/*
* NEWHOPE Ring-LWE scheme
* Based on the public domain reference implementation by the
* designers (https://github.com/tpoeppelmann/newhope)
*
* Further changes
* (C) 2016 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#include <botan/newhope.h>
#include <botan/hash.h>
#include <botan/stream_cipher.h>
#include <botan/loadstor.h>

namespace Botan {

typedef newhope_poly poly;

// Don't change this :)
#define PARAM_Q 12289
#define PARAM_N 1024

#define NEWHOPE_POLY_BYTES 1792
#define NEWHOPE_SEED_BYTES 32

namespace {

/* Incomplete-reduction routines; for details on allowed input ranges
 * and produced output ranges, see the description in the paper:
 * https://cryptojedi.org/papers/#newhope */

inline uint16_t montgomery_reduce(uint32_t a)
{
  const uint32_t qinv = 12287; // -inverse_mod(p,2^18)
  const uint32_t rlog = 18;

  uint32_t u;

  u = (a * qinv);
  u &= ((1<<rlog)-1);
  u *= PARAM_Q;
  a = a + u;
  return a >> 18;
}

inline uint16_t barrett_reduce(uint16_t a)
{
  uint32_t u = (static_cast<uint32_t>(a) * 5) >> 16;
  u *= PARAM_Q;
  a -= u;
  return a;
}

inline void mul_coefficients(uint16_t* poly, const uint16_t* factors)
{
    for(size_t i = 0; i < PARAM_N; i++)
      poly[i] = montgomery_reduce((poly[i] * factors[i]));
}

/* GS_bo_to_no; omegas need to be in Montgomery domain */
inline void ntt(uint16_t * a, const uint16_t* omega)
{
  for(size_t i=0;i<10;i+=2)
  {
    // Even level
    size_t distance = (1<<i);
    for(size_t start = 0; start < distance;start++)
    {
      size_t jTwiddle = 0;
      for(size_t j=start;j<PARAM_N-1;j+=2*distance)
      {
        uint16_t W = omega[jTwiddle++];
        uint16_t temp = a[j];
        a[j] = (temp + a[j + distance]); // Omit reduction (be lazy)
        a[j + distance] = montgomery_reduce((W * (static_cast<uint32_t>(temp) + 3*PARAM_Q - a[j + distance])));
      }
    }

    // Odd level
    distance <<= 1;
    for(size_t start = 0; start < distance;start++)
    {
      size_t jTwiddle = 0;
      for(size_t j=start;j<PARAM_N-1;j+=2*distance)
      {
        uint16_t W = omega[jTwiddle++];
        uint16_t temp = a[j];
        a[j] = barrett_reduce((temp + a[j + distance]));
        a[j + distance] = montgomery_reduce((W * (static_cast<uint32_t>(temp) + 3*PARAM_Q - a[j + distance])));
      }
    }
  }
}

inline void poly_frombytes(poly *r, const uint8_t *a)
{
  for(size_t i=0;i<PARAM_N/4;i++)
  {
  r->coeffs[4*i+0] =  a[7*i+0]       | ((static_cast<uint16_t>(a[7*i+1]) & 0x3f) << 8);
  r->coeffs[4*i+1] = (a[7*i+1] >> 6) | (static_cast<uint16_t>(a[7*i+2]) << 2) | (static_cast<uint16_t>(a[7*i+3] & 0x0f) << 10);
    r->coeffs[4*i+2] = (a[7*i+3] >> 4) | (static_cast<uint16_t>(a[7*i+4]) << 4) | (static_cast<uint16_t>(a[7*i+5] & 0x03) << 12);
    r->coeffs[4*i+3] = (a[7*i+5] >> 2) | (static_cast<uint16_t>(a[7*i+6]) << 6);
  }
}

inline void poly_tobytes(uint8_t *r, const poly *p)
{
  for(size_t i=0;i<PARAM_N/4;i++)
  {
    uint16_t t0 = barrett_reduce(p->coeffs[4*i+0]); //Make sure that coefficients have only 14 bits
    uint16_t t1 = barrett_reduce(p->coeffs[4*i+1]);
    uint16_t t2 = barrett_reduce(p->coeffs[4*i+2]);
    uint16_t t3 = barrett_reduce(p->coeffs[4*i+3]);

    uint16_t m;
    int16_t c;

    m = t0 - PARAM_Q;
    c = m;
    c >>= 15;
    t0 = m ^ ((t0^m)&c); // <Make sure that coefficients are in [0,q]

    m = t1 - PARAM_Q;
    c = m;
    c >>= 15;
    t1 = m ^ ((t1^m)&c); // <Make sure that coefficients are in [0,q]

    m = t2 - PARAM_Q;
    c = m;
    c >>= 15;
    t2 = m ^ ((t2^m)&c); // <Make sure that coefficients are in [0,q]

    m = t3 - PARAM_Q;
    c = m;
    c >>= 15;
    t3 = m ^ ((t3^m)&c); // <Make sure that coefficients are in [0,q]

    r[7*i+0] =  t0 & 0xff;
    r[7*i+1] = (t0 >> 8) | (t1 << 6);
    r[7*i+2] = (t1 >> 2);
    r[7*i+3] = (t1 >> 10) | (t2 << 4);
    r[7*i+4] = (t2 >> 4);
    r[7*i+5] = (t2 >> 12) | (t3 << 2);
    r[7*i+6] = (t3 >> 6);
  }
}

inline void poly_getnoise(Botan::RandomNumberGenerator& rng, poly *r)
{
  uint8_t buf[4*PARAM_N];

  rng.randomize(buf, 4*PARAM_N);

  for(size_t i=0;i<PARAM_N;i++)
  {
    uint32_t t = load_le<uint32_t>(buf, i);
    uint32_t d = 0;
    for(int j=0;j<8;j++)
      d += (t >> j) & 0x01010101;
    uint32_t a = ((d >> 8) & 0xff) + (d & 0xff);
    uint32_t b = (d >> 24) + ((d >> 16) & 0xff);
    r->coeffs[i] = a + PARAM_Q - b;
  }
}

inline void poly_pointwise(poly *r, const poly *a, const poly *b)
{
  for(size_t i=0;i<PARAM_N;i++)
    {
    uint16_t t = montgomery_reduce(3186*b->coeffs[i]); /* t is now in Montgomery domain */
    r->coeffs[i] = montgomery_reduce(a->coeffs[i] * t); /* r->coeffs[i] is back in normal domain */
    }
}

