Tw keygen

keygen.c

1 /* 2 * Falcon key pair generation. 3 * 4 * ==========================(LICENSE BEGIN)============================ 5 * 6 * Copyright (c) 2017-2019 Falcon Project 7 * 8 * Permission is hereby granted, free of charge, to any person obtaining 9 * a copy of this software and associated documentation files (the 10 * "Software"), to deal in the Software without restriction, including 11 * without limitation the rights to use, copy, modify, merge, publish, 12 * distribute, sublicense, and/or sell copies of the Software, and to 13 * permit persons to whom the Software is furnished to do so, subject to 14 * the following conditions: 15 * 16 * The above copyright notice and this permission notice shall be 17 * included in all copies or substantial portions of the Software. 18 * 19 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 20 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 21 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 22 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY 23 * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, 24 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 25 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 26 * 27 * ===========================(LICENSE END)============================= 28 * 29 * @author Thomas Pornin <thomas.pornin@nccgroup.com> 30 */ 31 32 #include"inner.h" 33 34 #define MKN(logn) ((size_t)1 << (logn)) 35 36 /* ==================================================================== */ 37 /* 38 * Modular arithmetics. 39 * 40 * We implement a few functions for computing modulo a small integer p. 41 * 42 * All functions require that 2^30 < p < 2^31. Moreover, operands must 43 * be in the 0..p-1 range. 44 * 45 * Modular addition and subtraction work for all such p. 46 * 47 * Montgomery multiplication requires that p is odd, and must be provided 48 * with an additional value p0i = -1/p mod 2^31. See below for some basics 49 * on Montgomery multiplication. 50 * 51 * Division computes an inverse modulo p by an exponentiation (with 52 * exponent p-2): this works only if p is prime. Multiplication 53 * requirements also apply, i.e. p must be odd and p0i must be provided. 54 * 55 * The NTT and inverse NTT need all of the above, and also that 56 * p = 1 mod 2048. 57 * 58 * ----------------------------------------------------------------------- 59 * 60 * We use Montgomery representation with 31-bit values: 61 * 62 * Let R = 2^31 mod p. When 2^30 < p < 2^31, R = 2^31 - p. 63 * Montgomery representation of an integer x modulo p is x*R mod p. 64 * 65 * Montgomery multiplication computes (x*y)/R mod p for 66 * operands x and y. Therefore: 67 * 68 * - if operands are x*R and y*R (Montgomery representations of x and 69 * y), then Montgomery multiplication computes (x*R*y*R)/R = (x*y)*R 70 * mod p, which is the Montgomery representation of the product x*y; 71 * 72 * - if operands are x*R and y (or x and y*R), then Montgomery 73 * multiplication returns x*y mod p: mixed-representation 74 * multiplications yield results in normal representation. 75 * 76 * To convert to Montgomery representation, we multiply by R, which is done 77 * by Montgomery-multiplying by R^2. Stand-alone conversion back from 78 * Montgomery representation is Montgomery-multiplication by 1. 79 */ 80 81 /* 82 * Precomputed small primes. Each element contains the following: 83 * 84 * p The prime itself. 85 * 86 * g A primitive root of phi = X^N+1 (in field Z_p). 87 * 88 * s The inverse of the product of all previous primes in the array, 89 * computed modulo p and in Montgomery representation. 90 * 91 * All primes are such that p = 1 mod 2048, and are lower than 2^31. They 92 * are listed in decreasing order. 