taigrr/arduinolibs
1
0
Fork 0
mirror of https://github.com/taigrr/arduinolibs synced 2025-01-18 04:33:12 -08:00
Code Issues Projects Releases Wiki Activity
arduinolibs/libraries/NewHope/NewHope.cpp
Rhys Weatherley 824e1c2eb2 Change the private key format in the NewHope API
2016-08-24 05:24:51 +10:00

1198 lines
46 KiB
C++
Raw Blame History

/*
* Copyright (C) 2016 Southern Storm Software, Pty Ltd.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
* DEALINGS IN THE SOFTWARE.
*/
#include "NewHope.h"
#include <Crypto.h>
#include <ChaCha.h>
#include <SHA3.h>
#include <SHAKE.h>
#include <RNG.h>
#include <string.h>
// Define this to 0 to disable the "torref" version, which will save
// some code and data memory if you don't need that variant.
#define NEWHOPE_TORREF 1
/**
* \class NewHope NewHope.h <NewHope.h>
* \brief NewHope post-quantum key exchange algorithm
*
* New Hope is an ephemeral key exchange algorithm, similar to Diffie-Hellman,
* which is believed to be resistant to quantum computers.
*
* \note The functions in this class need up to 7k of stack space to
* store temporary intermediate values in addition to up to 4k of
* memory in the application to store public and private key parameters.
* Due to these memory requirements, this class is only suitable for
* use on high-end ARM-based Arduino variants like the Arduino Due.
* It won't fit in the available memory on AVR-based Arduino variants.
*
* Key exchange occurs between two parties, Alice and Bob, and results
* in a 32-byte (256-bit) shared secret. Alice's public key is 1824
* bytes in size and Bob's public key is 2048 bytes in size.
*
* Alice, either the client or the server depending upon the application,
* generates a key pair as follows:
*
* \code
* uint8_t alice_public[NEWHOPE_SENDABYTES];
* NewHopePrivateKey alice_private;
* NewHope::keygen(alice_public, alice_private);
* \endcode
*
* Alice's application sends the contents of <tt>alice_public</tt> to Bob,
* who then performs the following operations:
*
* \code
* uint8_t bob_public[NEWHOPE_SENDABYTES];
* uint8_t shared_secret[NEWHOPE_SHAREDBYTES];
* NewHope::sharedb(shared_secret, bob_public, alice_public);
* \endcode
*
* Bob's application sends the contents of <tt>bob_public</tt> to Alice,
* and can then begin encrypting session traffic with <tt>shared_secret</tt>
* or some transformed version of it.
*
* When Alice's application receives <tt>bob_public</tt>, the application
* performs the folllowing final steps to generate her version of the
* shared secret:
*
* \code
* uint8_t shared_secret[NEWHOPE_SHAREDBYTES];
* NewHope::shareda(shared_secret, alice_private, bob_public);
* \endcode
*
* In the New Hope paper there are two versions of the algorithm described,
* referred to as "ref" and "torref" in author's reference C code. This
* class implements "ref" by default, but it is possible to enable the
* "torref" variant with an extra parameter on the keygen() and sharedb()
* function calls:
*
* \code
* NewHope::keygen(alice_public, alice_private, NewHope::Torref);
* NewHope::sharedb(shared_secret, bob_public, alice_public, NewHope::Torref);
* \endcode
*
* The shareda() function is the same for both "ref" and "torref".
*
* The "ref" and "torref" variants are not binary-compatible. Public keys
* generated with one variant will not work with the other variant. The
* application author must make a decision as to which variant they need
* and then use it universally. The paper contains more information on
* why an application may want to use "torref" instead of "ref".
*
* Reference: https://cryptojedi.org/crypto/#newhope
*/
/**
* \class NewHopePrivateKey NewHope.h <NewHope.h>
* \brief NewHope private key representation
*
* Instances of NewHopePrivateKey are used to hold the private key value
* for alice between the calls to keygen() and shareda(). It should be
* treated as opaque.
