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180 lines
16 KiB
C
180 lines
16 KiB
C
#include "inttypes.h"
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#include "ntt.h"
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#include "params.h"
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/* Precomputed NTT contants generated by Pari/GP script as follows:
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*
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* For n = 512:
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*
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* brv = [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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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,
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* 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]
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* n = 512; q = 12289; mont=2^18
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* g = Mod(10968, q);
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* omegas_inv_bitrev_montgomery = lift(vector(n/2, i, (g^2)^(-brv[2*(i-1)+1])*mont))
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* gammas_bitrev_montgomery = lift(vector(n, i, g^(brv[i])*mont))
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* gammas_inv_montgomery = lift(vector(n, i, g^(-(i-1))/n*mont))
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*
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*
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* For n = 1024:
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*
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* brv = [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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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, \
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* 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]
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*
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* n = 1024; q = 12289; mont=2^18
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* g = Mod(7, q);
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* omegas_inv_bitrev_montgomery = lift(vector(n/2, i, (g^2)^(-brv[2*(i-1)+1])*mont))
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* gammas_bitrev_montgomery = lift(vector(n, i, g^(brv[i])*mont))
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* gammas_inv_montgomery = lift(vector(n, i, g^(-(i-1))/n*mont))
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*/
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/************************************************************
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* Name: omegas_inv_bitrev_montgomery
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*
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* Description: Contains inverses of powers of nth root of unity
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* in Montgomery domain with R=2^18 in bit-reversed order
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************************************************************/
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const uint16_t PQCLEAN_NEWHOPE512CPA_CLEAN_omegas_inv_bitrev_montgomery[NEWHOPE_N / 2] = {
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4075, 6974, 4916, 4324, 7210, 3262, 2169, 11767, 3514, 1041, 5925, 11271, 6715, 10316, 11011, 9945,
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1190, 9606, 3818, 6118, 1050, 7753, 8429, 6844, 4449, 6833, 147, 3789, 7540, 6752, 4467, 4789,
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10367, 3879, 2033, 3998, 11316, 1254, 6854, 1359, 3988, 468, 11907, 11973, 8579, 6196, 5446, 6950,
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1987, 10587, 654, 3565, 3199, 12233, 7083, 6760, 6427, 6153, 3643, 6874, 4948, 6152, 11889, 1728,
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7280, 10333, 6008, 11404, 3532, 11286, 241, 12231, 11314, 4212, 8851, 9445, 3477, 6608, 12147, 1105,
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5594, 9260, 5886, 7507, 4213, 11785, 2302, 11684, 8687, 6221, 8209, 421, 7665, 6212, 8689, 3263,
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10710, 431, 9784, 5906, 9450, 8332, 2127, 151, 3174, 52, 1323, 9523, 6415, 11612, 3336, 6234,
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7048, 9369, 4169, 3127, 11279, 6821, 787, 3482, 3445, 4780, 7232, 7591, 7377, 2049, 1321, 192,
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9551, 6421, 5735, 9634, 10596, 9280, 723, 12115, 9364, 347, 1975, 3757, 10431, 7535, 11863, 3315,
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4493, 3202, 5369, 10232, 350, 10777, 6906, 10474, 1483, 6374, 49, 1263, 10706, 6347, 1489, 9789,
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7552, 1293, 4774, 5429, 3772, 418, 6381, 453, 9522, 156, 3969, 3991, 6956, 10258, 10008, 6413,
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8855, 3529, 218, 9381, 9259, 8174, 2361, 10446, 10335, 2051, 9407, 10484, 9842, 6147, 3963, 576,
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6523, 11637, 6099, 11994, 9370, 3762, 8273, 4077, 11964, 1404, 11143, 11341, 1159, 6299, 4049, 8561,