inline void poly_add(poly *r, const poly *a, const poly *b)
{
  for(size_t i=0;i<PARAM_N;i++)
    r->coeffs[i] = barrett_reduce(a->coeffs[i] + b->coeffs[i]);
}

inline void poly_ntt(poly *r)
{

static const uint16_t omegas_montgomery[PARAM_N/2] = {
   4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041, 8775, 2344,
   11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118, 2683, 1190, 4789,
   7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973, 382, 3988, 468, 6843, 5339,
   6196, 3710, 11316, 1254, 5435, 10930, 3998, 10256, 10367, 3879, 11889, 1728,
   6137, 4948, 5862, 6136, 3643, 6874, 8724, 654, 10302, 1702, 7083, 6760, 56,
   3199, 9987, 605, 11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689,
   4080, 11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142, 241,
   12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968, 12097, 7591,
   5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821, 11502, 8807, 12138,
   2127, 2839, 3957, 431, 1579, 6383, 9784, 5874, 677, 3336, 6234, 2766, 1323,
   9115, 12237, 2031, 6956, 6413, 2281, 3969, 3991, 12133, 9522, 4737, 10996,
   4774, 5429, 11871, 3772, 453, 5908, 2882, 1805, 2051, 1954, 11713, 3963,
   2447, 6142, 8174, 3030, 1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796,
   2057, 5369, 11939, 1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789,
   5942, 10706, 10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551,
   9634, 6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459,
   64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065, 835, 3570,
   4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922, 7967, 1958, 10211,
   1112, 3728, 4049, 11130, 5990, 1404, 325, 948, 11143, 6190, 295, 11637, 5766,
   8212, 8273, 2919, 8527, 6119, 6992, 8333, 1360, 2555, 6167, 1200, 7105, 7991,
   3329, 9597, 12121, 5106, 5961, 10695, 10327, 3051, 9923, 4896, 9326, 81,
   3091, 1000, 7969, 4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062,
   2294, 3553, 4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088,
   1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479, 1, 8246,
   7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961, 4591, 5728, 6461,
   5023, 9650, 7468, 949, 9664, 2975, 11726, 2744, 9283, 10092, 5067, 12171,
   2476, 3748, 11336, 6522, 827, 9452, 5374, 12159, 7935, 3296, 3949, 9893,
   4452, 10908, 2525, 3584, 8112, 8011, 10616, 4989, 6958, 11809, 9447, 12280,
   1022, 11950, 9821, 11745, 5791, 5092, 2089, 9005, 2881, 3289, 2013, 9048,
   729, 7901, 1260, 5755, 4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932,
   9558, 8830, 3637, 5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741,
   1207, 9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952,
   4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302, 6022, 7278,
   1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045, 2481, 5012, 7428, 354,
   6591, 9377, 11847, 2401, 1067, 7188, 11516, 390, 8511, 8456, 7270, 545, 8585,
   9611, 12047, 1537, 4143, 4714, 4885, 1017, 5084, 1632, 3066, 27, 1440, 8526,
   9273, 12046, 11618, 9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985,
   11869, 6730, 10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407,
   2686, 9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863,
   7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852, 12286,
   4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364, 3271, 4057,
   4414, 9442, 7917, 2174};