*
* Reference: https://cryptojedi.org/crypto/#newhope
*/
/**
* \def NEWHOPE_SENDABYTES
* \brief The number of bytes in the public key value sent by Alice.
*/
/**
* \def NEWHOPE_SENDBBYTES
* \brief The number of bytes in the public key value sent by Bob.
*/
/**
* \def NEWHOPE_SHAREDBYTES
* \brief The number of bytes in the shared secret.
*/
/** @cond */
// The following is public domain code from the reference C version of
// New Hope at https://cryptojedi.org/crypto/#newhope. This part of
// the Arduino port remains public domain. Original authors:
// Erdem Alkim, Léo Ducas, Thomas Pöppelmann, Peter Schwabe
#define PARAM_N 1024
#define PARAM_K 16
#define PARAM_Q 12289
#define POLY_BYTES 1792
#define NEWHOPE_SEEDBYTES 32
#define NEWHOPE_RECBYTES 256
static uint16_t const 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 uint16_t const 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 uint16_t const 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 uint16_t const 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 uint16_t const bitrev_table[PARAM_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
};
/* Incomplete-reduction routines; for details on allowed input ranges
* and produced output ranges, see the description in the paper:
* https://cryptojedi.org/papers/#newhope */
#define qinv 12287 // -inverse_mod(p,2^18)
#define rlog 18
inline uint16_t montgomery_reduce(uint32_t a)
{
uint32_t u;
u = (a * qinv);
u &= ((1<<rlog)-1);
u *= PARAM_Q;
a = a + u;
return a >> 18;
}
inline uint16_t barrett_reduce(uint16_t a)
{
uint32_t u;
u = ((uint32_t) a * 5) >> 16;
u *= PARAM_Q;
a -= u;
return a;
}
static void bitrev_vector(uint16_t* poly)
{
unsigned int i,r;
uint16_t tmp;
for(i = 0; i < PARAM_N; i++)
{
r = bitrev_table[i];
if (i < r)
{
tmp = poly[i];
poly[i] = poly[r];
poly[r] = tmp;
}
}
}
static void mul_coefficients(uint16_t* poly, const uint16_t* factors)
{
unsigned int i;
for(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 */
static 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)
{
// Even level
distance = (1<<i);
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<PARAM_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
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])));
}
}
// Odd level
distance <<= 1;
for(start = 0; start < distance;start++)
{
jTwiddle = 0;
for(j=start;j<PARAM_N-1;j+=2*distance)
{
W = omega[jTwiddle++];
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])));
}
}
}
}
static int32_t abs(int32_t v)
{
int32_t mask = v >> 31;
return (v ^ mask) - mask;
}
static int32_t f(int32_t *v0, int32_t *v1, uint32_t x)
{
int32_t xit, t, r, b;
// Next 6 lines compute t = x/PARAM_Q;
b = x*2730;
t = b >> 25;
b = x - t*12289;
b = 12288 - b;
b >>= 31;
