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NewHope.cpp
1 /*
2  * Copyright (C) 2016 Southern Storm Software, Pty Ltd.
3  *
4  * Permission is hereby granted, free of charge, to any person obtaining a
5  * copy of this software and associated documentation files (the "Software"),
6  * to deal in the Software without restriction, including without limitation
7  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
8  * and/or sell copies of the Software, and to permit persons to whom the
9  * Software is furnished to do so, subject to the following conditions:
10  *
11  * The above copyright notice and this permission notice shall be included
12  * in all copies or substantial portions of the Software.
13  *
14  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
15  * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
16  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
17  * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
18  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
19  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
20  * DEALINGS IN THE SOFTWARE.
21  */
22 
23 #include "NewHope.h"
24 #include <Crypto.h>
25 #include <ChaCha.h>
26 #include <SHA3.h>
27 #include <SHAKE.h>
28 #include <RNG.h>
29 #include <string.h>
30 
33 // Older Arduino IDE's don't define placement new. Provide our own definition.
34 void *operator new(size_t size, void *ptr)
35 {
36  return ptr;
37 }
38 
39 #if defined(__AVR__)
40 #include <avr/pgmspace.h>
41 #define table_read(name, index) (pgm_read_word(&((name)[(index)])))
42 #else
43 #define PROGMEM
44 #define table_read(name, index) ((name)[(index)])
45 #endif
46 
158 typedef struct
159 {
160  uint32_t input[16];
161  uint32_t output[16];
162 
163 } NewHopeChaChaState;
164 
165 // The following is public domain code from the reference C version of
166 // New Hope at https://cryptojedi.org/crypto/#newhope. This part of
167 // the Arduino port remains public domain. Original authors:
168 // Erdem Alkim, Léo Ducas, Thomas Pöppelmann, Peter Schwabe
169 
170 #define PARAM_N 1024
171 #define PARAM_K 16
172 #define PARAM_Q ((int32_t)12289)
173 #define POLY_BYTES 1792
174 #define NEWHOPE_SEEDBYTES 32
175 #define NEWHOPE_RECBYTES 256
176 
177 static uint16_t const omegas_montgomery[PARAM_N/2] PROGMEM = {
178  4075,6974,7373,7965,3262,5079,522,2169,6364,1018,1041,8775,2344,
179  11011,5574,1973,4536,1050,6844,3860,3818,6118,2683,1190,4789,7822,
180  7540,6752,5456,4449,3789,12142,11973,382,3988,468,6843,5339,6196,
181  3710,11316,1254,5435,10930,3998,10256,10367,3879,11889,1728,6137,
182  4948,5862,6136,3643,6874,8724,654,10302,1702,7083,6760,56,3199,9987,
183  605,11785,8076,5594,9260,6403,4782,6212,4624,9026,8689,4080,11868,
184  6221,3602,975,8077,8851,9445,5681,3477,1105,142,241,12231,1003,
185  3532,5009,1956,6008,11404,7377,2049,10968,12097,7591,5057,3445,
186  4780,2920,7048,3127,8120,11279,6821,11502,8807,12138,2127,2839,
187  3957,431,1579,6383,9784,5874,677,3336,6234,2766,1323,9115,12237,
188  2031,6956,6413,2281,3969,3991,12133,9522,4737,10996,4774,5429,11871,
189  3772,453,5908,2882,1805,2051,1954,11713,3963,2447,6142,8174,3030,
190  1843,2361,12071,2908,3529,3434,3202,7796,2057,5369,11939,1512,6906,
191  10474,11026,49,10806,5915,1489,9789,5942,10706,10431,7535,426,8974,
192  3757,10314,9364,347,5868,9551,9634,6554,10596,9280,11566,174,2948,
193  2503,6507,10723,11606,2459,64,3656,8455,5257,5919,7856,1747,9166,
194  5486,9235,6065,835,3570,4240,11580,4046,10970,9139,1058,8210,11848,
195  922,7967,1958,10211,1112,3728,4049,11130,5990,1404,325,948,11143,
196  6190,295,11637,5766,8212,8273,2919,8527,6119,6992,8333,1360,2555,
197  6167,1200,7105,7991,3329,9597,12121,5106,5961,10695,10327,3051,9923,
198  4896,9326,81,3091,1000,7969,4611,726,1853,12149,4255,11112,2768,
199  10654,1062,2294,3553,4805,2747,4846,8577,9154,1170,2319,790,11334,
200  9275,9088,1326,5086,9094,6429,11077,10643,3504,3542,8668,9744,1479,
201  1,8246,7143,11567,10984,4134,5736,4978,10938,5777,8961,4591,5728,
202  6461,5023,9650,7468,949,9664,2975,11726,2744,9283,10092,5067,12171,
203  2476,3748,11336,6522,827,9452,5374,12159,7935,3296,3949,9893,4452,
204  10908,2525,3584,8112,8011,10616,4989,6958,11809,9447,12280,1022,
205  11950,9821,11745,5791,5092,2089,9005,2881,3289,2013,9048,729,7901,
206  1260,5755,4632,11955,2426,10593,1428,4890,5911,3932,9558,8830,3637,
207  5542,145,5179,8595,3707,10530,355,3382,4231,9741,1207,9041,7012,1168,
208  10146,11224,4645,11885,10911,10377,435,7952,4096,493,9908,6845,6039,
209  2422,2187,9723,8643,9852,9302,6022,7278,1002,4284,5088,1607,7313,
210  875,8509,9430,1045,2481,5012,7428,354,6591,9377,11847,2401,1067,
211  7188,11516,390,8511,8456,7270,545,8585,9611,12047,1537,4143,4714,
212  4885,1017,5084,1632,3066,27,1440,8526,9273,12046,11618,9289,3400,
213  9890,3136,7098,8758,11813,7384,3985,11869,6730,10745,10111,2249,
214  4048,2884,11136,2126,1630,9103,5407,2686,9042,2969,8311,9424,
215  9919,8779,5332,10626,1777,4654,10863,7351,3636,9585,5291,8374,
216  2166,4919,12176,9140,12129,7852,12286,4895,10805,2780,5195,2305,
217  7247,9644,4053,10600,3364,3271,4057,4414,9442,7917,2174
218 };
219 
220 static uint16_t const omegas_inv_montgomery[PARAM_N/2] PROGMEM = {
221  4075,5315,4324,4916,10120,11767,7210,9027,10316,6715,1278,9945,
222  3514,11248,11271,5925,147,8500,7840,6833,5537,4749,4467,7500,11099,
223  9606,6171,8471,8429,5445,11239,7753,9090,12233,5529,5206,10587,
224  1987,11635,3565,5415,8646,6153,6427,7341,6152,10561,400,8410,1922,
225  2033,8291,1359,6854,11035,973,8579,6093,6950,5446,11821,8301,11907,
226  316,52,3174,10966,9523,6055,8953,11612,6415,2505,5906,10710,11858,
227  8332,9450,10162,151,3482,787,5468,1010,4169,9162,5241,9369,7509,
228  8844,7232,4698,192,1321,10240,4912,885,6281,10333,7280,8757,11286,
229  58,12048,12147,11184,8812,6608,2844,3438,4212,11314,8687,6068,421,
230  8209,3600,3263,7665,6077,7507,5886,3029,6695,4213,504,11684,2302,
231  1962,1594,6328,7183,168,2692,8960,4298,5184,11089,6122,9734,10929,
232  3956,5297,6170,3762,9370,4016,4077,6523,652,11994,6099,1146,11341,
233  11964,10885,6299,1159,8240,8561,11177,2078,10331,4322,11367,441,
234  4079,11231,3150,1319,8243,709,8049,8719,11454,6224,3054,6803,3123,
235  10542,4433,6370,7032,3834,8633,12225,9830,683,1566,5782,9786,9341,
236  12115,723,3009,1693,5735,2655,2738,6421,11942,2925,1975,8532,3315,
