NewHope cleanup

Remove old style casts, wrap some very long lines.

1 files changed, 300 insertions, 63 deletions

diff --git a/src/lib/pubkey/newhope/newhope.cpp b/src/lib/pubkey/newhope/newhope.cpp
index 35645e93c..356fd416e 100644
--- a/src/lib/pubkey/newhope/newhope.cpp
+++ b/src/lib/pubkey/newhope/newhope.cpp
@@ -47,9 +47,7 @@ inline uint16_t montgomery_reduce(uint32_t a)
 
 inline uint16_t barrett_reduce(uint16_t a)
 {
-  uint32_t u;
-
-  u = ((uint32_t) a * 5) >> 16;
+  uint32_t u = (static_cast<uint32_t>(a) * 5) >> 16;
   u *= PARAM_Q;
   a -= u;
   return a;
@@ -57,46 +55,40 @@ inline uint16_t barrett_reduce(uint16_t a)
 
 inline void mul_coefficients(uint16_t* poly, const uint16_t* factors)
 {
-    unsigned int i;
-
-    for(i = 0; i < PARAM_N; i++)
+    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)
 {
-  int i, start, j, jTwiddle, distance;
-  uint16_t temp, W;
-
-
-  for(i=0;i<10;i+=2)
+  for(size_t i=0;i<10;i+=2)
   {
     // Even level
-    distance = (1<<i);
-    for(start = 0; start < distance;start++)
+    size_t distance = (1<<i);
+    for(size_t start = 0; start < distance;start++)
     {
-      jTwiddle = 0;
-      for(j=start;j<PARAM_N-1;j+=2*distance)
+      size_t jTwiddle = 0;
+      for(size_t j=start;j<PARAM_N-1;j+=2*distance)
       {
-        W = omega[jTwiddle++];
-        temp = a[j];
+        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 * ((uint32_t)temp + 3*PARAM_Q - a[j + distance])));
+        a[j + distance] = montgomery_reduce((W * (static_cast<uint32_t>(temp) + 3*PARAM_Q - a[j + distance])));
       }
     }
 
     // Odd level
     distance <<= 1;
-    for(start = 0; start < distance;start++)
+    for(size_t start = 0; start < distance;start++)
     {
-      jTwiddle = 0;
-      for(j=start;j<PARAM_N-1;j+=2*distance)
+      size_t jTwiddle = 0;
+      for(size_t j=start;j<PARAM_N-1;j+=2*distance)
       {
-        W = omega[jTwiddle++];
-        temp = a[j];
+        uint16_t W = omega[jTwiddle++];
+        uint16_t temp = a[j];
         a[j] = barrett_reduce((temp + a[j + distance]));
-        a[j + distance] = montgomery_reduce((W * ((uint32_t)temp + 3*PARAM_Q - a[j + distance])));
+        a[j + distance] = montgomery_reduce((W * (static_cast<uint32_t>(temp) + 3*PARAM_Q - a[j + distance])));
       }
     }
   }
@@ -104,27 +96,26 @@ inline void ntt(uint16_t * a, const uint16_t* omega)
 
 inline void poly_frombytes(poly *r, const uint8_t *a)
 {
-  int i;
-  for(i=0;i<PARAM_N/4;i++)
+  for(size_t i=0;i<PARAM_N/4;i++)
   {
-    r->coeffs[4*i+0] =                               a[7*i+0]        | (((uint16_t)a[7*i+1] & 0x3f) << 8);
-    r->coeffs[4*i+1] = (a[7*i+1] >> 6) | (((uint16_t)a[7*i+2]) << 2) | (((uint16_t)a[7*i+3] & 0x0f) << 10);
-    r->coeffs[4*i+2] = (a[7*i+3] >> 4) | (((uint16_t)a[7*i+4]) << 4) | (((uint16_t)a[7*i+5] & 0x03) << 12);
-    r->coeffs[4*i+3] = (a[7*i+5] >> 2) | (((uint16_t)a[7*i+6]) << 6);
+  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)
 {
-  int i;
-  for(i=0;i<PARAM_N/4;i++)
+  for(size_t i=0;i<PARAM_N/4;i++)
   {
-    uint16_t t0,t1,t2,t3,m;
+    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;
-    t0 = barrett_reduce(p->coeffs[4*i+0]); //Make sure that coefficients have only 14 bits
-    t1 = barrett_reduce(p->coeffs[4*i+1]);
-    t2 = barrett_reduce(p->coeffs[4*i+2]);
-    t3 = barrett_reduce(p->coeffs[4*i+3]);
 