t -= b;
r = t & 1;
xit = (t>>1);
*v0 = xit+r; // v0 = round(x/(2*PARAM_Q))
t -= 1;
r = t & 1;
*v1 = (t>>1)+r;
return abs(x-((*v0)*2*PARAM_Q));
}
static int32_t g(int32_t x)
{
int32_t t,c,b;
// Next 6 lines compute t = x/(4*PARAM_Q);
b = x*2730;
t = b >> 27;
b = x - t*49156;
b = 49155 - b;
b >>= 31;
t -= b;
c = t & 1;
t = (t >> 1) + c; // t = round(x/(8*PARAM_Q))
t *= 8*PARAM_Q;
return abs(t - x);
}
static int16_t LDDecode(int32_t xi0, int32_t xi1, int32_t xi2, int32_t xi3)
{
int32_t t;
t = g(xi0);
t += g(xi1);
t += g(xi2);
t += g(xi3);
t -= 8*PARAM_Q;
t >>= 31;
return t&1;
}
static void crypto_chacha20_set_key(uint32_t *block, const unsigned char *k, const unsigned char *n);
static void helprec(uint16_t *c, const uint16_t *v, const unsigned char *seed, unsigned char nonce)
{
int32_t v0[4], v1[4], v_tmp[4], k;
unsigned char rbit;
unsigned char *rand;
unsigned char n[8];
uint32_t input[16];
uint32_t output[16];
int i;
for(i=0;i<7;i++)
n[i] = 0;
n[7] = nonce;
//crypto_stream_chacha20(rand,32,n,seed);
crypto_chacha20_set_key(input, seed, n);
ChaCha::hashCore(output, input, 20);
rand = (unsigned char *)output;
for(i=0; i<256; i++)
{
rbit = (rand[i>>3] >> (i&7)) & 1;
k = f(v0+0, v1+0, 8*v[ 0+i] + 4*rbit);
k += f(v0+1, v1+1, 8*v[256+i] + 4*rbit);
k += f(v0+2, v1+2, 8*v[512+i] + 4*rbit);
k += f(v0+3, v1+3, 8*v[768+i] + 4*rbit);
k = (2*PARAM_Q-1-k) >> 31;
v_tmp[0] = ((~k) & v0[0]) ^ (k & v1[0]);
v_tmp[1] = ((~k) & v0[1]) ^ (k & v1[1]);
v_tmp[2] = ((~k) & v0[2]) ^ (k & v1[2]);
v_tmp[3] = ((~k) & v0[3]) ^ (k & v1[3]);
c[ 0+i] = (v_tmp[0] - v_tmp[3]) & 3;
c[256+i] = (v_tmp[1] - v_tmp[3]) & 3;
c[512+i] = (v_tmp[2] - v_tmp[3]) & 3;
c[768+i] = ( -k + 2*v_tmp[3]) & 3;
}
clean(input);
clean(output);
}
static void rec(unsigned char *key, const uint16_t *v, const uint16_t *c)
{
int i;
int32_t tmp[4];
for(i=0;i<32;i++)
key[i] = 0;
for(i=0; i<256; i++)
{
tmp[0] = 16*PARAM_Q + 8*(int32_t)v[ 0+i] - PARAM_Q * (2*c[ 0+i]+c[768+i]);
tmp[1] = 16*PARAM_Q + 8*(int32_t)v[256+i] - PARAM_Q * (2*c[256+i]+c[768+i]);
tmp[2] = 16*PARAM_Q + 8*(int32_t)v[512+i] - PARAM_Q * (2*c[512+i]+c[768+i]);
tmp[3] = 16*PARAM_Q + 8*(int32_t)v[768+i] - PARAM_Q * ( c[768+i]);
key[i>>3] |= LDDecode(tmp[0], tmp[1], tmp[2], tmp[3]) << (i & 7);
}
}
static void poly_frombytes(uint16_t *r, const unsigned char *a)
{
int i;
for(i=0;i<PARAM_N/4;i++)
{
r[4*i+0] = a[7*i+0] | (((uint16_t)a[7*i+1] & 0x3f) << 8);
r[4*i+1] = (a[7*i+1] >> 6) | (((uint16_t)a[7*i+2]) << 2) | (((uint16_t)a[7*i+3] & 0x0f) << 10);
r[4*i+2] = (a[7*i+3] >> 4) | (((uint16_t)a[7*i+4]) << 4) | (((uint16_t)a[7*i+5] & 0x03) << 12);
r[4*i+3] = (a[7*i+5] >> 2) | (((uint16_t)a[7*i+6]) << 6);
}
}
static void poly_tobytes(unsigned char *r, const uint16_t *p)
{
int i;
uint16_t t0,t1,t2,t3,m;