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5961, 7183, 1962, 10695, 9597, 12121, 8960, 7991, 6992, 6170, 10929, 8333, 2555, 6167, 11089, 5184,
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3570, 4240, 11454, 6065, 3150, 10970, 709, 8243, 1058, 8210, 441, 11367, 10331, 7967, 1112, 2078,
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10542, 3123, 5486, 9235, 7856, 6370, 8455, 5257, 9341, 9786, 6507, 10723, 2459, 683, 8633, 64,
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};
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/************************************************************
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* Name: gammas_bitrev_montgomery
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*
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* Description: Contains powers of nth root of -1 in Montgomery
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* domain with R=2^18 in bit-reversed order
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************************************************************/
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const uint16_t PQCLEAN_NEWHOPE512CPA_CLEAN_gammas_bitrev_montgomery[NEWHOPE_N] = {
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4075, 5315, 7965, 7373, 522, 10120, 9027, 5079, 2344, 1278, 1973, 5574, 1018, 6364, 11248, 8775,
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7500, 7822, 5537, 4749, 8500, 12142, 5456, 7840, 5445, 3860, 4536, 11239, 6171, 8471, 2683, 11099,
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10561, 400, 6137, 7341, 5415, 8646, 6136, 5862, 5529, 5206, 56, 9090, 8724, 11635, 1702, 10302,
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5339, 6843, 6093, 3710, 316, 382, 11821, 8301, 10930, 5435, 11035, 973, 8291, 10256, 8410, 1922,
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12097, 10968, 10240, 4912, 4698, 5057, 7509, 8844, 8807, 11502, 5468, 1010, 9162, 8120, 2920, 5241,
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6055, 8953, 677, 5874, 2766, 10966, 12237, 9115, 12138, 10162, 3957, 2839, 6383, 2505, 11858, 1579,
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9026, 3600, 6077, 4624, 11868, 4080, 6068, 3602, 605, 9987, 504, 8076, 4782, 6403, 3029, 6695,
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11184, 142, 5681, 8812, 2844, 3438, 8077, 975, 58, 12048, 1003, 8757, 885, 6281, 1956, 5009,
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12225, 3656, 11606, 9830, 1566, 5782, 2503, 2948, 7032, 3834, 5919, 4433, 3054, 6803, 9166, 1747,
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10211, 11177, 4322, 1958, 922, 11848, 4079, 11231, 4046, 11580, 1319, 9139, 6224, 835, 8049, 8719,
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7105, 1200, 6122, 9734, 3956, 1360, 6119, 5297, 4298, 3329, 168, 2692, 1594, 10327, 5106, 6328,
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3728, 8240, 5990, 11130, 948, 1146, 10885, 325, 8212, 4016, 8527, 2919, 295, 6190, 652, 5766,
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11713, 8326, 6142, 2447, 1805, 2882, 10238, 1954, 1843, 9928, 4115, 3030, 2908, 12071, 8760, 3434,
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5876, 2281, 2031, 5333, 8298, 8320, 12133, 2767, 11836, 5908, 11871, 8517, 6860, 7515, 10996, 4737,
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2500, 10800, 5942, 1583, 11026, 12240, 5915, 10806, 1815, 5383, 1512, 11939, 2057, 6920, 9087, 7796,
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8974, 426, 4754, 1858, 8532, 10314, 11942, 2925, 174, 11566, 3009, 1693, 2655, 6554, 5868, 2738,
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11796, 8193, 9908, 5444, 10911, 1912, 7952, 435, 404, 7644, 11224, 10146, 7012, 11121, 11082, 9041,
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9723, 2187, 9867, 6250, 3646, 9852, 6267, 2987, 8509, 875, 4976, 10682, 8005, 5088, 7278, 11287,
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9223, 27, 3763, 10849, 11272, 7404, 5084, 10657, 8146, 4714, 12047, 10752, 2678, 3704, 545, 7270,
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1067, 5101, 442, 2401, 390, 11516, 3778, 8456, 1045, 9430, 9808, 5012, 9377, 6591, 11935, 4861,
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7852, 3, 3149, 12129, 12176, 4919, 10123, 3915, 3636, 7351, 2704, 5291, 1663, 1777, 1426, 7635,
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1484, 7394, 2780, 7094, 8236, 2645, 7247, 2305, 2847, 7875, 7917, 10115, 10600, 8925, 4057, 3271,
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9273, 243, 9289, 11618, 3136, 5191, 8889, 9890, 11869, 5559, 10111, 10745, 11813, 8758, 4905, 3985,
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9603, 9042, 3978, 9320, 3510, 5332, 9424, 2370, 9405, 11136, 2249, 8241, 10659, 10163, 9103, 6882,
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10810, 1, 5146, 4043, 8155, 5736, 11567, 1305, 1212, 10643, 9094, 5860, 8747, 8785, 8668, 2545,
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4591, 6561, 5023, 6461, 10938, 4978, 6512, 8961, 949, 2625, 2639, 7468, 11726, 2975, 9545, 9283,
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3091, 81, 11289, 7969, 9238, 9923, 2963, 7393, 12149, 1853, 11563, 7678, 8034, 11112, 1635, 9521,
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3201, 3014, 1326, 7203, 1170, 9970, 11334, 790, 3135, 3712, 4846, 2747, 3553, 7484, 11227, 2294,