237  11863,4754,1858,1583,6347,2500,10800,6374,1483,12240,1263,1815,
238  5383,10777,350,6920,10232,4493,9087,8855,8760,9381,218,9928,10446,
239  9259,4115,6147,9842,8326,576,10335,10238,10484,9407,6381,11836,8517,
240  418,6860,7515,1293,7552,2767,156,8298,8320,10008,5876,5333,10258,
241  10115,4372,2847,7875,8232,9018,8925,1689,8236,2645,5042,9984,7094,
242  9509,1484,7394,3,4437,160,3149,113,7370,10123,3915,6998,2704,8653,
243  4938,1426,7635,10512,1663,6957,3510,2370,2865,3978,9320,3247,9603,
244  6882,3186,10659,10163,1153,9405,8241,10040,2178,1544,5559,420,8304,
245  4905,476,3531,5191,9153,2399,8889,3000,671,243,3016,3763,10849,12262,
246  9223,10657,7205,11272,7404,7575,8146,10752,242,2678,3704,11744,
247  5019,3833,3778,11899,773,5101,11222,9888,442,2912,5698,11935,4861,
248  7277,9808,11244,2859,3780,11414,4976,10682,7201,8005,11287,5011,
249  6267,2987,2437,3646,2566,10102,9867,6250,5444,2381,11796,8193,4337,
250  11854,1912,1378,404,7644,1065,2143,11121,5277,3248,11082,2548,8058,
251  8907,11934,1759,8582,3694,7110,12144,6747,8652,3459,2731,8357,6378,
252  7399,10861,1696,9863,334,7657,6534,11029,4388,11560,3241,10276,9000,
253  9408,3284,10200,7197,6498,544,2468,339,11267,9,2842,480,5331,7300,
254  1673,4278,4177,8705,9764,1381,7837,2396,8340,8993,4354,130,6915,
255  2837,11462,5767,953,8541,9813,118,7222,2197,3006,9545,563,9314,
256  2625,11340,4821,2639,7266,5828,6561,7698,3328,6512,1351,7311,6553,
257  8155,1305,722,5146,4043,12288,10810,2545,3621,8747,8785,1646,1212,
258  5860,3195,7203,10963,3201,3014,955,11499,9970,11119,3135,3712,7443,
259  9542,7484,8736,9995,11227,1635,9521,1177,8034,140,10436,11563,7678,
260  4320,11289,9198,12208,2963,7393,2366,9238
261 };
262 
263 static uint16_t const psis_bitrev_montgomery[PARAM_N] PROGMEM = {
264  4075,6974,7373,7965,3262,5079,522,2169,6364,1018,1041,8775,2344,
265  11011,5574,1973,4536,1050,6844,3860,3818,6118,2683,1190,4789,7822,
266  7540,6752,5456,4449,3789,12142,11973,382,3988,468,6843,5339,6196,3710,
267  11316,1254,5435,10930,3998,10256,10367,3879,11889,1728,6137,4948,
268  5862,6136,3643,6874,8724,654,10302,1702,7083,6760,56,3199,9987,605,
269  11785,8076,5594,9260,6403,4782,6212,4624,9026,8689,4080,11868,6221,
270  3602,975,8077,8851,9445,5681,3477,1105,142,241,12231,1003,3532,5009,
271  1956,6008,11404,7377,2049,10968,12097,7591,5057,3445,4780,2920,
272  7048,3127,8120,11279,6821,11502,8807,12138,2127,2839,3957,431,1579,
273  6383,9784,5874,677,3336,6234,2766,1323,9115,12237,2031,6956,6413,
274  2281,3969,3991,12133,9522,4737,10996,4774,5429,11871,3772,453,
275  5908,2882,1805,2051,1954,11713,3963,2447,6142,8174,3030,1843,2361,
276  12071,2908,3529,3434,3202,7796,2057,5369,11939,1512,6906,10474,
277  11026,49,10806,5915,1489,9789,5942,10706,10431,7535,426,8974,3757,
278  10314,9364,347,5868,9551,9634,6554,10596,9280,11566,174,2948,2503,
279  6507,10723,11606,2459,64,3656,8455,5257,5919,7856,1747,9166,5486,
280  9235,6065,835,3570,4240,11580,4046,10970,9139,1058,8210,11848,922,
281  7967,1958,10211,1112,3728,4049,11130,5990,1404,325,948,11143,6190,
282  295,11637,5766,8212,8273,2919,8527,6119,6992,8333,1360,2555,6167,
283  1200,7105,7991,3329,9597,12121,5106,5961,10695,10327,3051,9923,
284  4896,9326,81,3091,1000,7969,4611,726,1853,12149,4255,11112,2768,
285  10654,1062,2294,3553,4805,2747,4846,8577,9154,1170,2319,790,11334,
286  9275,9088,1326,5086,9094,6429,11077,10643,3504,3542,8668,9744,1479,
287  1,8246,7143,11567,10984,4134,5736,4978,10938,5777,8961,4591,5728,
288  6461,5023,9650,7468,949,9664,2975,11726,2744,9283,10092,5067,12171,
289  2476,3748,11336,6522,827,9452,5374,12159,7935,3296,3949,9893,4452,
290  10908,2525,3584,8112,8011,10616,4989,6958,11809,9447,12280,1022,
291  11950,9821,11745,5791,5092,2089,9005,2881,3289,2013,9048,729,7901,
292  1260,5755,4632,11955,2426,10593,1428,4890,5911,3932,9558,8830,3637,
293  5542,145,5179,8595,3707,10530,355,3382,4231,9741,1207,9041,7012,
294  1168,10146,11224,4645,11885,10911,10377,435,7952,4096,493,9908,6845,
295  6039,2422,2187,9723,8643,9852,9302,6022,7278,1002,4284,5088,1607,
296  7313,875,8509,9430,1045,2481,5012,7428,354,6591,9377,11847,2401,
297  1067,7188,11516,390,8511,8456,7270,545,8585,9611,12047,1537,4143,
298  4714,4885,1017,5084,1632,3066,27,1440,8526,9273,12046,11618,9289,
299  3400,9890,3136,7098,8758,11813,7384,3985,11869,6730,10745,10111,
300  2249,4048,2884,11136,2126,1630,9103,5407,2686,9042,2969,8311,9424,
301  9919,8779,5332,10626,1777,4654,10863,7351,3636,9585,5291,8374,
302  2166,4919,12176,9140,12129,7852,12286,4895,10805,2780,5195,2305,
303  7247,9644,4053,10600,3364,3271,4057,4414,9442,7917,2174,3947,
304  11951,2455,6599,10545,10975,3654,2894,7681,7126,7287,12269,4119,
305  3343,2151,1522,7174,7350,11041,2442,2148,5959,6492,8330,8945,5598,
306  3624,10397,1325,6565,1945,11260,10077,2674,3338,3276,11034,506,
307  6505,1392,5478,8778,1178,2776,3408,10347,11124,2575,9489,12096,
308  6092,10058,4167,6085,923,11251,11912,4578,10669,11914,425,10453,
309  392,10104,8464,4235,8761,7376,2291,3375,7954,8896,6617,7790,1737,
310  11667,3982,9342,6680,636,6825,7383,512,4670,2900,12050,7735,994,
311  1687,11883,7021,146,10485,1403,5189,6094,2483,2054,3042,10945,
312  3981,10821,11826,8882,8151,180,9600,7684,5219,10880,6780,204,
313  11232,2600,7584,3121,3017,11053,7814,7043,4251,4739,11063,6771,
314  7073,9261,2360,11925,1928,11825,8024,3678,3205,3359,11197,5209,
315  8581,3238,8840,1136,9363,1826,3171,4489,7885,346,2068,1389,8257,
316  3163,4840,6127,8062,8921,612,4238,10763,8067,125,11749,10125,5416,
317  2110,716,9839,10584,11475,11873,3448,343,1908,4538,10423,7078,
318  4727,1208,11572,3589,2982,1373,1721,10753,4103,2429,4209,5412,
319  5993,9011,438,3515,7228,1218,8347,5232,8682,1327,7508,4924,448,
320  1014,10029,12221,4566,5836,12229,2717,1535,3200,5588,5845,412,
321  5102,7326,3744,3056,2528,7406,8314,9202,6454,6613,1417,10032,7784,
322  1518,3765,4176,5063,9828,2275,6636,4267,6463,2065,7725,3495,8328,
323  8755,8144,10533,5966,12077,9175,9520,5596,6302,8400,579,6781,11014,
324  5734,11113,11164,4860,1131,10844,9068,8016,9694,3837,567,9348,7000,
325  6627,7699,5082,682,11309,5207,4050,7087,844,7434,3769,293,9057,
326  6940,9344,10883,2633,8190,3944,5530,5604,3480,2171,9282,11024,2213,
327  8136,3805,767,12239,216,11520,6763,10353,7,8566,845,7235,3154,4360,