static const uint16_t psis_bitrev_montgomery[PARAM_N] = {
   4075, 6974, 7373, 7965, 3262, 5079, 522, 2169, 6364, 1018, 1041, 8775, 2344,
   11011, 5574, 1973, 4536, 1050, 6844, 3860, 3818, 6118, 2683, 1190, 4789,
   7822, 7540, 6752, 5456, 4449, 3789, 12142, 11973, 382, 3988, 468, 6843, 5339,
   6196, 3710, 11316, 1254, 5435, 10930, 3998, 10256, 10367, 3879, 11889, 1728,
   6137, 4948, 5862, 6136, 3643, 6874, 8724, 654, 10302, 1702, 7083, 6760, 56,
   3199, 9987, 605, 11785, 8076, 5594, 9260, 6403, 4782, 6212, 4624, 9026, 8689,
   4080, 11868, 6221, 3602, 975, 8077, 8851, 9445, 5681, 3477, 1105, 142, 241,
   12231, 1003, 3532, 5009, 1956, 6008, 11404, 7377, 2049, 10968, 12097, 7591,
   5057, 3445, 4780, 2920, 7048, 3127, 8120, 11279, 6821, 11502, 8807, 12138,
   2127, 2839, 3957, 431, 1579, 6383, 9784, 5874, 677, 3336, 6234, 2766, 1323,
   9115, 12237, 2031, 6956, 6413, 2281, 3969, 3991, 12133, 9522, 4737, 10996,
   4774, 5429, 11871, 3772, 453, 5908, 2882, 1805, 2051, 1954, 11713, 3963,
   2447, 6142, 8174, 3030, 1843, 2361, 12071, 2908, 3529, 3434, 3202, 7796,
   2057, 5369, 11939, 1512, 6906, 10474, 11026, 49, 10806, 5915, 1489, 9789,
   5942, 10706, 10431, 7535, 426, 8974, 3757, 10314, 9364, 347, 5868, 9551,
   9634, 6554, 10596, 9280, 11566, 174, 2948, 2503, 6507, 10723, 11606, 2459,
   64, 3656, 8455, 5257, 5919, 7856, 1747, 9166, 5486, 9235, 6065, 835, 3570,
   4240, 11580, 4046, 10970, 9139, 1058, 8210, 11848, 922, 7967, 1958, 10211,
   1112, 3728, 4049, 11130, 5990, 1404, 325, 948, 11143, 6190, 295, 11637, 5766,
   8212, 8273, 2919, 8527, 6119, 6992, 8333, 1360, 2555, 6167, 1200, 7105, 7991,
   3329, 9597, 12121, 5106, 5961, 10695, 10327, 3051, 9923, 4896, 9326, 81,
   3091, 1000, 7969, 4611, 726, 1853, 12149, 4255, 11112, 2768, 10654, 1062,
   2294, 3553, 4805, 2747, 4846, 8577, 9154, 1170, 2319, 790, 11334, 9275, 9088,
   1326, 5086, 9094, 6429, 11077, 10643, 3504, 3542, 8668, 9744, 1479, 1, 8246,
   7143, 11567, 10984, 4134, 5736, 4978, 10938, 5777, 8961, 4591, 5728, 6461,
   5023, 9650, 7468, 949, 9664, 2975, 11726, 2744, 9283, 10092, 5067, 12171,
   2476, 3748, 11336, 6522, 827, 9452, 5374, 12159, 7935, 3296, 3949, 9893,
   4452, 10908, 2525, 3584, 8112, 8011, 10616, 4989, 6958, 11809, 9447, 12280,
   1022, 11950, 9821, 11745, 5791, 5092, 2089, 9005, 2881, 3289, 2013, 9048,
   729, 7901, 1260, 5755, 4632, 11955, 2426, 10593, 1428, 4890, 5911, 3932,
   9558, 8830, 3637, 5542, 145, 5179, 8595, 3707, 10530, 355, 3382, 4231, 9741,
   1207, 9041, 7012, 1168, 10146, 11224, 4645, 11885, 10911, 10377, 435, 7952,
   4096, 493, 9908, 6845, 6039, 2422, 2187, 9723, 8643, 9852, 9302, 6022, 7278,
   1002, 4284, 5088, 1607, 7313, 875, 8509, 9430, 1045, 2481, 5012, 7428, 354,
   6591, 9377, 11847, 2401, 1067, 7188, 11516, 390, 8511, 8456, 7270, 545, 8585,
   9611, 12047, 1537, 4143, 4714, 4885, 1017, 5084, 1632, 3066, 27, 1440, 8526,
   9273, 12046, 11618, 9289, 3400, 9890, 3136, 7098, 8758, 11813, 7384, 3985,
   11869, 6730, 10745, 10111, 2249, 4048, 2884, 11136, 2126, 1630, 9103, 5407,
   2686, 9042, 2969, 8311, 9424, 9919, 8779, 5332, 10626, 1777, 4654, 10863,
   7351, 3636, 9585, 5291, 8374, 2166, 4919, 12176, 9140, 12129, 7852, 12286,
   4895, 10805, 2780, 5195, 2305, 7247, 9644, 4053, 10600, 3364, 3271, 4057,
   4414, 9442, 7917, 2174, 3947, 11951, 2455, 6599, 10545, 10975, 3654, 2894,
   7681, 7126, 7287, 12269, 4119, 3343, 2151, 1522, 7174, 7350, 11041, 2442,
   2148, 5959, 6492, 8330, 8945, 5598, 3624, 10397, 1325, 6565, 1945, 11260,
   10077, 2674, 3338, 3276, 11034, 506, 6505, 1392, 5478, 8778, 1178, 2776,
   3408, 10347, 11124, 2575, 9489, 12096, 6092, 10058, 4167, 6085, 923, 11251,
   11912, 4578, 10669, 11914, 425, 10453, 392, 10104, 8464, 4235, 8761, 7376,
   2291, 3375, 7954, 8896, 6617, 7790, 1737, 11667, 3982, 9342, 6680, 636, 6825,
   7383, 512, 4670, 2900, 12050, 7735, 994, 1687, 11883, 7021, 146, 10485, 1403,
   5189, 6094, 2483, 2054, 3042, 10945, 3981, 10821, 11826, 8882, 8151, 180,
   9600, 7684, 5219, 10880, 6780, 204, 11232, 2600, 7584, 3121, 3017, 11053,
   7814, 7043, 4251, 4739, 11063, 6771, 7073, 9261, 2360, 11925, 1928, 11825,
   8024, 3678, 3205, 3359, 11197, 5209, 8581, 3238, 8840, 1136, 9363, 1826,
   3171, 4489, 7885, 346, 2068, 1389, 8257, 3163, 4840, 6127, 8062, 8921, 612,
   4238, 10763, 8067, 125, 11749, 10125, 5416, 2110, 716, 9839, 10584, 11475,
   11873, 3448, 343, 1908, 4538, 10423, 7078, 4727, 1208, 11572, 3589, 2982,
   1373, 1721, 10753, 4103, 2429, 4209, 5412, 5993, 9011, 438, 3515, 7228, 1218,
   8347, 5232, 8682, 1327, 7508, 4924, 448, 1014, 10029, 12221, 4566, 5836,
   12229, 2717, 1535, 3200, 5588, 5845, 412, 5102, 7326, 3744, 3056, 2528, 7406,
   8314, 9202, 6454, 6613, 1417, 10032, 7784, 1518, 3765, 4176, 5063, 9828,
   2275, 6636, 4267, 6463, 2065, 7725, 3495, 8328, 8755, 8144, 10533, 5966,
   12077, 9175, 9520, 5596, 6302, 8400, 579, 6781, 11014, 5734, 11113, 11164,
   4860, 1131, 10844, 9068, 8016, 9694, 3837, 567, 9348, 7000, 6627, 7699, 5082,
   682, 11309, 5207, 4050, 7087, 844, 7434, 3769, 293, 9057, 6940, 9344, 10883,
   2633, 8190, 3944, 5530, 5604, 3480, 2171, 9282, 11024, 2213, 8136, 3805, 767,
   12239, 216, 11520, 6763, 10353, 7, 8566, 845, 7235, 3154, 4360, 3285, 10268,
   2832, 3572, 1282, 7559, 3229, 8360, 10583, 6105, 3120, 6643, 6203, 8536,
   8348, 6919, 3536, 9199, 10891, 11463, 5043, 1658, 5618, 8787, 5789, 4719,
   751, 11379, 6389, 10783, 3065, 7806, 6586, 2622, 5386, 510, 7628, 6921, 578,
   10345, 11839, 8929, 4684, 12226, 7154, 9916, 7302, 8481, 3670, 11066, 2334,
   1590, 7878, 10734, 1802, 1891, 5103, 6151, 8820, 3418, 7846, 9951, 4693, 417,
   9996, 9652, 4510, 2946, 5461, 365, 881, 1927, 1015, 11675, 11009, 1371,
   12265, 2485, 11385, 5039, 6742, 8449, 1842, 12217, 8176, 9577, 4834, 7937,
   9461, 2643, 11194, 3045, 6508, 4094, 3451, 7911, 11048, 5406, 4665, 3020,
   6616, 11345, 7519, 3669, 5287, 1790, 7014, 5410, 11038, 11249, 2035, 6125,
   10407, 4565, 7315, 5078, 10506, 2840, 2478, 9270, 4194, 9195, 4518, 7469,
   1160, 6878, 2730, 10421, 10036, 1734, 3815, 10939, 5832, 10595, 10759, 4423,
   8420, 9617, 7119, 11010, 11424, 9173, 189, 10080, 10526, 3466, 10588, 7592,
   3578, 11511, 7785, 9663, 530, 12150, 8957, 2532, 3317, 9349, 10243, 1481,
   9332, 3454, 3758, 7899, 4218, 2593, 11410, 2276, 982, 6513, 1849, 8494, 9021,
   4523, 7988, 8, 457, 648, 150, 8000, 2307, 2301, 874, 5650, 170, 9462, 2873,
   9855, 11498, 2535, 11169, 5808, 12268, 9687, 1901, 7171, 11787, 3846, 1573,
   6063, 3793, 466, 11259, 10608, 3821, 6320, 4649, 6263, 2929};

