b[1] ^= w;

  w = m & (a[2] ^ b[2]); a[2] ^= w; b[2] ^= w;

  w = m & (a[3] ^ b[3]); a[3] ^= w; b[3] ^= w;

  w = m & (a[4] ^ b[4]); a[4] ^= w; b[4] ^= w;

}

/*

 * Addition with no carry propagation. Limbs double in size.

 */

static inline void

f255_add(uint64_t *d, const uint64_t *a, const uint64_t *b)

{

  d[0] = a[0] + b[0];

  d[1] = a[1] + b[1];

  d[2] = a[2] + b[2];

  d[3] = a[3] + b[3];

  d[4] = a[4] + b[4];

}

/*

 * Subtraction.

 * On input, limbs must fit on 60 bits each. On output, result is

 * partially reduced, with max value 2^255+19456; moreover, all

 * limbs will fit on 51 bits, except the low limb, which may have

 * value up to 2^51+19455.

 */

static inline void

f255_sub(uint64_t *d, const uint64_t *a, const uint64_t *b)

{

  uint64_t cc, w;

  /*

   * We compute d = (2^255-19)*1024 + a - b. Since the limbs

   * fit on 60 bits, the maximum value of operands are slightly

   * more than 2^264, but much less than 2^265-19456. This

   * ensures that the result is positive.

   */

  /*

   * Initial carry is 19456, since we add 2^265-19456. Each

   * individual subtraction may yield a carry up to 513.

   */

  w = a[0] - b[0] - 19456;

  d[0] = w & MASK51;

  cc = -(w >> 51) & 0x3FF;

  w = a[1] - b[1] - cc;

  d[1] = w & MASK51;

  cc = -(w >> 51) & 0x3FF;

  w = a[2] - b[2] - cc;

  d[2] = w & MASK51;

  cc = -(w >> 51) & 0x3FF;

  w = a[3] - b[3] - cc;

  d[3] = w & MASK51;

  cc = -(w >> 51) & 0x3FF;

  d[4] = ((uint64_t)1 << 61) + a[4] - b[4] - cc;

  /*

   * Partial reduction. The intermediate result may be up to

   * slightly above 2^265, but less than 2^265+2^255. When we

   * truncate to 255 bits, the upper bits will be at most 1024.

   */

  d[0] += 19 * (d[4] >> 51);

  d[4] &= MASK51;

}

/*

 * UMUL51(hi, lo, x, y) computes:

 *

 *   hi = floor((x * y) / (2^51))

 *   lo = x * y mod 2^51

 *

 * Note that lo < 2^51, but "hi" may be larger, if the input operands are

 * larger.

 */

#if BR_INT128

#define UMUL51(hi, lo, x, y)   do { \

    unsigned __int128 umul_tmp; \

    umul_tmp = (unsigned __int128)(x) * (unsigned __int128)(y); \

    (hi) = (uint64_t)(umul_tmp >> 51); \

    (lo) = (uint64_t)umul_tmp & MASK51; \

  } while (0)

#elif BR_UMUL128

#define UMUL51(hi, lo, x, y)   do { \

    uint64_t umul_hi, umul_lo; \

    umul_lo = _umul128((x), (y), &umul_hi); \

    (hi) = (umul_hi << 13) | (umul_lo >> 51); \

    (lo) = umul_lo & MASK51; \

  } while (0)

#endif

/*

 * Multiplication.

 * On input, limbs must fit on 54 bits each.

 * On output, limb 0 is at most 2^51 + 155647, and other limbs fit

 * on 51 bits each.

 */

static inline void

f255_mul(uint64_t *d, uint64_t *a, uint64_t *b)

{

  uint64_t t[10], hi, lo, w, cc;

  /*

   * Perform cross products, accumulating values without carry

   * propagation.

   *

   * Since input limbs fit on 54 bits each, each individual

   * UMUL51 will produce a "hi" of less than 2^57. The maximum

   * sum will be at most 5*(2^57-1) + 4*(2^51-1) (for t[5]),

   * i.e. less than 324*2^51.