328  3285,10268,2832,3572,1282,7559,3229,8360,10583,6105,3120,6643,6203,
329  8536,8348,6919,3536,9199,10891,11463,5043,1658,5618,8787,5789,4719,
330  751,11379,6389,10783,3065,7806,6586,2622,5386,510,7628,6921,578,
331  10345,11839,8929,4684,12226,7154,9916,7302,8481,3670,11066,2334,
332  1590,7878,10734,1802,1891,5103,6151,8820,3418,7846,9951,4693,417,
333  9996,9652,4510,2946,5461,365,881,1927,1015,11675,11009,1371,12265,
334  2485,11385,5039,6742,8449,1842,12217,8176,9577,4834,7937,9461,2643,
335  11194,3045,6508,4094,3451,7911,11048,5406,4665,3020,6616,11345,
336  7519,3669,5287,1790,7014,5410,11038,11249,2035,6125,10407,4565,
337  7315,5078,10506,2840,2478,9270,4194,9195,4518,7469,1160,6878,2730,
338  10421,10036,1734,3815,10939,5832,10595,10759,4423,8420,9617,7119,
339  11010,11424,9173,189,10080,10526,3466,10588,7592,3578,11511,7785,
340  9663,530,12150,8957,2532,3317,9349,10243,1481,9332,3454,3758,7899,
341  4218,2593,11410,2276,982,6513,1849,8494,9021,4523,7988,8,457,648,
342  150,8000,2307,2301,874,5650,170,9462,2873,9855,11498,2535,11169,
343  5808,12268,9687,1901,7171,11787,3846,1573,6063,3793,466,11259,
344  10608,3821,6320,4649,6263,2929
345 };
346 
347 static uint16_t const psis_inv_montgomery[PARAM_N] PROGMEM = {
348  256,10570,1510,7238,1034,7170,6291,7921,11665,3422,4000,2327,
349  2088,5565,795,10647,1521,5484,2539,7385,1055,7173,8047,11683,
350  1669,1994,3796,5809,4341,9398,11876,12230,10525,12037,12253,
351  3506,4012,9351,4847,2448,7372,9831,3160,2207,5582,2553,7387,6322,
352  9681,1383,10731,1533,219,5298,4268,7632,6357,9686,8406,4712,9451,
353  10128,4958,5975,11387,8649,11769,6948,11526,12180,1740,10782,
354  6807,2728,7412,4570,4164,4106,11120,12122,8754,11784,3439,5758,
355  11356,6889,9762,11928,1704,1999,10819,12079,12259,7018,11536,
356  1648,1991,2040,2047,2048,10826,12080,8748,8272,8204,1172,1923,
357  7297,2798,7422,6327,4415,7653,6360,11442,12168,7005,8023,9924,
358  8440,8228,2931,7441,1063,3663,5790,9605,10150,1450,8985,11817,
359  10466,10273,12001,3470,7518,1074,1909,7295,9820,4914,702,5367,
360  7789,8135,9940,1420,3714,11064,12114,12264,1752,5517,9566,11900,
361  1700,3754,5803,829,1874,7290,2797,10933,5073,7747,8129,6428,
362  6185,11417,1631,233,5300,9535,10140,11982,8734,8270,2937,10953,
363  8587,8249,2934,9197,4825,5956,4362,9401,1343,3703,529,10609,
364  12049,6988,6265,895,3639,4031,4087,4095,585,10617,8539,4731,
365  4187,9376,3095,9220,10095,10220,1460,10742,12068,1724,5513,
366  11321,6884,2739,5658,6075,4379,11159,10372,8504,4726,9453,3106,
367  7466,11600,10435,8513,9994,8450,9985,3182,10988,8592,2983,9204,
368  4826,2445,5616,6069,867,3635,5786,11360,5134,2489,10889,12089,
369  1727,7269,2794,9177,1311,5454,9557,6632,2703,9164,10087,1441,
370  3717,531,3587,2268,324,5313,759,1864,5533,2546,7386,9833,8427,
371  4715,11207,1601,7251,4547,11183,12131,1733,10781,10318,1474,
372  10744,5046,4232,11138,10369,6748,964,7160,4534,7670,8118,8182,
373  4680,11202,6867,981,8918,1274,182,26,7026,8026,11680,12202,
374  10521,1503,7237,4545,5916,9623,8397,11733,10454,3249,9242,6587,
375  941,1890,270,10572,6777,9746,6659,6218,6155,6146,878,1881,7291,
376  11575,12187,1741,7271,8061,11685,6936,4502,9421,4857,4205,7623,
377  1089,10689,1527,8996,10063,11971,10488,6765,2722,3900,9335,11867,
378  6962,11528,5158,4248,4118,5855,2592,5637,6072,2623,7397,8079,
379  9932,4930,5971,853,3633,519,8852,11798,3441,11025,1575,225,8810,
380  11792,12218,3501,9278,3081,9218,4828,7712,8124,11694,12204,3499,
381  4011,573,3593,5780,7848,9899,10192,1456,208,7052,2763,7417,11593,
382  10434,12024,8740,11782,10461,3250,5731,7841,9898,1414,202,3540,
383  7528,2831,2160,10842,5060,4234,4116,588,84,12,7024,2759,9172,6577,
384  11473,1639,9012,3043,7457,6332,11438,1634,1989,9062,11828,8712,
385  11778,12216,10523,6770,9745,10170,4964,9487,6622,946,8913,6540,
386  6201,4397,9406,8366,9973,8447,8229,11709,8695,10020,3187,5722,
387  2573,10901,6824,4486,4152,9371,8361,2950,2177,311,1800,9035,
388  8313,11721,3430,490,70,10,1757,251,3547,7529,11609,3414,7510,
389  4584,4166,9373,1339,5458,7802,11648,1664,7260,9815,10180,6721,
390  9738,10169,8475,8233,9954,1422,8981,1283,5450,11312,1616,3742,
391  11068,10359,4991,713,3613,9294,8350,4704,672,96,7036,9783,11931,
392  3460,5761,823,10651,12055,10500,1500,5481,783,3623,11051,8601,
393  8251,8201,11705,10450,5004,4226,7626,2845,2162,3820,7568,9859,
394  3164,452,10598,1514,5483,6050,6131,4387,7649,8115,6426,918,8909,
395  8295,1185,5436,11310,8638,1234,5443,11311,5127,2488,2111,10835,
396  5059,7745,2862,3920,560,80,1767,2008,3798,11076,6849,2734,10924,
397  12094,8750,1250,10712,6797,971,7161,1023,8924,4786,7706,4612,4170,
398  7618,6355,4419,5898,11376,10403,10264,6733,4473,639,5358,2521,
399  9138,3061,5704,4326,618,5355,765,5376,768,7132,4530,9425,3102,
400  9221,6584,11474,10417,10266,12000,6981,6264,4406,2385,7363,4563,
401  4163,7617,9866,3165,9230,11852,10471,5007,5982,11388,5138,734,
402  3616,11050,12112,6997,11533,12181,10518,12036,3475,2252,7344,
403  9827,4915,9480,6621,4457,7659,9872,6677,4465,4149,7615,4599,657,
404  3605,515,10607,6782,4480,640,1847,3775,5806,2585,5636,9583,1369,
405  10729,8555,10000,11962,5220,7768,8132,8184,9947,1421,203,29,8782,
406  11788,1684,10774,10317,4985,9490,8378,4708,11206,5112,5997,7879,
407  11659,12199,8765,10030,4944,5973,6120,6141,6144,7900,11662,1666,
408  238,34,3516,5769,9602,8394,9977,6692,956,10670,6791,9748,11926,
409  8726,11780,5194,742,106,8793,10034,3189,10989,5081,4237,5872,4350,
410  2377,10873,6820,6241,11425,10410,10265,3222,5727,9596,4882,2453,
411  2106,3812,11078,12116,5242,4260,11142,8614,11764,12214,5256,4262,
412  4120,11122,5100,11262,5120,2487,5622,9581,8391,8221,2930,10952,
413  12098,6995,6266,9673,4893,699,3611,4027,5842,11368,1624,232,8811,
414  8281,1183,169,8802,3013,2186,5579,797,3625,4029,11109,1587,7249,
415  11569,8675,6506,2685,10917,12093,12261,12285,1755,7273,1039,1904,
416  272,3550,9285,3082,5707,6082,4380,7648,11626,5172,4250,9385,8363,
417  8217,4685,5936,848,8899,6538,934,1889,3781,9318,10109,10222,6727,
418  961,5404,772,5377,9546,8386,1198,8949,3034,2189,7335,4559,5918,2601,
419  10905,5069,9502,3113,7467,8089,11689,5181,9518,8382,2953,3933,4073,
420  4093,7607,8109,2914,5683,4323,11151,1593,10761,6804,972,3650,2277,
421  5592,4310,7638,9869,4921,703,1856,9043,4803,9464,1352,8971,11815,