  mul_coefficients(r->coeffs, psis_bitrev_montgomery);
  ntt(r->coeffs, omegas_montgomery);
}

inline void bitrev_vector(uint16_t* poly)
{
static const uint16_t bitrev_table[1024] = {
  0,512,256,768,128,640,384,896,64,576,320,832,192,704,448,960,32,544,288,800,160,672,416,928,96,608,352,864,224,736,480,992,
  16,528,272,784,144,656,400,912,80,592,336,848,208,720,464,976,48,560,304,816,176,688,432,944,112,624,368,880,240,752,496,1008,
  8,520,264,776,136,648,392,904,72,584,328,840,200,712,456,968,40,552,296,808,168,680,424,936,104,616,360,872,232,744,488,1000,
  24,536,280,792,152,664,408,920,88,600,344,856,216,728,472,984,56,568,312,824,184,696,440,952,120,632,376,888,248,760,504,1016,
  4,516,260,772,132,644,388,900,68,580,324,836,196,708,452,964,36,548,292,804,164,676,420,932,100,612,356,868,228,740,484,996,
  20,532,276,788,148,660,404,916,84,596,340,852,212,724,468,980,52,564,308,820,180,692,436,948,116,628,372,884,244,756,500,1012,
  12,524,268,780,140,652,396,908,76,588,332,844,204,716,460,972,44,556,300,812,172,684,428,940,108,620,364,876,236,748,492,1004,
  28,540,284,796,156,668,412,924,92,604,348,860,220,732,476,988,60,572,316,828,188,700,444,956,124,636,380,892,252,764,508,1020,
  2,514,258,770,130,642,386,898,66,578,322,834,194,706,450,962,34,546,290,802,162,674,418,930,98,610,354,866,226,738,482,994,
  18,530,274,786,146,658,402,914,82,594,338,850,210,722,466,978,50,562,306,818,178,690,434,946,114,626,370,882,242,754,498,1010,
  10,522,266,778,138,650,394,906,74,586,330,842,202,714,458,970,42,554,298,810,170,682,426,938,106,618,362,874,234,746,490,1002,
  26,538,282,794,154,666,410,922,90,602,346,858,218,730,474,986,58,570,314,826,186,698,442,954,122,634,378,890,250,762,506,1018,
  6,518,262,774,134,646,390,902,70,582,326,838,198,710,454,966,38,550,294,806,166,678,422,934,102,614,358,870,230,742,486,998,
  22,534,278,790,150,662,406,918,86,598,342,854,214,726,470,982,54,566,310,822,182,694,438,950,118,630,374,886,246,758,502,1014,
  14,526,270,782,142,654,398,910,78,590,334,846,206,718,462,974,46,558,302,814,174,686,430,942,110,622,366,878,238,750,494,1006,
  30,542,286,798,158,670,414,926,94,606,350,862,222,734,478,990,62,574,318,830,190,702,446,958,126,638,382,894,254,766,510,1022,
  1,513,257,769,129,641,385,897,65,577,321,833,193,705,449,961,33,545,289,801,161,673,417,929,97,609,353,865,225,737,481,993,
  17,529,273,785,145,657,401,913,81,593,337,849,209,721,465,977,49,561,305,817,177,689,433,945,113,625,369,881,241,753,497,1009,
  9,521,265,777,137,649,393,905,73,585,329,841,201,713,457,969,41,553,297,809,169,681,425,937,105,617,361,873,233,745,489,1001,
  25,537,281,793,153,665,409,921,89,601,345,857,217,729,473,985,57,569,313,825,185,697,441,953,121,633,377,889,249,761,505,1017,
  5,517,261,773,133,645,389,901,69,581,325,837,197,709,453,965,37,549,293,805,165,677,421,933,101,613,357,869,229,741,485,997,
  21,533,277,789,149,661,405,917,85,597,341,853,213,725,469,981,53,565,309,821,181,693,437,949,117,629,373,885,245,757,501,1013,
  13,525,269,781,141,653,397,909,77,589,333,845,205,717,461,973,45,557,301,813,173,685,429,941,109,621,365,877,237,749,493,1005,
  29,541,285,797,157,669,413,925,93,605,349,861,221,733,477,989,61,573,317,829,189,701,445,957,125,637,381,893,253,765,509,1021,
  3,515,259,771,131,643,387,899,67,579,323,835,195,707,451,963,35,547,291,803,163,675,419,931,99,611,355,867,227,739,483,995,
  19,531,275,787,147,659,403,915,83,595,339,851,211,723,467,979,51,563,307,819,179,691,435,947,115,627,371,883,243,755,499,1011,
  11,523,267,779,139,651,395,907,75,587,331,843,203,715,459,971,43,555,299,811,171,683,427,939,107,619,363,875,235,747,491,1003,
  27,539,283,795,155,667,411,923,91,603,347,859,219,731,475,987,59,571,315,827,187,699,443,955,123,635,379,891,251,763,507,1019,
  7,519,263,775,135,647,391,903,71,583,327,839,199,711,455,967,39,551,295,807,167,679,423,935,103,615,359,871,231,743,487,999,
  23,535,279,791,151,663,407,919,87,599,343,855,215,727,471,983,55,567,311,823,183,695,439,951,119,631,375,887,247,759,503,1015,
  15,527,271,783,143,655,399,911,79,591,335,847,207,719,463,975,47,559,303,815,175,687,431,943,111,623,367,879,239,751,495,1007,
  31,543,287,799,159,671,415,927,95,607,351,863,223,735,479,991,63,575,319,831,191,703,447,959,127,639,383,895,255,767,511,1023
};

    unsigned int i,r;
    uint16_t tmp;

