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ntt.c
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//
// Created by Evgeniy Kramsakov on 18.01.2022.
//
#include "ntt.h"
#include "params.h"
#include "reduce.h"
#if (RINGCT_N == 512)
/************************************************************
* Name: bitrev_table
*
* Description: Contains bit-reversed 9-bit indices to be used to re-order
* polynomials before number theoratic transform
************************************************************/
static uint64_t bitrev_table [RINGCT_N] = {
0,256,128,384,64,320,192,448,32,288,160,416,96,352,224,480,16,272,144,400,80,336,208,464,48,304,176,432,112,368,240,496,8,
264,136,392,72,328,200,456,40,296,168,424,104,360,232,488,24,280,152,408,88,344,216,472,56,312,184,440,120,376,248,504,4,
260,132,388,68,324,196,452,36,292,164,420,100,356,228,484,20,276,148,404,84,340,212,468,52,308,180,436,116,372,244,500,12,
268,140,396,76,332,204,460,44,300,172,428,108,364,236,492,28,284,156,412,92,348,220,476,60,316,188,444,124,380,252,508,2,
258,130,386,66,322,194,450,34,290,162,418,98,354,226,482,18,274,146,402,82,338,210,466,50,306,178,434,114,370,242,498,10,
266,138,394,74,330,202,458,42,298,170,426,106,362,234,490,26,282,154,410,90,346,218,474,58,314,186,442,122,378,250,506,6,
262,134,390,70,326,198,454,38,294,166,422,102,358,230,486,22,278,150,406,86,342,214,470,54,310,182,438,118,374,246,502,14,
270,142,398,78,334,206,462,46,302,174,430,110,366,238,494,30,286,158,414,94,350,222,478,62,318,190,446,126,382,254,510,1,
257,129,385,65,321,193,449,33,289,161,417,97,353,225,481,17,273,145,401,81,337,209,465,49,305,177,433,113,369,241,497,9,
265,137,393,73,329,201,457,41,297,169,425,105,361,233,489,25,281,153,409,89,345,217,473,57,313,185,441,121,377,249,505,5,
261,133,389,69,325,197,453,37,293,165,421,101,357,229,485,21,277,149,405,85,341,213,469,53,309,181,437,117,373,245,501,13,
269,141,397,77,333,205,461,45,301,173,429,109,365,237,493,29,285,157,413,93,349,221,477,61,317,189,445,125,381,253,509,3,
259,131,387,67,323,195,451,35,291,163,419,99,355,227,483,19,275,147,403,83,339,211,467,51,307,179,435,115,371,243,499,11,
267,139,395,75,331,203,459,43,299,171,427,107,363,235,491,27,283,155,411,91,347,219,475,59,315,187,443,123,379,251,507,7,
263,135,391,71,327,199,455,39,295,167,423,103,359,231,487,23,279,151,407,87,343,215,471,55,311,183,439,119,375,247,503,15,
271,143,399,79,335,207,463,47,303,175,431,111,367,239,495,31,287,159,415,95,351,223,479,63,319,191,447,127,383,255,511
};
#elif (RINGCT_N == 1024)
/************************************************************
* Name: bitrev_table
*
* Description: Contains bit-reversed 10-bit indices to be used to re-order
* polynomials before number theoratic transform
************************************************************/
static uint64_t bitrev_table[RINGCT_N] = {
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
};
#elif (RINGCT_N == 4) // toy example
static uint64_t bitrev_table[RINGCT_N] = {
0, 2, 1, 3
};
#else
#error "RINGCT_N must be either 512 or 1024 or 4"
#endif
/*************************************************
* Name: bitrev_vector_newhope
*
* Description: Permutes coefficients of a polynomial into bitreversed order
*
* Arguments: - uint16_t* poly_newhope: pointer to in/output polynomial
**************************************************/
void bitrev_vector(uint64_t* poly)
{
unsigned int i,r;
uint64_t tmp;
for(i = 0; i < RINGCT_N; i++)
{
r = bitrev_table[i];
if (i < r)
{
tmp = poly[i];
poly[i] = poly[r];
poly[r] = tmp;
}
}
}
/*************************************************
* Name: mul_coefficients
*
* Description: Performs pointwise (coefficient-wise) multiplication
* of two polynomials
* Arguments: - uint16_t* poly_newhope: pointer to in/output polynomial