422  5199,7765,6376,4422,7654,2849,407,8836,6529,7955,2892,9191,1313,
423  10721,12065,12257,1751,9028,8312,2943,2176,3822,546,78,8789,11789,
424  10462,12028,6985,4509,9422,1346,5459,4291,613,10621,6784,9747,3148,
425  7472,2823,5670,810,7138,8042,4660,7688,6365,6176,6149,2634,5643,
426  9584,10147,11983,5223,9524,11894,10477,8519,1217,3685,2282,326,
427  10580,3267,7489,4581,2410,5611,11335,6886,8006,8166,11700,3427,
428  11023,8597,10006,3185,455,65,5276,7776,4622,5927,7869,9902,11948,
429  5218,2501,5624,2559,10899,1557,1978,10816,10323,8497,4725,675,1852,
430  10798,12076,10503,3256,9243,3076,2195,10847,12083,10504,12034,10497
431 };
432 
433 static uint16_t const bitrev_table[PARAM_N] PROGMEM = {
434  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,
435  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,
436  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,
437  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,
438  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,
439  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,
440  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,
441  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,
442  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,
443  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,
444  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,
445  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,
446  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,
447  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,
448  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,
449  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,
450  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,
451  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,
452  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,
453  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,
454  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,
455  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,
456  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,
457  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,
458  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,
459  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,
460  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,
461  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,
462  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,
463  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,
464  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,
465  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
466 };
467 
468 /* Incomplete-reduction routines; for details on allowed input ranges
469  * and produced output ranges, see the description in the paper:
470  * https://cryptojedi.org/papers/#newhope */
471 
472 #define qinv 12287 // -inverse_mod(p,2^18)
473 #define rlog 18
474 
475 inline uint16_t montgomery_reduce(uint32_t a)
476 {
477  uint32_t u;
478 
479  u = (a * qinv);
480  u &= ((((uint32_t)1)<<rlog)-1);
481  u *= PARAM_Q;
482  a = a + u;
483  return a >> 18;
484 }
485 
486 inline uint16_t barrett_reduce(uint16_t a)
487 {
488  uint32_t u;
489 
490  u = ((uint32_t) a * 5) >> 16;
491  u *= PARAM_Q;
492  a -= u;
493  return a;
494 }
495 
496 static void bitrev_vector(uint16_t* poly)
497 {
498  unsigned int i,r;
499  uint16_t tmp;
500 
501  for(i = 0; i < PARAM_N; i++)
502  {
503  r = table_read(bitrev_table,i);
504  if (i < r)
505  {
506  tmp = poly[i];
507  poly[i] = poly[r];
508  poly[r] = tmp;
509  }
510  }
511 }
512 
513 static void mul_coefficients(uint16_t* poly, const uint16_t* factors)
514 {
515  unsigned int i;
516 
517  for(i = 0; i < PARAM_N; i++)
518  poly[i] = montgomery_reduce((poly[i] * (uint32_t)table_read(factors,i)));
519 }
520 
521 /* GS_bo_to_no; omegas need to be in Montgomery domain */
522 static void ntt(uint16_t * a, const uint16_t* omega)
523 {
524  int i, start, j, jTwiddle, distance;
525  uint16_t temp, W;
526 
527 
528  for(i=0;i<10;i+=2)
529  {
530  // Even level
531  distance = (1<<i);
532  for(start = 0; start < distance;start++)
533  {
534  jTwiddle = 0;
535  for(j=start;j<PARAM_N-1;j+=2*distance)
536  {
537  W = table_read(omega,jTwiddle++);
538  temp = a[j];
539  a[j] = (temp + a[j + distance]); // Omit reduction (be lazy)
540  a[j + distance] = montgomery_reduce((W * ((uint32_t)temp + 3*PARAM_Q - a[j + distance])));
541  }
542  }
543 
544  // Odd level
545  distance <<= 1;
546  for(start = 0; start < distance;start++)
547  {
548  jTwiddle = 0;
549  for(j=start;j<PARAM_N-1;j+=2*distance)
550  {
551  W = table_read(omega,jTwiddle++);
552  temp = a[j];
553  a[j] = barrett_reduce((temp + a[j + distance]));
554  a[j + distance] = montgomery_reduce((W * ((uint32_t)temp + 3*PARAM_Q - a[j + distance])));
555  }
556  }
557  }
558 }
559 
560 static int32_t abs(int32_t v)
561 {
562  int32_t mask = v >> 31;
563  return (v ^ mask) - mask;
564 }
565 
566 static int32_t f(int32_t *v0, int32_t *v1, uint32_t x)
567 {
568  int32_t xit, t, r, b;
569 
570  // Next 6 lines compute t = x/PARAM_Q;
571  b = x*2730;
572  t = b >> 25;
573  b = x - t*12289;
574  b = 12288 - b;
575  b >>= 31;
576  t -= b;
577 
578  r = t & 1;
579  xit = (t>>1);
580  *v0 = xit+r; // v0 = round(x/(2*PARAM_Q))
581 
582  t -= 1;
583  r = t & 1;
584  *v1 = (t>>1)+r;
585 
586  return abs(x-((*v0)*2*PARAM_Q));
587 }
588 
589 static int32_t g(int32_t x)
590 {
591  int32_t t,c,b;
592 
593  // Next 6 lines compute t = x/(4*PARAM_Q);
594  b = x*2730;
595  t = b >> 27;
596  b = x - t*49156;
597  b = 49155 - b;
598  b >>= 31;
599  t -= b;
600 
601  c = t & 1;
602  t = (t >> 1) + c; // t = round(x/(8*PARAM_Q))
603 
604  t *= 8*PARAM_Q;
605 
606  return abs(t - x);
607 }
608 
609 static int16_t LDDecode(int32_t xi0, int32_t xi1, int32_t xi2, int32_t xi3)
610 {
611  int32_t t;
612 
613  t = g(xi0);
614  t += g(xi1);
615  t += g(xi2);
616  t += g(xi3);
617 
618  t -= 8*PARAM_Q;
619  t >>= 31;
620  return t&1;
621 }
622 
623 static void helprec(NewHopeChaChaState *chacha, uint16_t *c, const uint16_t *v, unsigned char nonce)
624 {
625  int32_t v0[4], v1[4], v_tmp[4], k;
626  unsigned char rbit;
627  unsigned char *rand;
628  int i;
629 
630  chacha->input[12] = 0;
631  chacha->input[13] = 0;
632  chacha->input[14] = 0;
633  chacha->input[15] = (((uint32_t)nonce) << 24); // Assumes little-endian.