    for(i = 0; i < PARAM_N; i++)
    {
        r = bitrev_table[i];
        if (i < r)
        {
          tmp = poly[i];
          poly[i] = poly[r];
          poly[r] = tmp;
        }
    }
}

inline void poly_invntt(poly *r)
{
static const uint16_t omegas_inv_montgomery[PARAM_N/2] = {
   4075, 5315, 4324, 4916, 10120, 11767, 7210, 9027, 10316, 6715, 1278, 9945,
   3514, 11248, 11271, 5925, 147, 8500, 7840, 6833, 5537, 4749, 4467, 7500,
   11099, 9606, 6171, 8471, 8429, 5445, 11239, 7753, 9090, 12233, 5529, 5206,
   10587, 1987, 11635, 3565, 5415, 8646, 6153, 6427, 7341, 6152, 10561, 400,
   8410, 1922, 2033, 8291, 1359, 6854, 11035, 973, 8579, 6093, 6950, 5446,
   11821, 8301, 11907, 316, 52, 3174, 10966, 9523, 6055, 8953, 11612, 6415,
   2505, 5906, 10710, 11858, 8332, 9450, 10162, 151, 3482, 787, 5468, 1010,
   4169, 9162, 5241, 9369, 7509, 8844, 7232, 4698, 192, 1321, 10240, 4912, 885,
   6281, 10333, 7280, 8757, 11286, 58, 12048, 12147, 11184, 8812, 6608, 2844,
   3438, 4212, 11314, 8687, 6068, 421, 8209, 3600, 3263, 7665, 6077, 7507, 5886,
   3029, 6695, 4213, 504, 11684, 2302, 1962, 1594, 6328, 7183, 168, 2692, 8960,
   4298, 5184, 11089, 6122, 9734, 10929, 3956, 5297, 6170, 3762, 9370, 4016,
   4077, 6523, 652, 11994, 6099, 1146, 11341, 11964, 10885, 6299, 1159, 8240,
   8561, 11177, 2078, 10331, 4322, 11367, 441, 4079, 11231, 3150, 1319, 8243,
   709, 8049, 8719, 11454, 6224, 3054, 6803, 3123, 10542, 4433, 6370, 7032,
   3834, 8633, 12225, 9830, 683, 1566, 5782, 9786, 9341, 12115, 723, 3009, 1693,
   5735, 2655, 2738, 6421, 11942, 2925, 1975, 8532, 3315, 11863, 4754, 1858,
   1583, 6347, 2500, 10800, 6374, 1483, 12240, 1263, 1815, 5383, 10777, 350,
   6920, 10232, 4493, 9087, 8855, 8760, 9381, 218, 9928, 10446, 9259, 4115,
   6147, 9842, 8326, 576, 10335, 10238, 10484, 9407, 6381, 11836, 8517, 418,
   6860, 7515, 1293, 7552, 2767, 156, 8298, 8320, 10008, 5876, 5333, 10258,
   10115, 4372, 2847, 7875, 8232, 9018, 8925, 1689, 8236, 2645, 5042, 9984,
   7094, 9509, 1484, 7394, 3, 4437, 160, 3149, 113, 7370, 10123, 3915, 6998,
   2704, 8653, 4938, 1426, 7635, 10512, 1663, 6957, 3510, 2370, 2865, 3978,
   9320, 3247, 9603, 6882, 3186, 10659, 10163, 1153, 9405, 8241, 10040, 2178,
   1544, 5559, 420, 8304, 4905, 476, 3531, 5191, 9153, 2399, 8889, 3000, 671,
   243, 3016, 3763, 10849, 12262, 9223, 10657, 7205, 11272, 7404, 7575, 8146,
   10752, 242, 2678, 3704, 11744, 5019, 3833, 3778, 11899, 773, 5101, 11222,
   9888, 442, 2912, 5698, 11935, 4861, 7277, 9808, 11244, 2859, 3780, 11414,
   4976, 10682, 7201, 8005, 11287, 5011, 6267, 2987, 2437, 3646, 2566, 10102,
   9867, 6250, 5444, 2381, 11796, 8193, 4337, 11854, 1912, 1378, 404, 7644,
   1065, 2143, 11121, 5277, 3248, 11082, 2548, 8058, 8907, 11934, 1759, 8582,
   3694, 7110, 12144, 6747, 8652, 3459, 2731, 8357, 6378, 7399, 10861, 1696,
   9863, 334, 7657, 6534, 11029, 4388, 11560, 3241, 10276, 9000, 9408, 3284,
   10200, 7197, 6498, 544, 2468, 339, 11267, 9, 2842, 480, 5331, 7300, 1673,
   4278, 4177, 8705, 9764, 1381, 7837, 2396, 8340, 8993, 4354, 130, 6915, 2837,
   11462, 5767, 953, 8541, 9813, 118, 7222, 2197, 3006, 9545, 563, 9314, 2625,
   11340, 4821, 2639, 7266, 5828, 6561, 7698, 3328, 6512, 1351, 7311, 6553,
   8155, 1305, 722, 5146, 4043, 12288, 10810, 2545, 3621, 8747, 8785, 1646,
   1212, 5860, 3195, 7203, 10963, 3201, 3014, 955, 11499, 9970, 11119, 3135,
   3712, 7443, 9542, 7484, 8736, 9995, 11227, 1635, 9521, 1177, 8034, 140,
   10436, 11563, 7678, 4320, 11289, 9198, 12208, 2963, 7393, 2366, 9238 };