int16_t c;
for(i=0;i<PARAM_N/4;i++)
{
t0 = barrett_reduce(p[4*i+0]); //Make sure that coefficients have only 14 bits
t1 = barrett_reduce(p[4*i+1]);
t2 = barrett_reduce(p[4*i+2]);
t3 = barrett_reduce(p[4*i+3]);
m = t0 - PARAM_Q;
c = m;
c >>= 15;
t0 = m ^ ((t0^m)&c); // <Make sure that coefficients are in [0,q]
m = t1 - PARAM_Q;
c = m;
c >>= 15;
t1 = m ^ ((t1^m)&c); // <Make sure that coefficients are in [0,q]
m = t2 - PARAM_Q;
c = m;
c >>= 15;
t2 = m ^ ((t2^m)&c); // <Make sure that coefficients are in [0,q]
m = t3 - PARAM_Q;
c = m;
c >>= 15;
t3 = m ^ ((t3^m)&c); // <Make sure that coefficients are in [0,q]
r[7*i+0] = t0 & 0xff;
r[7*i+1] = (t0 >> 8) | (t1 << 6);
r[7*i+2] = (t1 >> 2);
r[7*i+3] = (t1 >> 10) | (t2 << 4);
r[7*i+4] = (t2 >> 4);
r[7*i+5] = (t2 >> 12) | (t3 << 2);
r[7*i+6] = (t3 >> 6);
}
}
static void poly_pointwise(uint16_t *r, const uint16_t *a, const uint16_t *b)
{
int i;
uint16_t t;
for(i=0;i<PARAM_N;i++)
{
t = montgomery_reduce(3186*b[i]); /* t is now in Montgomery domain */
r[i] = montgomery_reduce(a[i] * t); /* r->coeffs[i] is back in normal domain */
}
}
static void poly_add(uint16_t *r, const uint16_t *a, const uint16_t *b)
{
int i;
for(i=0;i<PARAM_N;i++)
r[i] = barrett_reduce(a[i] + b[i]);
}
static void poly_ntt(uint16_t *r)
{
mul_coefficients(r, psis_bitrev_montgomery);
ntt(r, omegas_montgomery);
}
static void poly_invntt(uint16_t *r)
{
bitrev_vector(r);
ntt(r, omegas_inv_montgomery);
mul_coefficients(r, psis_inv_montgomery);
}
static void encode_a(unsigned char *r, const uint16_t *pk, const unsigned char *seed)
{
int i;
poly_tobytes(r, pk);
for(i=0;i<NEWHOPE_SEEDBYTES;i++)
r[POLY_BYTES+i] = seed[i];
}
static void encode_b(unsigned char *r, const uint16_t *b, const uint16_t *c)
{
int i;
poly_tobytes(r,b);
for(i=0;i<PARAM_N/4;i++)
r[POLY_BYTES+i] = c[4*i] | (c[4*i+1] << 2) | (c[4*i+2] << 4) | (c[4*i+3] << 6);
}
static void decode_b_2nd_half(uint16_t *c, const unsigned char *r)
{
int i;
for(i=0;i<PARAM_N/4;i++)
{
c[4*i+0] = r[POLY_BYTES+i] & 0x03;
c[4*i+1] = (r[POLY_BYTES+i] >> 2) & 0x03;
c[4*i+2] = (r[POLY_BYTES+i] >> 4) & 0x03;
c[4*i+3] = (r[POLY_BYTES+i] >> 6);
}
}
#if NEWHOPE_TORREF
#define _5q (5*PARAM_Q)
#define compare_and_swap(x,i,j) \
c = _5q - 1 - x[16*(i)];\
c >>= 31;\
t = x[16*(i)] ^ x[16*(j)];\
t &= c;\
x[16*(i)] ^= t;\
x[16*(j)] ^= t;
// Code size efficient (but slower) version of the Batcher sort.
// https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort
static void oddeven_merge(uint16_t *x, unsigned lo, unsigned hi, unsigned r)
{
unsigned step = r * 2;
unsigned i;
int32_t c;
uint16_t t;
if (lo >= 84)
return;
if (step < (hi - lo)) {
if ((step * 2) >= (hi - lo) && hi < 84) {
// The next recursion down is a leaf, so unroll a little.