634  ChaCha::hashCore(chacha->output, chacha->input, 20);
635  rand = (unsigned char *)chacha->output;
636 
637  for(i=0; i<256; i++)
638  {
639  rbit = (rand[i>>3] >> (i&7)) & 1;
640 
641  k = f(v0+0, v1+0, 8*(int32_t)v[ 0+i] + 4*rbit);
642  k += f(v0+1, v1+1, 8*(int32_t)v[256+i] + 4*rbit);
643  k += f(v0+2, v1+2, 8*(int32_t)v[512+i] + 4*rbit);
644  k += f(v0+3, v1+3, 8*(int32_t)v[768+i] + 4*rbit);
645 
646  k = (2*PARAM_Q-1-k) >> 31;
647 
648  v_tmp[0] = ((~k) & v0[0]) ^ (k & v1[0]);
649  v_tmp[1] = ((~k) & v0[1]) ^ (k & v1[1]);
650  v_tmp[2] = ((~k) & v0[2]) ^ (k & v1[2]);
651  v_tmp[3] = ((~k) & v0[3]) ^ (k & v1[3]);
652 
653  c[ 0+i] = (v_tmp[0] - v_tmp[3]) & 3;
654  c[256+i] = (v_tmp[1] - v_tmp[3]) & 3;
655  c[512+i] = (v_tmp[2] - v_tmp[3]) & 3;
656  c[768+i] = ( -k + 2*v_tmp[3]) & 3;
657  }
658 
659  clean(&chacha, sizeof(chacha));
660 }
661 
662 static void rec(unsigned char *key, const uint16_t *v, const uint16_t *c)
663 {
664  int i;
665  int32_t tmp[4];
666 
667  for(i=0;i<32;i++)
668  key[i] = 0;
669 
670  for(i=0; i<256; i++)
671  {
672  tmp[0] = 16*PARAM_Q + 8*(int32_t)v[ 0+i] - PARAM_Q * (2*(int32_t)c[ 0+i]+c[768+i]);
673  tmp[1] = 16*PARAM_Q + 8*(int32_t)v[256+i] - PARAM_Q * (2*(int32_t)c[256+i]+c[768+i]);
674  tmp[2] = 16*PARAM_Q + 8*(int32_t)v[512+i] - PARAM_Q * (2*(int32_t)c[512+i]+c[768+i]);
675  tmp[3] = 16*PARAM_Q + 8*(int32_t)v[768+i] - PARAM_Q * ( c[768+i]);
676 
677  key[i>>3] |= LDDecode(tmp[0], tmp[1], tmp[2], tmp[3]) << (i & 7);
678  }
679 }
680 
681 static void poly_frombytes(uint16_t *r, const unsigned char *a)
682 {
683  int i;
684  for(i=0;i<PARAM_N/4;i++)
685  {
686  r[4*i+0] = a[7*i+0] | (((uint16_t)a[7*i+1] & 0x3f) << 8);
687  r[4*i+1] = (a[7*i+1] >> 6) | (((uint16_t)a[7*i+2]) << 2) | (((uint16_t)a[7*i+3] & 0x0f) << 10);
688  r[4*i+2] = (a[7*i+3] >> 4) | (((uint16_t)a[7*i+4]) << 4) | (((uint16_t)a[7*i+5] & 0x03) << 12);
689  r[4*i+3] = (a[7*i+5] >> 2) | (((uint16_t)a[7*i+6]) << 6);
690  }
691 }
692 
693 static void poly_tobytes(unsigned char *r, const uint16_t *p)
694 {
695  int i;
696  uint16_t t0,t1,t2,t3,m;
697  int16_t c;
698  for(i=0;i<PARAM_N/4;i++)
699  {
700  t0 = barrett_reduce(p[4*i+0]); //Make sure that coefficients have only 14 bits
701  t1 = barrett_reduce(p[4*i+1]);
702  t2 = barrett_reduce(p[4*i+2]);
703  t3 = barrett_reduce(p[4*i+3]);
704 
705  m = t0 - PARAM_Q;
706  c = m;
707  c >>= 15;
708  t0 = m ^ ((t0^m)&c); // <Make sure that coefficients are in [0,q]
709 
710  m = t1 - PARAM_Q;
711  c = m;
712  c >>= 15;
713  t1 = m ^ ((t1^m)&c); // <Make sure that coefficients are in [0,q]
714 
715  m = t2 - PARAM_Q;
716  c = m;
717  c >>= 15;
718  t2 = m ^ ((t2^m)&c); // <Make sure that coefficients are in [0,q]
719 
720  m = t3 - PARAM_Q;
721  c = m;
722  c >>= 15;
723  t3 = m ^ ((t3^m)&c); // <Make sure that coefficients are in [0,q]
724 
725  r[7*i+0] = t0 & 0xff;
726  r[7*i+1] = (t0 >> 8) | (t1 << 6);
727  r[7*i+2] = (t1 >> 2);
728  r[7*i+3] = (t1 >> 10) | (t2 << 4);
729  r[7*i+4] = (t2 >> 4);
730  r[7*i+5] = (t2 >> 12) | (t3 << 2);
731  r[7*i+6] = (t3 >> 6);
732  }
733 }
734 
735 static void poly_pointwise(uint16_t *r, const uint16_t *a, const uint16_t *b)
736 {
737  int i;
738  uint16_t t;
739  for(i=0;i<PARAM_N;i++)
740  {
741  t = montgomery_reduce(3186*(uint32_t)b[i]); /* t is now in Montgomery domain */
742  r[i] = montgomery_reduce(a[i] * (uint32_t)t); /* r->coeffs[i] is back in normal domain */
743  }
744 }
745 
746 static void poly_add(uint16_t *r, const uint16_t *a, const uint16_t *b)
747 {
748  int i;
749  for(i=0;i<PARAM_N;i++)
750  r[i] = barrett_reduce(a[i] + (uint32_t)b[i]);
751 }
752 
753 static void poly_ntt(uint16_t *r)
754 {
755  mul_coefficients(r, psis_bitrev_montgomery);
756  ntt(r, omegas_montgomery);
757 }
758 
759 static void poly_invntt(uint16_t *r)
760 {
761  bitrev_vector(r);
762  ntt(r, omegas_inv_montgomery);
763  mul_coefficients(r, psis_inv_montgomery);
764 }
765 
766 static void encode_b_2nd_half(unsigned char *r, const uint16_t *c)
767 {
768  int i;
769  for(i=0;i<PARAM_N/4;i++)
770  r[POLY_BYTES+i] = c[4*i] | (c[4*i+1] << 2) | (c[4*i+2] << 4) | (c[4*i+3] << 6);
771 }
772 
773 static void decode_b_2nd_half(uint16_t *c, const unsigned char *r)
774 {
775  int i;
776  for(i=0;i<PARAM_N/4;i++)
777  {
778  c[4*i+0] = r[POLY_BYTES+i] & 0x03;
779  c[4*i+1] = (r[POLY_BYTES+i] >> 2) & 0x03;
780  c[4*i+2] = (r[POLY_BYTES+i] >> 4) & 0x03;
781  c[4*i+3] = (r[POLY_BYTES+i] >> 6);
782  }
783 }
784 
785 #define _5q (5*PARAM_Q)
786 
787 #define compare_and_swap(x,i,j) \
788  c = _5q - 1 - x[16*(i)];\
789  c >>= 31;\
790  t = x[16*(i)] ^ x[16*(j)];\
791  t &= c;\
792  x[16*(i)] ^= t;\
793  x[16*(j)] ^= t;
794 
795 static void batcher84(uint16_t *x);
796 
797 static int discardtopoly(uint16_t *x)
798 {
799  int32_t i, r=0;
800 
801  for(i=0;i<16;i++)
802  batcher84(x+i);
803 
804  // Check whether we're safe:
805  for(i=1008;i<1024;i++)
806  r |= 61444 - x[i];
807  if(r >>= 31) return -1;
808 
809  return 0;
810 }
811 
812 // End of public domain code imported from the C reference code.