static const uint16_t psis_inv_montgomery[PARAM_N] = {
   256, 10570, 1510, 7238, 1034, 7170, 6291, 7921, 11665, 3422, 4000, 2327,
   2088, 5565, 795, 10647, 1521, 5484, 2539, 7385, 1055, 7173, 8047, 11683,
   1669, 1994, 3796, 5809, 4341, 9398, 11876, 12230, 10525, 12037, 12253, 3506,
   4012, 9351, 4847, 2448, 7372, 9831, 3160, 2207, 5582, 2553, 7387, 6322, 9681,
   1383, 10731, 1533, 219, 5298, 4268, 7632, 6357, 9686, 8406, 4712, 9451,
   10128, 4958, 5975, 11387, 8649, 11769, 6948, 11526, 12180, 1740, 10782, 6807,
   2728, 7412, 4570, 4164, 4106, 11120, 12122, 8754, 11784, 3439, 5758, 11356,
   6889, 9762, 11928, 1704, 1999, 10819, 12079, 12259, 7018, 11536, 1648, 1991,
   2040, 2047, 2048, 10826, 12080, 8748, 8272, 8204, 1172, 1923, 7297, 2798,
   7422, 6327, 4415, 7653, 6360, 11442, 12168, 7005, 8023, 9924, 8440, 8228,
   2931, 7441, 1063, 3663, 5790, 9605, 10150, 1450, 8985, 11817, 10466, 10273,
   12001, 3470, 7518, 1074, 1909, 7295, 9820, 4914, 702, 5367, 7789, 8135, 9940,
   1420, 3714, 11064, 12114, 12264, 1752, 5517, 9566, 11900, 1700, 3754, 5803,
   829, 1874, 7290, 2797, 10933, 5073, 7747, 8129, 6428, 6185, 11417, 1631, 233,
   5300, 9535, 10140, 11982, 8734, 8270, 2937, 10953, 8587, 8249, 2934, 9197,
   4825, 5956, 4362, 9401, 1343, 3703, 529, 10609, 12049, 6988, 6265, 895, 3639,
   4031, 4087, 4095, 585, 10617, 8539, 4731, 4187, 9376, 3095, 9220, 10095,
   10220, 1460, 10742, 12068, 1724, 5513, 11321, 6884, 2739, 5658, 6075, 4379,
   11159, 10372, 8504, 4726, 9453, 3106, 7466, 11600, 10435, 8513, 9994, 8450,
   9985, 3182, 10988, 8592, 2983, 9204, 4826, 2445, 5616, 6069, 867, 3635, 5786,
   11360, 5134, 2489, 10889, 12089, 1727, 7269, 2794, 9177, 1311, 5454, 9557,
   6632, 2703, 9164, 10087, 1441, 3717, 531, 3587, 2268, 324, 5313, 759, 1864,
   5533, 2546, 7386, 9833, 8427, 4715, 11207, 1601, 7251, 4547, 11183, 12131,
   1733, 10781, 10318, 1474, 10744, 5046, 4232, 11138, 10369, 6748, 964, 7160,
   4534, 7670, 8118, 8182, 4680, 11202, 6867, 981, 8918, 1274, 182, 26, 7026,
   8026, 11680, 12202, 10521, 1503, 7237, 4545, 5916, 9623, 8397, 11733, 10454,
   3249, 9242, 6587, 941, 1890, 270, 10572, 6777, 9746, 6659, 6218, 6155, 6146,
   878, 1881, 7291, 11575, 12187, 1741, 7271, 8061, 11685, 6936, 4502, 9421,
   4857, 4205, 7623, 1089, 10689, 1527, 8996, 10063, 11971, 10488, 6765, 2722,
   3900, 9335, 11867, 6962, 11528, 5158, 4248, 4118, 5855, 2592, 5637, 6072,
   2623, 7397, 8079, 9932, 4930, 5971, 853, 3633, 519, 8852, 11798, 3441, 11025,
   1575, 225, 8810, 11792, 12218, 3501, 9278, 3081, 9218, 4828, 7712, 8124,
   11694, 12204, 3499, 4011, 573, 3593, 5780, 7848, 9899, 10192, 1456, 208,
   7052, 2763, 7417, 11593, 10434, 12024, 8740, 11782, 10461, 3250, 5731, 7841,
   9898, 1414, 202, 3540, 7528, 2831, 2160, 10842, 5060, 4234, 4116, 588, 84,
   12, 7024, 2759, 9172, 6577, 11473, 1639, 9012, 3043, 7457, 6332, 11438, 1634,
   1989, 9062, 11828, 8712, 11778, 12216, 10523, 6770, 9745, 10170, 4964, 9487,
   6622, 946, 8913, 6540, 6201, 4397, 9406, 8366, 9973, 8447, 8229, 11709, 8695,
   10020, 3187, 5722, 2573, 10901, 6824, 4486, 4152, 9371, 8361, 2950, 2177,
   311, 1800, 9035, 8313, 11721, 3430, 490, 70, 10, 1757, 251, 3547, 7529,
   11609, 3414, 7510, 4584, 4166, 9373, 1339, 5458, 7802, 11648, 1664, 7260,
   9815, 10180, 6721, 9738, 10169, 8475, 8233, 9954, 1422, 8981, 1283, 5450,
   11312, 1616, 3742, 11068, 10359, 4991, 713, 3613, 9294, 8350, 4704, 672, 96,
   7036, 9783, 11931, 3460, 5761, 823, 10651, 12055, 10500, 1500, 5481, 783,
   3623, 11051, 8601, 8251, 8201, 11705, 10450, 5004, 4226, 7626, 2845, 2162,
   3820, 7568, 9859, 3164, 452, 10598, 1514, 5483, 6050, 6131, 4387, 7649, 8115,
   6426, 918, 8909, 8295, 1185, 5436, 11310, 8638, 1234, 5443, 11311, 5127,
   2488, 2111, 10835, 5059, 7745, 2862, 3920, 560, 80, 1767, 2008, 3798, 11076,
   6849, 2734, 10924, 12094, 8750, 1250, 10712, 6797, 971, 7161, 1023, 8924,
   4786, 7706, 4612, 4170, 7618, 6355, 4419, 5898, 11376, 10403, 10264, 6733,
   4473, 639, 5358, 2521, 9138, 3061, 5704, 4326, 618, 5355, 765, 5376, 768,
   7132, 4530, 9425, 3102, 9221, 6584, 11474, 10417, 10266, 12000, 6981, 6264,
   4406, 2385, 7363, 4563, 4163, 7617, 9866, 3165, 9230, 11852, 10471, 5007,
   5982, 11388, 5138, 734, 3616, 11050, 12112, 6997, 11533, 12181, 10518, 12036,
   3475, 2252, 7344, 9827, 4915, 9480, 6621, 4457, 7659, 9872, 6677, 4465, 4149,
   7615, 4599, 657, 3605, 515, 10607, 6782, 4480, 640, 1847, 3775, 5806, 2585,
   5636, 9583, 1369, 10729, 8555, 10000, 11962, 5220, 7768, 8132, 8184, 9947,
   1421, 203, 29, 8782, 11788, 1684, 10774, 10317, 4985, 9490, 8378, 4708,
   11206, 5112, 5997, 7879, 11659, 12199, 8765, 10030, 4944, 5973, 6120, 6141,
   6144, 7900, 11662, 1666, 238, 34, 3516, 5769, 9602, 8394, 9977, 6692, 956,
   10670, 6791, 9748, 11926, 8726, 11780, 5194, 742, 106, 8793, 10034, 3189,
   10989, 5081, 4237, 5872, 4350, 2377, 10873, 6820, 6241, 11425, 10410, 10265,
   3222, 5727, 9596, 4882, 2453, 2106, 3812, 11078, 12116, 5242, 4260, 11142,
   8614, 11764, 12214, 5256, 4262, 4120, 11122, 5100, 11262, 5120, 2487, 5622,
   9581, 8391, 8221, 2930, 10952, 12098, 6995, 6266, 9673, 4893, 699, 3611,
   4027, 5842, 11368, 1624, 232, 8811, 8281, 1183, 169, 8802, 3013, 2186, 5579,
   797, 3625, 4029, 11109, 1587, 7249, 11569, 8675, 6506, 2685, 10917, 12093,
   12261, 12285, 1755, 7273, 1039, 1904, 272, 3550, 9285, 3082, 5707, 6082,
   4380, 7648, 11626, 5172, 4250, 9385, 8363, 8217, 4685, 5936, 848, 8899, 6538,
   934, 1889, 3781, 9318, 10109, 10222, 6727, 961, 5404, 772, 5377, 9546, 8386,
   1198, 8949, 3034, 2189, 7335, 4559, 5918, 2601, 10905, 5069, 9502, 3113,
   7467, 8089, 11689, 5181, 9518, 8382, 2953, 3933, 4073, 4093, 7607, 8109,
   2914, 5683, 4323, 11151, 1593, 10761, 6804, 972, 3650, 2277, 5592, 4310,
   7638, 9869, 4921, 703, 1856, 9043, 4803, 9464, 1352, 8971, 11815, 5199, 7765,
   6376, 4422, 7654, 2849, 407, 8836, 6529, 7955, 2892, 9191, 1313, 10721,
   12065, 12257, 1751, 9028, 8312, 2943, 2176, 3822, 546, 78, 8789, 11789,
   10462, 12028, 6985, 4509, 9422, 1346, 5459, 4291, 613, 10621, 6784, 9747,
   3148, 7472, 2823, 5670, 810, 7138, 8042, 4660, 7688, 6365, 6176, 6149, 2634,
   5643, 9584, 10147, 11983, 5223, 9524, 11894, 10477, 8519, 1217, 3685, 2282,
   326, 10580, 3267, 7489, 4581, 2410, 5611, 11335, 6886, 8006, 8166, 11700,
   3427, 11023, 8597, 10006, 3185, 455, 65, 5276, 7776, 4622, 5927, 7869, 9902,
   11948, 5218, 2501, 5624, 2559, 10899, 1557, 1978, 10816, 10323, 8497, 4725,
   675, 1852, 10798, 12076, 10503, 3256, 9243, 3076, 2195, 10847, 12083, 10504,
   12034, 10497 };