   */

  UMUL51(t[1], t[0], a[0], b[0]);

  UMUL51(t[2], lo, a[1], b[0]); t[1] += lo;

  UMUL51(hi, lo, a[0], b[1]); t[1] += lo; t[2] += hi;

  UMUL51(t[3], lo, a[2], b[0]); t[2] += lo;

  UMUL51(hi, lo, a[1], b[1]); t[2] += lo; t[3] += hi;

  UMUL51(hi, lo, a[0], b[2]); t[2] += lo; t[3] += hi;

  UMUL51(t[4], lo, a[3], b[0]); t[3] += lo;

  UMUL51(hi, lo, a[2], b[1]); t[3] += lo; t[4] += hi;

  UMUL51(hi, lo, a[1], b[2]); t[3] += lo; t[4] += hi;

  UMUL51(hi, lo, a[0], b[3]); t[3] += lo; t[4] += hi;

  UMUL51(t[5], lo, a[4], b[0]); t[4] += lo;

  UMUL51(hi, lo, a[3], b[1]); t[4] += lo; t[5] += hi;

  UMUL51(hi, lo, a[2], b[2]); t[4] += lo; t[5] += hi;

  UMUL51(hi, lo, a[1], b[3]); t[4] += lo; t[5] += hi;

  UMUL51(hi, lo, a[0], b[4]); t[4] += lo; t[5] += hi;

  UMUL51(t[6], lo, a[4], b[1]); t[5] += lo;

  UMUL51(hi, lo, a[3], b[2]); t[5] += lo; t[6] += hi;

  UMUL51(hi, lo, a[2], b[3]); t[5] += lo; t[6] += hi;

  UMUL51(hi, lo, a[1], b[4]); t[5] += lo; t[6] += hi;

  UMUL51(t[7], lo, a[4], b[2]); t[6] += lo;

  UMUL51(hi, lo, a[3], b[3]); t[6] += lo; t[7] += hi;

  UMUL51(hi, lo, a[2], b[4]); t[6] += lo; t[7] += hi;

  UMUL51(t[8], lo, a[4], b[3]); t[7] += lo;

  UMUL51(hi, lo, a[3], b[4]); t[7] += lo; t[8] += hi;

  UMUL51(t[9], lo, a[4], b[4]); t[8] += lo;

  /*

   * The upper words t[5]..t[9] are folded back into the lower

   * words, using the rule that 2^255 = 19 in the field.

   *

   * Since each t[i] is less than 324*2^51, the additions below

   * will yield less than 6480*2^51 in each limb; this fits in

   * 64 bits (6480*2^51 < 8192*2^51 = 2^64), hence there is

   * no overflow.

   */

  t[0] += 19 * t[5];

  t[1] += 19 * t[6];

  t[2] += 19 * t[7];

  t[3] += 19 * t[8];

  t[4] += 19 * t[9];

  /*

   * Propagate carries.

   */

  w = t[0];

  d[0] = w & MASK51;

  cc = w >> 51;

  w = t[1] + cc;

  d[1] = w & MASK51;

  cc = w >> 51;

  w = t[2] + cc;

  d[2] = w & MASK51;

  cc = w >> 51;

  w = t[3] + cc;

  d[3] = w & MASK51;

  cc = w >> 51;

  w = t[4] + cc;

  d[4] = w & MASK51;

  cc = w >> 51;

  /*

   * Since the limbs were 64-bit values, the top carry is at

   * most 8192 (in practice, that cannot be reached). We simply

   * performed a partial reduction.

   */

  d[0] += 19 * cc;

}

/*

 * Multiplication by A24 = 121665.

 * Input must have limbs of 60 bits at most.

 */

static inline void

f255_mul_a24(uint64_t *d, const uint64_t *a)

{

  uint64_t t[5], cc, w;

  /*

   * 121665 = 15 * 8111. We first multiply by 15, with carry

   * propagation and partial reduction.

   */

  w = a[0] * 15;

  t[0] = w & MASK51;

  cc = w >> 51;

  w = a[1] * 15 + cc;

  t[1] = w & MASK51;

  cc = w >> 51;

  w = a[2] * 15 + cc;

  t[2] = w & MASK51;

  cc = w >> 51;

  w = a[3] * 15 + cc;

  t[3] = w & MASK51;

  cc = w >> 51;

  w = a[4] * 15 + cc;

  t[4] = w & MASK51;

  t[0] += 19 * (w >> 51);

  /*

   * Then multiplication by 8111. At that point, we known that

   * t[0] is less than 2^51 + 19*8192, and other limbs are less

   * than 2^51; thus, there will be no overflow.