     m = t0 - PARAM_Q;
     c = m;
@@ -162,7 +153,7 @@ inline void poly_getnoise(Botan::RandomNumberGenerator& rng, poly *r)
 
   rng.randomize(buf, 4*PARAM_N);
 
-  for(int i=0;i<PARAM_N;i++)
+  for(size_t i=0;i<PARAM_N;i++)
   {
     uint32_t t = load_le<u32bit>(buf, i);
     uint32_t d = 0;
@@ -176,31 +167,153 @@ inline void poly_getnoise(Botan::RandomNumberGenerator& rng, poly *r)
 
 inline void poly_pointwise(poly *r, const poly *a, const poly *b)
 {
-  int i;
-  uint16_t t;
-  for(i=0;i<PARAM_N;i++)
-  {
-    t       = montgomery_reduce(3186*b->coeffs[i]); /* t is now in Montgomery domain */
+  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)
 {
-  int i;
-  for(i=0;i<PARAM_N;i++)
+  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};
+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((uint16_t *)r->coeffs, omegas_montgomery);
+  ntt(r->coeffs, omegas_montgomery);
 }
 
 inline void bitrev_vector(uint16_t* poly)
@@ -257,12 +370,138 @@ static const uint16_t bitrev_table[1024] = {
 
 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};
+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((uint16_t *)r->coeffs, omegas_inv_montgomery);
+  ntt(r->coeffs, omegas_inv_montgomery);
   mul_coefficients(r->coeffs, psis_inv_montgomery);
 }
 
@@ -285,17 +524,15 @@ inline void decode_a(poly *pk, uint8_t *seed, const uint8_t *r)
 
 inline void encode_b(uint8_t *r, const poly *b, const poly *c)
 {
-  int i;
   poly_tobytes(r,b);
-  for(i=0;i<PARAM_N/4;i++)
+  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)
 {
-  int i;
   poly_frombytes(b, r);
-  for(i=0;i<PARAM_N/4;i++)
+  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;
@@ -412,10 +649,10 @@ inline void rec(uint8_t *key, const poly *v, const poly *c)
 
   for(i=0; i<256; i++)
   {
-    tmp[0] = 16*PARAM_Q + 8*(int32_t)v->coeffs[  0+i] - PARAM_Q * (2*c->coeffs[  0+i]+c->coeffs[768+i]);
-    tmp[1] = 16*PARAM_Q + 8*(int32_t)v->coeffs[256+i] - PARAM_Q * (2*c->coeffs[256+i]+c->coeffs[768+i]);
-    tmp[2] = 16*PARAM_Q + 8*(int32_t)v->coeffs[512+i] - PARAM_Q * (2*c->coeffs[512+i]+c->coeffs[768+i]);
-    tmp[3] = 16*PARAM_Q + 8*(int32_t)v->coeffs[768+i] - PARAM_Q * (              c->coeffs[768+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);
   }
@@ -446,7 +683,7 @@ void gen_a(poly *a, const uint8_t *seed, Newhope_Mode mode)
 
    while(ctr < PARAM_N)
       {
-      uint16_t val = (buf[pos] | ((uint16_t) buf[pos+1] << 8)) & 0x3fff; // Specialized for q = 12889
+      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;