  bitrev_vector(r->coeffs);
  ntt(r->coeffs, omegas_inv_montgomery);
  mul_coefficients(r->coeffs, psis_inv_montgomery);
}


inline void encode_a(uint8_t *r, const poly *pk, const uint8_t *seed)
{
  int i;
  poly_tobytes(r, pk);
  for(i=0;i<NEWHOPE_SEED_BYTES;i++)
    r[NEWHOPE_POLY_BYTES+i] = seed[i];
}

inline void decode_a(poly *pk, uint8_t *seed, const uint8_t *r)
{
  int i;
  poly_frombytes(pk, r);
  for(i=0;i<NEWHOPE_SEED_BYTES;i++)
    seed[i] = r[NEWHOPE_POLY_BYTES+i];
}

inline void encode_b(uint8_t *r, const poly *b, const poly *c)
{
  poly_tobytes(r,b);
  for(size_t i=0;i<PARAM_N/4;i++)
    r[NEWHOPE_POLY_BYTES+i] = c->coeffs[4*i] | (c->coeffs[4*i+1] << 2) | (c->coeffs[4*i+2] << 4) | (c->coeffs[4*i+3] << 6);
}

inline void decode_b(poly *b, poly *c, const uint8_t *r)
{
  poly_frombytes(b, r);
  for(size_t i=0;i<PARAM_N/4;i++)
  {
    c->coeffs[4*i+0] =  r[NEWHOPE_POLY_BYTES+i]       & 0x03;
    c->coeffs[4*i+1] = (r[NEWHOPE_POLY_BYTES+i] >> 2) & 0x03;
    c->coeffs[4*i+2] = (r[NEWHOPE_POLY_BYTES+i] >> 4) & 0x03;
    c->coeffs[4*i+3] = (r[NEWHOPE_POLY_BYTES+i] >> 6);
  }
}

inline int32_t ct_abs(int32_t v)
{
  int32_t mask = v >> 31;
  return (v ^ mask) - mask;
}


inline int32_t f(int32_t *v0, int32_t *v1, int32_t x)
{
  int32_t xit, t, r, b;

  // Next 6 lines compute t = x/PARAM_Q;
  b = x*2730;
  t = b >> 25;
  b = x - t*12289;
  b = 12288 - b;
  b >>= 31;
  t -= b;

  r = t & 1;
  xit = (t>>1);
  *v0 = xit+r; // v0 = round(x/(2*PARAM_Q))

  t -= 1;
  r = t & 1;
  *v1 = (t>>1)+r;

  return ct_abs(x-((*v0)*2*PARAM_Q));
}

inline int32_t g(int32_t x)
{
  int32_t t,c,b;