813 
814 // Code size efficient (but slower) version of the Batcher sort.
815 // https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort
816 static void oddeven_merge(uint16_t *x, unsigned lo, unsigned hi, unsigned r)
817 {
818  unsigned step = r * 2;
819  unsigned i;
820  int32_t c;
821  uint16_t t;
822  if (lo >= 84)
823  return;
824  if (step < (hi - lo)) {
825  if ((step * 2) >= (hi - lo) && hi < 84) {
826  // The next recursion down is a leaf, so unroll a little.
827  compare_and_swap(x, lo, lo + step);
828  compare_and_swap(x, lo + r, lo + r + step);
829  compare_and_swap(x, lo + r, lo + step);
830  return;
831  }
832  oddeven_merge(x, lo, hi, step);
833  oddeven_merge(x, lo + r, hi, step);
834  for (i = lo + r; i < (hi - r) && (i + r) < 84; i += step) {
835  compare_and_swap(x, i, i + r);
836  }
837  } else if ((lo + r) < 84) {
838  compare_and_swap(x, lo, lo + r);
839  }
840 }
841 static void oddeven_merge_sort_range(uint16_t *x, unsigned lo, unsigned hi)
842 {
843  if (lo == hi || lo >= 84)
844  return;
845  unsigned mid = lo + ((hi - lo) / 2);
846  if ((hi - lo) == 3 && hi < 84) {
847  // Optimization for sub lists of size 4. Unroll the comparisons.
848  int32_t c;
849  uint16_t t;
850  compare_and_swap(x, lo , lo + 1);
851  compare_and_swap(x, lo + 2, lo + 3);
852  compare_and_swap(x, lo , lo + 2);
853  compare_and_swap(x, lo + 1, lo + 3);
854  compare_and_swap(x, lo + 1, lo + 2);
855  return;
856  }
857  oddeven_merge_sort_range(x, lo, mid);
858  oddeven_merge_sort_range(x, mid + 1, hi);
859  oddeven_merge(x, lo, hi, 1);
860 }
861 static void batcher84(uint16_t *x)
862 {
863  // Batcher sort is defined over a power of two list size but 84
864  // is not a power of two. Round up to the next power of two and
865  // then ignore any swap with an index that is out of range.
866  oddeven_merge_sort_range(x, 0, 127);
867 }
868 
869 // Formats the ChaCha20 input block using a key.
870 static void crypto_chacha20_set_key(uint32_t *block, const unsigned char *k)
871 {
872  static const char tag256[] PROGMEM = "expand 32-byte k";
873 #if defined(__AVR__)
874  memcpy_P(block, tag256, 16);
875 #else
876  memcpy(block, tag256, 16);
877 #endif
878  memcpy(block + 4, k, 32);
879  memset(block + 12, 0, 8);
880 }
881 
882 static void poly_uniform(SHAKE128 *shake, uint16_t *a, const unsigned char *seed)
883 {
884  int ctr = 0;
885  int posn = PARAM_N;
886  uint16_t val;
887 
888  // Absorb the seed material into the SHAKE128 object.
889  shake->update(seed, NEWHOPE_SEEDBYTES);
890 
891  while (ctr < PARAM_N) {
892  // Extract data from the SHAKE128 object directly into "a".
893  if (posn >= PARAM_N) {
894  shake->extend((uint8_t *)(a + ctr),
895  (PARAM_N - ctr) * sizeof(uint16_t));
896  posn = ctr;
897  }
898 
899  // Process as much of the data as we can, discarding values
900  // that are greater than or equal to 5 * PARAM_Q.
901  while (posn < PARAM_N) {
902  val = a[posn++];
903  if (val < (5 * PARAM_Q))
904  a[ctr++] = val;
905  }
906  }
907 }
908 
909 static void poly_uniform_torref(SHAKE128 *shake, uint16_t *a, const unsigned char *seed)
910 {
911  shake->update(seed, 32);
912  do {
913  shake->extend((uint8_t *)a, 84 * 16 * sizeof(uint16_t));
914  } while (discardtopoly(a));
915 }
916 
917 static void poly_getnoise(uint16_t *r, NewHopeChaChaState *chacha, unsigned char nonce)
918 {
919  int i, j;
920  uint32_t a, b;
921 
922  // Note: The rest of this function assumes that we are running on a
923  // little-endian CPU. Since we're generating random noise from a
924  // random seed, it doesn't actually matter what the endian-ness is
925  // as it will be just as random in both directions. It's only a
926  // problem for verifying fixed test vectors.
927 
928  chacha->input[12] = 0;
929  chacha->input[13] = 0;
930  chacha->input[14] = nonce; // Assumes little-endian.
931  chacha->input[15] = 0;
932 
933  for (i = 0; i < PARAM_N; ++i) {
934  // Generate a new block of random data if necessary.
935  j = i % 16;
936  if (j == 0) {
937  ChaCha::hashCore(chacha->output, chacha->input, 20);
938  ++(chacha->input[12]); // Assumes little-endian.
939  }
940 
941  // This is a slightly more efficient way to count bits than in
942  // the reference C implementation. The technique is from:
943  // https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel
944  a = chacha->output[j] & 0xFFFF; // Assumes little-endian.
945  a = a - ((a >> 1) & 0x5555);
946  a = (a & 0x3333) + ((a >> 2) & 0x3333);
947  a = ((a >> 4) + a) & 0x0F0F;
948  a = ((a >> 8) + a) & 0x00FF;
949 
950  b = (chacha->output[j] >> 16) & 0xFFFF; // Assumes little-endian.