compare_and_swap(x, lo, lo + step);
compare_and_swap(x, lo + r, lo + r + step);
compare_and_swap(x, lo + r, lo + step);
return;
}
oddeven_merge(x, lo, hi, step);
oddeven_merge(x, lo + r, hi, step);
for (i = lo + r; i < (hi - r) && (i + r) < 84; i += step) {
compare_and_swap(x, i, i + r);
}
} else if ((lo + r) < 84) {
compare_and_swap(x, lo, lo + r);
}
}
static void oddeven_merge_sort_range(uint16_t *x, unsigned lo, unsigned hi)
{
if (lo == hi || lo >= 84)
return;
unsigned mid = lo + ((hi - lo) / 2);
if ((hi - lo) == 3 && hi < 84) {
// Optimization for sub lists of size 4. Unroll the comparisons.
int32_t c;
uint16_t t;
compare_and_swap(x, lo , lo + 1);
compare_and_swap(x, lo + 2, lo + 3);
compare_and_swap(x, lo , lo + 2);
compare_and_swap(x, lo + 1, lo + 3);
compare_and_swap(x, lo + 1, lo + 2);
return;
}
oddeven_merge_sort_range(x, lo, mid);
oddeven_merge_sort_range(x, mid + 1, hi);
oddeven_merge(x, lo, hi, 1);
}
static void batcher84(uint16_t *x)
{
// Batcher sort is defined over a power of two list size but 84
// is not a power of two. Round up to the next power of two and
// then ignore any swap with an index that is out of range.
oddeven_merge_sort_range(x, 0, 127);
}
static int discardtopoly(uint16_t *x)
{
int32_t i, r=0;
for(i=0;i<16;i++)
batcher84(x+i);
// Check whether we're safe:
for(i=1008;i<1024;i++)
r |= 61444 - x[i];
if(r >>= 31) return -1;
return 0;
}
#endif // NEWHOPE_TORREF
// End of public domain code imported from the C reference code.
class NewHopePoly
{
public:
NewHopePoly();
~NewHopePoly();
void clear();
private:
uint16_t coeffs[1024];
friend class NewHope;
};
// Formats the ChaCha20 input block using a key and nonce.
static void crypto_chacha20_set_key(uint32_t *block, const unsigned char *k, const unsigned char *n)
{
static const char tag256[] = "expand 32-byte k";
memcpy(block, tag256, 16);
memcpy(block + 4, k, 32);
memset(block + 12, 0, 8);
if (n)
memcpy(block + 14, n, 8);
else
memset(block + 14, 0, 8);
}
static void poly_uniform(uint16_t *a, const unsigned char *seed)
{
SHAKE128 shake;
int ctr = 0;
int posn = PARAM_N;
uint16_t val;
// Absorb the seed material into the SHAKE128 object.
shake.update(seed, NEWHOPE_SEEDBYTES);
while (ctr < PARAM_N) {
// Extract data from the SHAKE128 object directly into "a".
if (posn >= PARAM_N) {
shake.extend((uint8_t *)(a + ctr),
(PARAM_N - ctr) * sizeof(uint16_t));
posn = ctr;
}
// Process as much of the data as we can, discarding values
// that are greater than or equal to 5 * PARAM_Q.
while (posn < PARAM_N) {
val = a[posn++];
if (val < (5 * PARAM_Q))
a[ctr++] = val;
}
}
}
#if NEWHOPE_TORREF
// Extended version of NewHopePoly that can hold the complete
// intermediate state for poly_uniform_torref(). This allows us
// to generate the polynomial in-place and save 2k of stack space.
class NewHopePolyExtended
{
public:
~NewHopePolyExtended() { clean(coeffs); }
uint16_t coeffs[84 * 16];
};
static void poly_uniform_torref(uint16_t *a, const unsigned char *seed)
{
SHAKE128 shake;
shake.update(seed, 32);
do {
shake.extend((uint8_t *)a, 84 * 16 * sizeof(uint16_t));
} while (discardtopoly(a));
}
#else // !NEWHOPE_TORREF
typedef NewHopePoly NewHopePolyExtended;
static void poly_uniform_torref(uint16_t *a, const unsigned char *seed)
{
poly_uniform(a, seed);
}
#endif // NEWHOPE_TORREF
static void poly_getnoise(uint16_t *r, unsigned char *seed, unsigned char nonce)
{
uint32_t input[16];
uint32_t buf[16];
int i, j;
uint32_t a, b;
// Note: The rest of this function assumes that we are running on a
// little-endian CPU. Since we're generating random noise from a
// random seed, it doesn't actually matter what the endian-ness is
// as it will be just as random in both directions. It's only a
// problem for verifying fixed test vectors.