  // Next 6 lines compute t = x/(4*PARAM_Q);
  b = x*2730;
  t = b >> 27;
  b = x - t*49156;
  b = 49155 - b;
  b >>= 31;
  t -= b;

  c = t & 1;
  t = (t >> 1) + c; // t = round(x/(8*PARAM_Q))

  t *= 8*PARAM_Q;

  return ct_abs(t - x);
}


inline int16_t LDDecode(int32_t xi0, int32_t xi1, int32_t xi2, int32_t xi3)
{
  int32_t t;

  t  = g(xi0);
  t += g(xi1);
  t += g(xi2);
  t += g(xi3);

  t -= 8*PARAM_Q;
  t >>= 31;
  return t&1;
}

inline void helprec(poly *c, const poly *v, RandomNumberGenerator& rng)
{
  int32_t v0[4], v1[4];
  uint8_t rand[32];
  int i;

  rng.randomize(rand, 32);

  for(i=0; i<256; i++)
  {
    uint8_t rbit = (rand[i>>3] >> (i&7)) & 1;
    int32_t k;

    k  = f(v0+0, v1+0, 8*v->coeffs[  0+i] + 4*rbit);
    k += f(v0+1, v1+1, 8*v->coeffs[256+i] + 4*rbit);
    k += f(v0+2, v1+2, 8*v->coeffs[512+i] + 4*rbit);
    k += f(v0+3, v1+3, 8*v->coeffs[768+i] + 4*rbit);

    k = (2*PARAM_Q-1-k) >> 31;

    int32_t v_tmp[4];
    v_tmp[0] = ((~k) & v0[0]) ^ (k & v1[0]);
    v_tmp[1] = ((~k) & v0[1]) ^ (k & v1[1]);
    v_tmp[2] = ((~k) & v0[2]) ^ (k & v1[2]);
    v_tmp[3] = ((~k) & v0[3]) ^ (k & v1[3]);

    c->coeffs[  0+i] = (v_tmp[0] -   v_tmp[3]) & 3;
    c->coeffs[256+i] = (v_tmp[1] -   v_tmp[3]) & 3;
    c->coeffs[512+i] = (v_tmp[2] -   v_tmp[3]) & 3;
    c->coeffs[768+i] = (   -k    + 2*v_tmp[3]) & 3;
  }
}

inline void rec(uint8_t *key, const poly *v, const poly *c)
{
  int i;
  int32_t tmp[4];

  for(i=0;i<32;i++)
    key[i] = 0;

  for(i=0; i<256; i++)
  {
    tmp[0] = 16*PARAM_Q + 8*static_cast<int32_t>(v->coeffs[  0+i]) - PARAM_Q * (2*c->coeffs[  0+i]+c->coeffs[768+i]);
    tmp[1] = 16*PARAM_Q + 8*static_cast<int32_t>(v->coeffs[256+i]) - PARAM_Q * (2*c->coeffs[256+i]+c->coeffs[768+i]);
    tmp[2] = 16*PARAM_Q + 8*static_cast<int32_t>(v->coeffs[512+i]) - PARAM_Q * (2*c->coeffs[512+i]+c->coeffs[768+i]);
    tmp[3] = 16*PARAM_Q + 8*static_cast<int32_t>(v->coeffs[768+i]) - PARAM_Q * (              c->coeffs[768+i]);

    key[i>>3] |= LDDecode(tmp[0], tmp[1], tmp[2], tmp[3]) << (i & 7);
  }
}

void gen_a(poly *a, const uint8_t *seed, Newhope_Mode mode)
   {
   std::vector<uint8_t> buf(168*16);

   std::unique_ptr<StreamCipher> xof;

   if(mode == Newhope_Mode::BoringSSL)
      {
      xof = StreamCipher::create_or_throw("CTR-BE(AES-128)");
      xof->set_key(seed, 16);
      xof->set_iv(seed + 16, 16);
      }
   else
      {
      xof = StreamCipher::create_or_throw("SHAKE-128");
      xof->set_key(seed, NEWHOPE_SEED_BYTES);
      }

   zeroise(buf);
   xof->encrypt(buf);

   unsigned int pos=0, ctr=0;

   while(ctr < PARAM_N)
      {
      uint16_t val = (buf[pos] | (static_cast<uint16_t>(buf[pos+1]) << 8)) & 0x3fff; // Specialized for q = 12889
      if(val < PARAM_Q)
         a->coeffs[ctr++] = val;
      pos += 2;
      if(pos >= buf.size())
         {
         zeroise(buf);
         xof->encrypt(buf);
         pos = 0;
         }
      }
   }

}

// API FUNCTIONS

void newhope_keygen(uint8_t *send, poly *sk, RandomNumberGenerator& rng,
                    Newhope_Mode mode)
{
  poly a, e, r, pk;
  uint8_t seed[NEWHOPE_SEED_BYTES];

  rng.randomize(seed, NEWHOPE_SEED_BYTES);

  gen_a(&a, seed, mode);

  poly_getnoise(rng, sk);
  poly_ntt(sk);

  poly_getnoise(rng, &e);
  poly_ntt(&e);

  poly_pointwise(&r,sk,&a);
  poly_add(&pk,&e,&r);

  encode_a(send, &pk, seed);
}

void newhope_sharedb(uint8_t *sharedkey, uint8_t *send, const uint8_t *received,
                     RandomNumberGenerator& rng,
                     Newhope_Mode mode)
{
  poly sp, ep, v, a, pka, c, epp, bp;
  uint8_t seed[NEWHOPE_SEED_BYTES];

  decode_a(&pka, seed, received);
  gen_a(&a, seed, mode);

  poly_getnoise(rng, &sp);
  poly_ntt(&sp);
  poly_getnoise(rng, &ep);
  poly_ntt(&ep);

  poly_pointwise(&bp, &a, &sp);
  poly_add(&bp, &bp, &ep);

  poly_pointwise(&v, &pka, &sp);
  poly_invntt(&v);

  poly_getnoise(rng, &epp);
  poly_add(&v, &v, &epp);

  helprec(&c, &v, rng);

  encode_b(send, &bp, &c);

  rec(sharedkey, &v, &c);

  std::unique_ptr<HashFunction> hash(HashFunction::create(
     (mode == Newhope_Mode::SHA3) ? "SHA-3(256)" : "SHA-256"));

  if(!hash)
     throw Exception("NewHope hash function not available");

  hash->update(sharedkey, 32);
  hash->final(sharedkey);
}


void newhope_shareda(uint8_t *sharedkey, const poly *sk, const uint8_t *received,
                     Newhope_Mode mode)
{
  poly v,bp, c;

  decode_b(&bp, &c, received);

  poly_pointwise(&v,sk,&bp);
  poly_invntt(&v);

  rec(sharedkey, &v, &c);

  std::unique_ptr<HashFunction> hash(HashFunction::create(
     (mode == Newhope_Mode::SHA3) ? "SHA-3(256)" : "SHA-256"));

  if(!hash)
     throw Exception("NewHope hash function not available");

  hash->update(sharedkey, 32);
  hash->final(sharedkey);
}

}

#undef PARAM_N
#undef PARAM_Q