   */

  w = t[0] * 8111;

  d[0] = w & MASK51;

  cc = w >> 51;

  w = t[1] * 8111 + cc;

  d[1] = w & MASK51;

  cc = w >> 51;

  w = t[2] * 8111 + cc;

  d[2] = w & MASK51;

  cc = w >> 51;

  w = t[3] * 8111 + cc;

  d[3] = w & MASK51;

  cc = w >> 51;

  w = t[4] * 8111 + cc;

  d[4] = w & MASK51;

  d[0] += 19 * (w >> 51);

}

/*

 * Finalize reduction.

 * On input, limbs must fit on 51 bits, except possibly the low limb,

 * which may be slightly above 2^51.

 */

static inline void

f255_final_reduce(uint64_t *a)

{

  uint64_t t[5], cc, w;

  /*

   * We add 19. If the result (in t[]) is below 2^255, then a[]

   * is already less than 2^255-19, thus already reduced.

   * Otherwise, we subtract 2^255 from t[], in which case we

   * have t = a - (2^255-19), and that's our result.

   */

  w = a[0] + 19;

  t[0] = w & MASK51;

  cc = w >> 51;

  w = a[1] + cc;

  t[1] = w & MASK51;

  cc = w >> 51;

  w = a[2] + cc;

  t[2] = w & MASK51;

  cc = w >> 51;

  w = a[3] + cc;

  t[3] = w & MASK51;

  cc = w >> 51;

  w = a[4] + cc;

  t[4] = w & MASK51;

  cc = w >> 51;

  /*

   * The bit 255 of t is in cc. If that bit is 0, when a[] must

   * be unchanged; otherwise, it must be replaced with t[].

   */

  cc = -cc;

  a[0] ^= cc & (a[0] ^ t[0]);

  a[1] ^= cc & (a[1] ^ t[1]);

  a[2] ^= cc & (a[2] ^ t[2]);

  a[3] ^= cc & (a[3] ^ t[3]);

  a[4] ^= cc & (a[4] ^ t[4]);

}

static uint32_t

api_mul(unsigned char *G, size_t Glen,

  const unsigned char *kb, size_t kblen, int curve)

{

  unsigned char k[32];

  uint64_t x1[5], x2[5], z2[5], x3[5], z3[5];

  uint32_t swap;

  int i;

  (void)curve;

  /*

   * Points are encoded over exactly 32 bytes. Multipliers must fit

   * in 32 bytes as well.

   */

  if (Glen != 32 || kblen > 32) {

    return 0;

  }

  /*

   * RFC 7748 mandates that the high bit of the last point byte must

   * be ignored/cleared; the "& MASK51" in the initialization for

   * x1[4] clears that bit.

   */

  x1[0] = br_dec64le(&G[0]) & MASK51;

  x1[1] = (br_dec64le(&G[6]) >> 3) & MASK51;

  x1[2] = (br_dec64le(&G[12]) >> 6) & MASK51;

  x1[3] = (br_dec64le(&G[19]) >> 1) & MASK51;

  x1[4] = (br_dec64le(&G[24]) >> 12) & MASK51;

  /*

   * We can use memset() to clear values, because exact-width types

   * like uint64_t are guaranteed to have no padding bits or

   * trap representations.

   */

  memset(x2, 0, sizeof x2);

  x2[0] = 1;

  memset(z2, 0, sizeof z2);

  memcpy(x3, x1, sizeof x1);

  memcpy(z3, x2, sizeof x2);

  /*

   * The multiplier is provided in big-endian notation, and

   * possibly shorter than 32 bytes.

   */

  memset(k, 0, (sizeof k) - kblen);

  memcpy(k + (sizeof k) - kblen, kb, kblen);

  k[31] &= 0xF8;

  k[0] &= 0x7F;

  k[0] |= 0x40;

  swap = 0;

  for (i = 254; i >= 0; i --) {

    uint64_t a[5], aa[5], b[5], bb[5], e[5];

    uint64_t c[5], d[5], da[5], cb[5];

    uint32_t kt;

    kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;

    swap ^= kt;

    f255_cswap(x2, x3, swap);

    f255_cswap(z2, z3, swap);

    swap = kt;

    /*

     * At that point, limbs of x_2 and z_2 are assumed to fit

     * on at most 52 bits each.

     *

     * Each f255_add() adds one bit to the maximum range of

     * the values, but f255_sub() and f255_mul() bring back

     * the limbs into 52 bits. All f255_add() outputs are

     * used only as inputs for f255_mul(), which ensures

     * that limbs remain in the proper range.