crypto_chacha20_set_key(input, seed, 0);
input[14] = nonce; // Assumes little-endian.
for (i = 0; i < PARAM_N; ++i) {
// Generate a new block of random data if necessary.
j = i % 16;
if (j == 0) {
ChaCha::hashCore(buf, input, 20);
++(input[12]); // Assumes little-endian.
}
// This is a slightly more efficient way to count bits than in
// the reference C implementation. The technique is from:
// https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel
a = buf[j] & 0xFFFF; // Assumes little-endian.
a = a - ((a >> 1) & 0x5555);
a = (a & 0x3333) + ((a >> 2) & 0x3333);
a = ((a >> 4) + a) & 0x0F0F;
a = ((a >> 8) + a) & 0x00FF;
b = (buf[j] >> 16) & 0xFFFF; // Assumes little-endian.
b = b - ((b >> 1) & 0x5555);
b = (b & 0x3333) + ((b >> 2) & 0x3333);
b = ((b >> 4) + b) & 0x0F0F;
b = ((b >> 8) + b) & 0x00FF;
r[i] = a + PARAM_Q - b;
}
clean(input);
clean(buf);
}
static void sha3256(unsigned char *output, const unsigned char *input, unsigned int inputByteLen)
{
SHA3_256 sha3;
sha3.update(input, inputByteLen);
sha3.finalize(output, 32);
}
/**
* \brief Constructs a new "poly" object for the NewHope algorithm.
*/
NewHopePoly::NewHopePoly()
{
}
/**
* \brief Clears sensitive data and destroys this "poly" object.
*/
NewHopePoly::~NewHopePoly()
{
clean(coeffs);
}
/**
* \brief Clears sensitive data in this "poly" object.
*/
void NewHopePoly::clear()
{
clean(coeffs);
}
/** @endcond */
/**
* \enum NewHope::Variant
* \brief Describes the variant of the New Hope algorithm to implement.
*/
/**
* \var NewHope::Ref
* \brief The standard "reference" version of the New Hope algorithm.
*/
/**
* \var NewHope::Torref
* \brief The alternative "torref" version of the New Hope algorithm.
*
* \note The NewHope class can be compiled without support for "torref"
* to save memory. In that case, Torref is identical to Ref.
*/
/**
* \brief Generates the key pair for Alice in a New Hope key exchange.
*
* \param send The public key value for Alice to be sent to Bob.
* \param sk The private key value for Alice to be passed to shareda() later.
* \param variant The variant of the New Hope algorithm to use, usually Ref.
* \param random_seed Points to 64 bytes of random data to use to generate
* the key pair. This is intended for test vectors only and should be set
* to NULL in real applications.
*
* The \a send value should be sent to Bob over the communications link
* and then it can be discarded. The \a sk value must be retained until
* the later call to sharedb().
*
* \sa sharedb(), shareda()
*/
void NewHope::keygen(uint8_t send[NEWHOPE_SENDABYTES], NewHopePrivateKey &sk,
Variant variant, const uint8_t *random_seed)
{
NewHopePolyExtended a;
NewHopePoly pk;
uint8_t seed[NEWHOPE_SEEDBYTES];
uint8_t noiseseed[32];
if (!random_seed) {
RNG.rand(seed, NEWHOPE_SEEDBYTES);
RNG.rand(noiseseed, 32);
} else {
memcpy(seed, random_seed, NEWHOPE_SEEDBYTES);
memcpy(noiseseed, random_seed + NEWHOPE_SEEDBYTES, 32);
}
sha3256(seed, seed, NEWHOPE_SEEDBYTES);
// The order of calls is rearranged compared to the reference C version.