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11267, 9, 9447, 11809, 11950, 2468, 5791, 11745, 10908, 9764, 8112, 3584, 4989, 5331, 4278, 10616,
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4452, 9893, 8340, 8993, 130, 7935, 9452, 6915, 8541, 11336, 11462, 5767, 7222, 2197, 12171, 9813,
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3241, 729, 3289, 10276, 9408, 3284, 2089, 5092, 11029, 4388, 5755, 7657, 10861, 1696, 2426, 11955,
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4231, 2548, 11934, 3382, 10530, 3707, 3694, 7110, 3637, 8830, 6747, 145, 7399, 5911, 2731, 8357,
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};
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/************************************************************
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* Name: gammas_inv_montgomery
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*
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* Description: Contains inverses of powers of nth root of -1
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* divided by n in Montgomery domain with R=2^18
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************************************************************/
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const uint16_t PQCLEAN_NEWHOPE512CPA_CLEAN_gammas_inv_montgomery[NEWHOPE_N] = {
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512, 3944, 4267, 5411, 9615, 5900, 3205, 6063, 9261, 2021, 3087, 4770, 1029, 1590, 343, 530,
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8307, 4273, 2769, 9617, 923, 7302, 4404, 2434, 1468, 9004, 8682, 11194, 2894, 11924, 5061, 8071,
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1687, 10883, 8755, 7724, 11111, 6671, 7800, 6320, 2600, 6203, 4963, 6164, 9847, 6151, 11475, 10243,
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3825, 11607, 1275, 3869, 425, 5386, 4238, 9988, 5509, 11522, 10029, 7937, 3343, 6742, 9307, 10440,
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11295, 3480, 3765, 1160, 1255, 4483, 8611, 9687, 11063, 3229, 7784, 9269, 6691, 7186, 10423, 10588,
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11667, 11722, 3889, 12100, 9489, 12226, 3163, 12268, 9247, 12282, 11275, 4094, 11951, 5461, 8080, 10013,
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10886, 7434, 7725, 2478, 2575, 826, 9051, 8468, 3017, 6919, 5102, 10499, 5797, 7596, 10125, 2532,
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3375, 844, 1125, 8474, 375, 6921, 125, 2307, 4138, 769, 9572, 8449, 7287, 11009, 2429, 7766,
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4906, 6685, 9828, 10421, 3276, 7570, 1092, 10716, 364, 3572, 8314, 5287, 10964, 9955, 7751, 11511,
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6680, 3837, 6323, 1279, 6204, 8619, 2068, 2873, 8882, 5054, 7057, 5781, 10545, 1927, 3515, 8835,
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5268, 2945, 1756, 5078, 8778, 5789, 2926, 6026, 9168, 6105, 3056, 2035, 5115, 8871, 1705, 2957,
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8761, 5082, 11113, 1694, 11897, 4661, 8062, 5650, 10880, 10076, 7723, 7455, 10767, 2485, 3589, 9021,
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9389, 3007, 7226, 9195, 6505, 3065, 10361, 5118, 7550, 1706, 6613, 4665, 10397, 1555, 7562, 8711,
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6617, 7000, 6302, 10526, 6197, 7605, 6162, 2535, 2054, 845, 4781, 4378, 5690, 9652, 5993, 11410,
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6094, 11996, 10224, 8095, 3408, 10891, 1136, 11823, 4475, 3941, 5588, 5410, 5959, 9996, 10179, 3332,
|
|
3393, 5207, 1131, 5832, 377, 1944, 4222, 648, 9600, 216, 3200, 72, 5163, 24, 1721, 8,
|
|
4670, 4099, 5653, 9559, 10077, 11379, 3359, 3793, 5216, 9457, 5835, 11345, 1945, 7878, 8841, 2626,
|
|
2947, 9068, 9175, 7119, 11251, 2373, 11943, 791, 3981, 4360, 1327, 9646, 8635, 11408, 11071, 7899,
|
|
11883, 2633, 3961, 4974, 9513, 1658, 3171, 4649, 1057, 5646, 8545, 1882, 11041, 8820, 11873, 2940,
|
|
8054, 980, 6781, 4423, 10453, 9667, 11677, 11415, 12085, 3805, 12221, 9461, 8170, 7250, 10916, 6513,
|
|
7735, 2171, 10771, 4820, 11783, 5703, 8024, 1901, 6771, 4730, 2257, 5673, 8945, 1891, 7078, 8823,
|
|
10552, 2941, 11710, 9173, 12096, 7154, 4032, 6481, 1344, 10353, 448, 3451, 8342, 9343, 6877, 11307,
|
|
10485, 3769, 3495, 9449, 1165, 7246, 8581, 10608, 11053, 3536, 11877, 5275, 3959, 9951, 5416, 3317,
|
|
9998, 5202, 7429, 1734, 10669, 578, 11749, 4289, 12109, 5526, 12229, 1842, 12269, 614, 8186, 4301,
|
|
6825, 5530, 2275, 10036, 8951, 11538, 7080, 3846, 2360, 1282, 4883, 8620, 5724, 11066, 1908, 7785,
|
|
636, 2595, 212, 865, 4167, 8481, 1389, 2827, 463, 9135, 8347, 3045, 10975, 1015, 11851, 8531,
|
|
12143, 6940, 8144, 10506, 6811, 3502, 10463, 9360, 7584, 3120, 2528, 1040, 4939, 4443, 9839, 1481,
|
|
7376, 4590, 6555, 1530, 2185, 510, 8921, 170, 7070, 4153, 6453, 9577, 2151, 11385, 717, 3795,
|
|
239, 1265, 4176, 4518, 1392, 1506, 464, 502, 4251, 8360, 1417, 6883, 8665, 10487, 11081, 7592,
|
|
7790, 6627, 6693, 2209, 2231, 8929, 4840, 11169, 9806, 3723, 7365, 1241, 2455, 4510, 9011, 9696,
|
|
7100, 3232, 6463, 9270, 10347, 3090, 3449, 1030, 5246, 8536, 5845, 11038, 10141, 11872, 11573, 12150,
|
|
7954, 4050, 10844, 1350, 7711, 450, 10763, 150, 7684, 50, 10754, 4113, 7681, 1371, 10753, 457,
|
|
};
|