* - const uint16_t* factors: pointer to input polynomial, coefficients
* are assumed to be in Montgomery representation
**************************************************/
void mul_coefficients(uint64_t* poly, const uint64_t* factors)
{
unsigned int i;
for(i = 0; i < RINGCT_N; i++)
poly[i] = montgomery_reduce((poly[i] * factors[i]));
}
#if (RINGCT_N == 512)
/*************************************************
* Name: ntt
*
* Description: Computes number-theoretic transform (NTT) of
* a polynomial in place; inputs assumed to be in
* bitreversed order, output in normal order
*
* Arguments: - uint16_t * a: pointer to in/output polynomial
* - const uint16_t* omega: pointer to input powers of root of unity omega;
* assumed to be in Montgomery domain
**************************************************/
void ntt(uint64_t * a, const uint64_t* omega)
{
int i, start, j, jTwiddle, distance;
uint64_t temp, W;
for(i=0;i<9;i+=2)
{
// Even level
distance = (1<<i);
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<RINGCT_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
temp = a[j];
a[j] = (temp + a[j + distance]) % RINGCT_Q;
a[j + distance] = montgomery_reduce((W * (temp + (uint64_t)3*RINGCT_Q - a[j + distance])));
}
}
if(i+1<9){
// Odd level
distance <<= 1;
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<RINGCT_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
temp = a[j];
a[j] = (temp + a[j + distance]) % RINGCT_Q;
a[j + distance] = montgomery_reduce((W * (temp + (uint64_t)3*RINGCT_Q - a[j + distance])));
}
}
}
}
}
#elif (RINGCT_N == 1024)
void /*************************************************
* Name: ntt
*
* Description: Computes number-theoretic transform (NTT) of
* a polynomial in place; inputs assumed to be in
* bitreversed order, output in normal order
*
* Arguments: - uint16_t * a: pointer to in/output polynomial
* - const uint16_t* omega: pointer to input powers of root of unity omega;
* assumed to be in Montgomery domain
**************************************************/
ntt(uint64_t * a, const uint64_t* omega)
{
int i, start, j, jTwiddle, distance;
uint64_t temp, W;
for(i=0;i<10;i+=2)
{
// Even level
distance = (1<<i);
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<RINGCT_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
temp = a[j];
a[j] = (temp + a[j + distance]) % RINGCT_Q; // Omit reduction (be lazy)
a[j + distance] = montgomery_reduce((W * (temp + (uint64_t) 3*RINGCT_Q - a[j + distance])));
}
}
// Odd level
distance <<= 1;
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<RINGCT_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
temp = a[j];
a[j] = (temp + a[j + distance]) % RINGCT_Q;
a[j + distance] = montgomery_reduce((W * (temp + (uint64_t) 3*RINGCT_Q - a[j + distance])));
}
}
}
}
#elif (RINGCT_N == 4)
void /*************************************************
* Name: ntt
*
* Description: Computes number-theoretic transform (NTT) of
* a polynomial in place; inputs assumed to be in
* bitreversed order, output in normal order
*
* Arguments: - uint64_t * a: pointer to in/output polynomial
* - const uint16_t* omega: pointer to input powers of root of unity omega;
* assumed to be in Montgomery domain
**************************************************/
ntt(uint64_t * a, const uint64_t* omega)
{
int i, start, j, jTwiddle, distance;
uint64_t temp, W;
for(i=0;i<2;i++)
{
// Even level
distance = (1<<i);
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<RINGCT_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
temp = a[j];
a[j] = (temp + a[j + distance]) % RINGCT_Q; // Omit reduction (be lazy)
a[j + distance] = montgomery_reduce((W * (temp + (uint64_t ) 3*RINGCT_Q - a[j + distance])));
}
}
}
}
#else
#error "RINGCT_N must be either 512 or 1024 or 4"
#endif