// This allows us to get away with two temporary poly objects (a, pk)
// instead of four (a, e, r, pk). This saves 4k of stack space.
if (variant == Ref)
poly_uniform(a.coeffs, seed);
else
poly_uniform_torref(a.coeffs, seed);
poly_getnoise(sk.coeffs, noiseseed, 0);
poly_ntt(sk.coeffs);
poly_pointwise(pk.coeffs, sk.coeffs, a.coeffs);
poly_getnoise(a.coeffs, noiseseed, 1);
poly_ntt(a.coeffs);
poly_add(pk.coeffs, a.coeffs, pk.coeffs);
encode_a(send, pk.coeffs, seed);
clean(seed);
clean(noiseseed);
}
/**
* \brief Generates the public key and shared secret for Bob.
*
* \param shared_key The shared secret key.
* \param send The public key value for Bob to be sent to Alice.
* \param received The public key value that was received from Alice.
* \param variant The variant of the New Hope algorithm to use, usually Ref.
* \param random_seed Points to 32 bytes of random data to use to generate
* the temporary private key for Bob. This is intended for test vectors
* only and should be set to NULL in real applications.
*
* The \a send value should be sent to Alice over the communications link
* and then it can be discarded. Bob can immediately start encrypting
* session traffic with \a shared_key or some transformed version of it.
*
* \sa shareda(), keygen()
*/
void NewHope::sharedb(uint8_t shared_key[NEWHOPE_SHAREDBYTES],
uint8_t send[NEWHOPE_SENDBBYTES],
uint8_t received[NEWHOPE_SENDABYTES],
Variant variant, const uint8_t *random_seed)
{
NewHopePolyExtended a;
NewHopePoly v, bp;
unsigned char noiseseed[32];
if (!random_seed)
RNG.rand(noiseseed, 32);
else
memcpy(noiseseed, random_seed, 32);
// The order of calls is rearranged compared to the reference C version.
// This allows us to get away with 3 temporary poly objects (v, a, bp)
// instead of 8 (sp, ep, v, a, pka, c, epp, bp). Saves 10k of stack space.
if (variant == Ref)
poly_uniform(a.coeffs, received + POLY_BYTES);
else
poly_uniform_torref(a.coeffs, received + POLY_BYTES);
poly_getnoise(v.coeffs, noiseseed, 0);
poly_ntt(v.coeffs);
poly_pointwise(bp.coeffs, a.coeffs, v.coeffs);
poly_getnoise(a.coeffs, noiseseed, 1);
poly_ntt(a.coeffs);
poly_add(bp.coeffs, bp.coeffs, a.coeffs);
poly_frombytes(a.coeffs, received);
poly_pointwise(v.coeffs, a.coeffs, v.coeffs);
poly_invntt(v.coeffs);
poly_getnoise(a.coeffs, noiseseed, 2);
poly_add(v.coeffs, v.coeffs, a.coeffs);
helprec(a.coeffs, v.coeffs, noiseseed, 3);
encode_b(send, bp.coeffs, a.coeffs);
rec(shared_key, v.coeffs, a.coeffs);
sha3256(shared_key, shared_key, 32);
clean(noiseseed);
}
/**
* \brief Generates the shared secret for Alice.
*
* \param shared_key The shared secret key.
* \param sk Alice's secret private key which was generated by keygen().
* \param received The public key value that was received from Bob.
*
* \sa sharedb(), keygen()
*/
void NewHope::shareda(uint8_t shared_key[NEWHOPE_SHAREDBYTES],
const NewHopePrivateKey &sk,
uint8_t received[NEWHOPE_SENDBBYTES])
{
NewHopePoly v, bp;
// The order of calls is rearranged compared to the reference C version.
// This allows us to get away with two temporary poly objects (v, bp)
// instead of three (v, bp, c). This saves 2k of stack space.
poly_frombytes(bp.coeffs, received);
poly_pointwise(v.coeffs, sk.coeffs, bp.coeffs);
poly_invntt(v.coeffs);
decode_b_2nd_half(bp.coeffs, received);
rec(shared_key, v.coeffs, bp.coeffs);
sha3256(shared_key, shared_key, 32);
}
Reference in New Issue View Git Blame Copy Permalink