951  b = b - ((b >> 1) & 0x5555);
952  b = (b & 0x3333) + ((b >> 2) & 0x3333);
953  b = ((b >> 4) + b) & 0x0F0F;
954  b = ((b >> 8) + b) & 0x00FF;
955 
956  r[i] = a + PARAM_Q - b;
957  }
958 
959  clean(&chacha, sizeof(chacha));
960 }
961 
984 #define ALLOC_OBJ(type, name) \
985  uint64_t name##_x[(sizeof(type) + sizeof(uint64_t) - 1) / sizeof(uint64_t)]
986 
987 #define INIT_OBJ(type, name) \
988  type *name = new (state.name##_x) type
989 
990 #if defined(__AVR__)
991 #define NEWHOPE_BYTE_ALIGNED 1
992 #else
993 #define NEWHOPE_BYTE_ALIGNED 0
994 #endif
995 
1014 void NewHope::keygen(uint8_t send[NEWHOPE_SENDABYTES], NewHopePrivateKey &sk,
1015  Variant variant, const uint8_t *random_seed)
1016 {
1017  // The order of calls is rearranged compared to the reference C version.
1018  // This allows us to get away with two temporary poly objects (a, pk)
1019  // instead of four (a, e, r, pk). This saves 4k of stack space.
1020  //
1021  // We also combine most of the state into a single union, which allows
1022  // us to overlap some of the larger objects and reuse the stack space
1023  // at different points within this function.
1024  union {
1025  struct {
1026  uint16_t a[PARAM_N]; // Value of "a" as a "poly" object.
1027  uint16_t pk[PARAM_N]; // Value of "pk" as a "poly" object.
1028  };
1029  struct {
1030  uint16_t a_ext[84 * 16]; // Value of "a" for torref uniform.
1031  ALLOC_OBJ(SHAKE128, shake); // SHAKE128 object for poly_uniform().
1032  };
1033  ALLOC_OBJ(SHA3_256, sha3); // SHA3 object for hashing the seed.
1034  } state;
1035 
1036  // Hide the ChaCha state and the noise seed inside "send".
1037 #if NEWHOPE_BYTE_ALIGNED
1038  #define chacha (*((NewHopeChaChaState *)send))
1039 #else
1040  NewHopeChaChaState chacha;
1041 #endif
1042 #if NEWHOPE_SMALL_FOOTPRINT
1043  #define noiseseed (sk.seed)
1044 #else
1045  #define noiseseed (send + sizeof(NewHopeChaChaState))
1046 #endif
1047 
1048  if (!random_seed) {
1049  RNG.rand(send + POLY_BYTES, NEWHOPE_SEEDBYTES);
1050  RNG.rand(noiseseed, 32);
1051  } else {
1052  memcpy(send + POLY_BYTES, random_seed, NEWHOPE_SEEDBYTES);
1053  memcpy(noiseseed, random_seed + NEWHOPE_SEEDBYTES, 32);
1054  }
1055  INIT_OBJ(SHA3_256, sha3);
1056  sha3->update(send + POLY_BYTES, NEWHOPE_SEEDBYTES);
1057  sha3->finalize(send + POLY_BYTES, NEWHOPE_SEEDBYTES);
1058 
1059  INIT_OBJ(SHAKE128, shake);
1060  if (variant == Ref)
1061  poly_uniform(shake, state.a, send + POLY_BYTES);
1062  else
1063  poly_uniform_torref(shake, state.a_ext, send + POLY_BYTES);
1064 
1065  crypto_chacha20_set_key(chacha.input, noiseseed);
1066 
1067 #if NEWHOPE_SMALL_FOOTPRINT
1068  poly_getnoise(state.pk, &chacha, 0);
1069  poly_ntt(state.pk);
1070  poly_pointwise(state.pk, state.pk, state.a);
1071 #else
1072  poly_getnoise(sk.coeffs, &chacha, 0);
1073  poly_ntt(sk.coeffs);
1074  poly_pointwise(state.pk, sk.coeffs, state.a);
1075 #endif
1076 
1077  poly_getnoise(state.a, &chacha, 1);
1078  poly_ntt(state.a);
1079 
1080  poly_add(state.pk, state.a, state.pk);
1081 
1082  poly_tobytes(send, state.pk);
1083 
1084  clean(&state, sizeof(state));
1085 #if !NEWHOPE_BYTE_ALIGNED
1086  clean(&chacha, sizeof(chacha));
1087 #endif
1088  #undef noiseseed
1089  #undef chacha
1090 }
1091 
1116 void NewHope::sharedb(uint8_t shared_key[NEWHOPE_SHAREDBYTES],
1117  uint8_t send[NEWHOPE_SENDBBYTES],
1118  uint8_t received[NEWHOPE_SENDABYTES],
1119  Variant variant, const uint8_t *random_seed)
1120 {
1121 #if NEWHOPE_SMALL_FOOTPRINT && NEWHOPE_BYTE_ALIGNED
1122  // The order of calls is rearranged compared to the reference C version.
1123  // This allows us to get away with 2 temporary poly objects (v, a)
1124  // instead of 8 (sp, ep, v, a, pka, c, epp, bp). Saves 12k of stack space.
1125  // To achieve this, we reuse "send" as the third temporary poly object bp.
1126  //
1127  // We also combine most of the state into a single union, which allows
1128  // us to overlap some of the larger objects and reuse the stack space
1129  // at different points within this function.
1130  union {
1131  struct {
1132  uint16_t a[PARAM_N]; // Value of "a" as a "poly" object.
1133  uint16_t v[PARAM_N]; // Value of "v" as a "poly" object.
1134  };
1135  struct {
1136  uint16_t a_ext[84 * 16]; // Value of "a" for torref uniform.
1137  ALLOC_OBJ(SHAKE128, shake); // SHAKE128 object for poly_uniform().
1138  };
1139  ALLOC_OBJ(SHA3_256, sha3); // SHA3 object for hashing the result.
1140  } state;
1141  uint8_t seed[32];
1142  NewHopeChaChaState chacha;
1143  #define bp ((uint16_t *)send)
1144 
1145  if (!random_seed) {
1146  RNG.rand(seed, 32);
1147  crypto_chacha20_set_key(chacha.input, seed);
1148  } else {
1149  crypto_chacha20_set_key(chacha.input, random_seed);
1150  }
1151 
1152  poly_frombytes(state.a, received);
1153  memcpy(seed, received + POLY_BYTES, 32);
1154 
1155  poly_getnoise(bp, &chacha, 0);
1156  poly_ntt(bp);
1157 
1158  poly_pointwise(state.v, state.a, bp);
1159  poly_invntt(state.v);
1160 
1161  poly_getnoise(bp, &chacha, 2);
1162 
1163  poly_add(state.v, state.v, bp);
1164 
1165  helprec(&chacha, state.a, state.v, 3);
1166 
1167  encode_b_2nd_half(send, state.a);
1168 
1169  rec(shared_key, state.v, state.a);
1170 
1171  INIT_OBJ(SHA3_256, sha3);
1172  sha3->update(shared_key, 32);
1173  sha3->finalize(shared_key, 32);
1174 
1175  INIT_OBJ(SHAKE128, shake);
1176  if (variant == Ref)
1177  poly_uniform(shake, state.a, seed);
1178  else
1179  poly_uniform_torref(shake, state.a_ext, seed);
1180 
1181  poly_getnoise(state.v, &chacha, 0);
1182  poly_ntt(state.v);
1183 
1184  poly_pointwise(state.a, state.a, state.v);
1185 
1186  poly_getnoise(state.v, &chacha, 1);
1187  poly_ntt(state.v);
1188 
1189  poly_add(state.a, state.a, state.v);
1190 
1191  poly_tobytes(send, state.a);
1192 
1193  clean(&state, sizeof(state));
1194  clean(&chacha, sizeof(chacha));
1195  clean(seed, sizeof(seed));
1196  #undef bp
1197 #else
1198  // The order of calls is rearranged compared to the reference C version.