     */

    /* A = x_2 + z_2   -- limbs fit on 53 bits each */

    f255_add(a, x2, z2);

    /* AA = A^2 */

    f255_mul(aa, a, a);

    /* B = x_2 - z_2 */

    f255_sub(b, x2, z2);

    /* BB = B^2 */

    f255_mul(bb, b, b);

    /* E = AA - BB */

    f255_sub(e, aa, bb);

    /* C = x_3 + z_3   -- limbs fit on 53 bits each */

    f255_add(c, x3, z3);

    /* D = x_3 - z_3 */

    f255_sub(d, x3, z3);

    /* DA = D * A */

    f255_mul(da, d, a);

    /* CB = C * B */

    f255_mul(cb, c, b);

    /* x_3 = (DA + CB)^2 */

    f255_add(x3, da, cb);

    f255_mul(x3, x3, x3);

    /* z_3 = x_1 * (DA - CB)^2 */

    f255_sub(z3, da, cb);

    f255_mul(z3, z3, z3);

    f255_mul(z3, x1, z3);

    /* x_2 = AA * BB */

    f255_mul(x2, aa, bb);

    /* z_2 = E * (AA + a24 * E) */

    f255_mul_a24(z2, e);

    f255_add(z2, aa, z2);

    f255_mul(z2, e, z2);

  }

  f255_cswap(x2, x3, swap);

  f255_cswap(z2, z3, swap);

  /*

   * Compute 1/z2 = z2^(p-2). Since p = 2^255-19, we can mutualize

   * most non-squarings. We use x1 and x3, now useless, as temporaries.

   */

  memcpy(x1, z2, sizeof z2);

  for (i = 0; i < 15; i ++) {

    f255_mul(x1, x1, x1);

    f255_mul(x1, x1, z2);

  }

  memcpy(x3, x1, sizeof x1);

  for (i = 0; i < 14; i ++) {

    int j;

    for (j = 0; j < 16; j ++) {

      f255_mul(x3, x3, x3);

    }

    f255_mul(x3, x3, x1);

  }

  for (i = 14; i >= 0; i --) {

    f255_mul(x3, x3, x3);

    if ((0xFFEB >> i) & 1) {

      f255_mul(x3, z2, x3);

    }

  }

  /*

   * Compute x2/z2. We have 1/z2 in x3.

   */

  f255_mul(x2, x2, x3);

  f255_final_reduce(x2);

  /*

   * Encode the final x2 value in little-endian. We first assemble

   * the limbs into 64-bit values.

   */

  x2[0] |= x2[1] << 51;

  x2[1] = (x2[1] >> 13) | (x2[2] << 38);

  x2[2] = (x2[2] >> 26) | (x2[3] << 25);

  x2[3] = (x2[3] >> 39) | (x2[4] << 12);

  br_enc64le(G, x2[0]);

  br_enc64le(G + 8, x2[1]);

  br_enc64le(G + 16, x2[2]);

  br_enc64le(G + 24, x2[3]);

  return 1;

}

static size_t

api_mulgen(unsigned char *R,

  const unsigned char *x, size_t xlen, int curve)

{

  const unsigned char *G;

  size_t Glen;

  G = api_generator(curve, &Glen);

  memcpy(R, G, Glen);

  api_mul(R, Glen, x, xlen, curve);

  return Glen;

}

static uint32_t

api_muladd(unsigned char *A, const unsigned char *B, size_t len,

  const unsigned char *x, size_t xlen,

  const unsigned char *y, size_t ylen, int curve)

{

  /*

   * We don't implement this method, since it is used for ECDSA

   * only, and there is no ECDSA over Curve25519 (which instead

   * uses EdDSA).

   */

  (void)A;

  (void)B;

  (void)len;

  (void)x;

  (void)xlen;

  (void)y;

  (void)ylen;

  (void)curve;

  return 0;

}

/* see bearssl_ec.h */

const br_ec_impl br_ec_c25519_m62 = {

  (uint32_t)0x20000000,

  &api_generator,

  &api_order,

  &api_xoff,

  &api_mul,

  &api_mulgen,

  &api_muladd

};

/* see bearssl_ec.h */

const br_ec_impl *

br_ec_c25519_m62_get(void)

{

  return &br_ec_c25519_m62;

}

#else

/* see bearssl_ec.h */

const br_ec_impl *

br_ec_c25519_m62_get(void)

{

  return 0;

}

#endif