1199  // This allows us to get away with 3 temporary poly objects (v, a, bp)
1200  // instead of 8 (sp, ep, v, a, pka, c, epp, bp). Saves 10k of stack space.
1201  //
1202  // We also combine most of the state into a single union, which allows
1203  // us to overlap some of the larger objects and reuse the stack space
1204  // at different points within this function.
1205  union {
1206  struct {
1207  uint16_t a[PARAM_N]; // Value of "a" as a "poly" object.
1208  uint16_t v[PARAM_N]; // Value of "v" as a "poly" object.
1209  uint16_t bp[PARAM_N]; // Value of "bp" as a "poly" object.
1210  };
1211  struct {
1212  uint16_t a_ext[84 * 16]; // Value of "a" for torref uniform.
1213  ALLOC_OBJ(SHAKE128, shake); // SHAKE128 object for poly_uniform().
1214  };
1215  ALLOC_OBJ(SHA3_256, sha3); // SHA3 object for hashing the result.
1216  } state;
1217 
1218  // Hide the ChaCha state and the noise seed inside "send".
1219  // Put them at the end of the "send" buffer in case "received"
1220  // overlaps with the start of "send".
1221 #if NEWHOPE_BYTE_ALIGNED
1222  #define chacha (*((NewHopeChaChaState *)(send + NEWHOPE_SENDABYTES)))
1223 #else
1224  NewHopeChaChaState chacha;
1225 #endif
1226  #define noiseseed (send + NEWHOPE_SENDABYTES + sizeof(NewHopeChaChaState))
1227 
1228  if (!random_seed)
1229  RNG.rand(noiseseed, 32);
1230  else
1231  memcpy(noiseseed, random_seed, 32);
1232 
1233  INIT_OBJ(SHAKE128, shake);
1234  if (variant == Ref)
1235  poly_uniform(shake, state.a, received + POLY_BYTES);
1236  else
1237  poly_uniform_torref(shake, state.a_ext, received + POLY_BYTES);
1238 
1239  crypto_chacha20_set_key(chacha.input, noiseseed);
1240 
1241  poly_getnoise(state.v, &chacha, 0);
1242  poly_ntt(state.v);
1243 
1244  poly_pointwise(state.bp, state.a, state.v);
1245 
1246  poly_getnoise(state.a, &chacha, 1);
1247  poly_ntt(state.a);
1248 
1249  poly_add(state.bp, state.bp, state.a);
1250 
1251  poly_frombytes(state.a, received);
1252 
1253  poly_pointwise(state.v, state.a, state.v);
1254  poly_invntt(state.v);
1255 
1256  poly_getnoise(state.a, &chacha, 2);
1257  poly_add(state.v, state.v, state.a);
1258 
1259  helprec(&chacha, state.a, state.v, 3);
1260 
1261  poly_tobytes(send, state.bp);
1262  encode_b_2nd_half(send, state.a);
1263 
1264  rec(shared_key, state.v, state.a);
1265 
1266  INIT_OBJ(SHA3_256, sha3);
1267  sha3->update(shared_key, 32);
1268  sha3->finalize(shared_key, 32);
1269 
1270  clean(&state, sizeof(state));
1271 #if !NEWHOPE_BYTE_ALIGNED
1272  clean(&chacha, sizeof(chacha));
1273 #endif
1274 #undef noiseseed
1275 #undef chacha
1276 #endif
1277 }
1278 
1288 void NewHope::shareda(uint8_t shared_key[NEWHOPE_SHAREDBYTES],
1289  const NewHopePrivateKey &sk,
1290  uint8_t received[NEWHOPE_SENDBBYTES])
1291 {
1292  // The order of calls is rearranged compared to the reference C version.
1293  // This allows us to get away with two temporary poly objects (v, bp)
1294  // instead of three (v, bp, c). This saves 2k of stack space.
1295  //
1296  // We also combine most of the state into a single union, which allows
1297  // us to overlap some of the larger objects and reuse the stack space
1298  // at different points within this function.
1299  union {
1300  struct {
1301  uint16_t v[PARAM_N]; // Value of "v" as a "poly" object.
1302  uint16_t bp[PARAM_N]; // Value of "bp" as a "poly" object.
1303  };
1304  struct {
1305  uint16_t v_alt[PARAM_N];
1306  ALLOC_OBJ(NewHopeChaChaState, chacha);
1307  };
1308  ALLOC_OBJ(SHA3_256, sha3); // SHA3 object for hashing the result.
1309  } state;
1310 
1311 #if NEWHOPE_SMALL_FOOTPRINT
1312  // Re-create the full private key for Alice from the seed.
1313  INIT_OBJ(NewHopeChaChaState, chacha);
1314  crypto_chacha20_set_key(chacha->input, sk.seed);
1315  poly_getnoise(state.v, chacha, 0);
1316  poly_ntt(state.v);
1317  poly_frombytes(state.bp, received);
1318  poly_pointwise(state.v, state.v, state.bp);
1319  poly_invntt(state.v);
1320 #else
1321  // Alice's full private key was supplied.
1322  poly_frombytes(state.bp, received);
1323  poly_pointwise(state.v, sk.coeffs, state.bp);
1324  poly_invntt(state.v);
1325 #endif
1326 
1327  decode_b_2nd_half(state.bp, received);
1328 
1329  rec(shared_key, state.v, state.bp);
1330 
1331  INIT_OBJ(SHA3_256, sha3);
1332  sha3->update(shared_key, 32);
1333  sha3->finalize(shared_key, 32);
1334 
1335  clean(&state, sizeof(state));
1336 }
void rand(uint8_t *data, size_t len)
Generates random bytes into a caller-supplied buffer.
Definition: RNG.cpp:508
Variant
Describes the variant of the New Hope algorithm to implement.
Definition: NewHope.h:57
SHAKE Extendable-Output Function (XOF) with 128-bit security.
Definition: SHAKE.h:52
static void keygen(uint8_t send[NEWHOPE_SENDABYTES], NewHopePrivateKey &sk, Variant variant=Ref, const uint8_t *random_seed=0)
Generates the key pair for Alice in a New Hope key exchange.
Definition: NewHope.cpp:1014
static void shareda(uint8_t shared_key[NEWHOPE_SHAREDBYTES], const NewHopePrivateKey &sk, uint8_t received[NEWHOPE_SENDBBYTES])
Generates the shared secret for Alice.
Definition: NewHope.cpp:1288
NewHope private key representation.
Definition: NewHope.h:38
static void sharedb(uint8_t shared_key[NEWHOPE_SHAREDBYTES], uint8_t send[NEWHOPE_SENDBBYTES], uint8_t received[NEWHOPE_SENDABYTES], Variant variant=Ref, const uint8_t *random_seed=0)
Generates the public key and shared secret for Bob.
Definition: NewHope.cpp:1116
void update(const void *data, size_t len)
Updates the XOF with more data.
Definition: SHAKE.cpp:64
static void hashCore(uint32_t *output, const uint32_t *input, uint8_t rounds)
Executes the ChaCha hash core on an input memory block.
Definition: ChaCha.cpp:253
SHA3-256 hash algorithm.
Definition: SHA3.h:29
The standard "reference" version of the New Hope algorithm.
Definition: NewHope.h:59
void extend(uint8_t *data, size_t len)
Generates extendable output from this XOF.
Definition: SHAKE.cpp:71