93 */ 94 95 typedefstruct{ 96 uint32_t p; 97 uint32_t g; 98 uint32_t s; 99 } small_prime; 100 101 static const small_prime PRIMES[] = { 102 {2147473409,383167813,10239}, 103 {2147389441,211808905,471403745}, 104 {2147387393,37672282,1329335065}, 105 {2147377153,1977035326,968223422}, 106 {2147358721,1067163706,132460015}, 107 {2147352577,1606082042,598693809}, 108 {2147346433,2033915641,1056257184}, 109 {2147338241,1653770625,421286710}, 110 {2147309569,631200819,1111201074}, 111 {2147297281,2038364663,1042003613}, 112 {2147295233,1962540515,19440033}, 113 {2147239937,2100082663,353296760}, 114 {2147235841,1991153006,1703918027}, 115 {2147217409,516405114,1258919613}, 116 {2147205121,409347988,1089726929}, 117 {2147196929,927788991,1946238668}, 118 {2147178497,1136922411,1347028164}, 119 {2147100673,868626236,701164723}, 120 {2147082241,1897279176,617820870}, 121 {2147074049,1888819123,158382189}, 122 {2147051521,25006327,522758543}, 123 {2147043329,327546255,37227845}, 124 {2147039233,766324424,1133356428}, 125 {2146988033,1862817362,73861329}, 126 {2146963457,404622040,653019435}, 127 {2146959361,1936581214,995143093}, 128 {2146938881,1559770096,634921513}, 129 {2146908161,422623708,1985060172}, 130 {2146885633,1751189170,298238186}, 131 {2146871297,578919515,291810829}, 132 {2146846721,1114060353,915902322}, 133 {2146834433,2069565474,47859524}, 134 {2146818049,1552824584,646281055}, 135 {2146775041,1906267847,1597832891}, 136 {2146756609,1847414714,1228090888}, 137 {2146744321,1818792070,1176377637}, 138 {2146738177,1118066398,1054971214}, 139 {2146736129,52057278,933422153}, 140 {2146713601,592259376,1406621510}, 141 {2146695169,263161877,1514178701}, 142 {2146656257,685363115,384505091}, 143 {2146650113,927727032,537575289}, 144 {2146646017,52575506,1799464037}, 145 {2146643969,1276803876,1348954416}, 146 {2146603009,814028633,1521547704}, 147 {2146572289,1846678872,1310832121}, 148 {2146547713,919368090,1019041349}, 149 {2146508801,671847612,38582496}, 150 {2146492417,283911680,532424562}, 151 {2146490369,1780044827,896447978}, 152 {2146459649,327980850,1327906900}, 153 {2146447361,1310561493,958645253}, 154 {2146441217,412148926,287271128}, 155 {2146437121,293186449,2009822534}, 156 {2146430977,179034356,1359155584}, 157 {2146418689,1517345488,1790248672}, 158 {2146406401,1615820390,1584833571}, 159 {2146404353,826651445,607120498}, 160 {2146379777,3816988,1897049071}, 161 {2146363393,1221409784,1986921567}, 162 {2146355201,1388081168,849968120}, 163 {2146336769,1803473237,1655544036}, 164 {2146312193,1023484977,273671831}, 165 {2146293761,1074591448,467406983}, 166 {2146283521,831604668,1523950494}, 167 {2146203649,712865423,1170834574}, 168 {2146154497,1764991362,1064856763}, 169 {2146142209,627386213,1406840151}, 170 {2146127873,1638674429,2088393537}, 171 {2146099201,1516001018,690673370}, 172 {2146093057,1294931393,315136610}, 173 {2146091009,1942399533,973539425}, 174 {2146078721,1843461814,2132275436}, 175 {2146060289,1098740778,360423481}, 176 {2146048001,1617213232,1951981294}, 177 {2146041857,1805783169,2075683489}, 178 {2146019329,272027909,1753219918}, 179 {2145986561,1206530344,2034028118}, 180 {2145976321,1243769360,1173377644}, 181 {2145964033,887200839,1281344586}, 182 {2145906689,1651026455,906178216}, 183 {2145875969,1673238256,1043521212}, 184 {2145871873,1226591210,1399796492}, 185 {2145841153,1465353397,1324527802}, 186 {2145832961,1150638905,554084759}, 187 {2145816577,221601706,427340863}, 188 {2145785857,608896761,316590738}, 189 {2145755137,1712054942,1684294304}, 190 {2145742849,1302302867,724873116}, 191 {2145728513,516717693,431671476}, 192 {2145699841,524575579,1619722537}, 193 {2145691649,1925625239,982974435}, 194 {2145687553,463795662,1293154300}, 195 {2145673217,771716636,881778029}, 196 {2145630209,1509556977,837364988}, 197 {2145595393,229091856,851648427}, 198 {2145587201,1796903241,635342424}, 199 {2145525761,715310882,1677228081}, 200 {2145495041,1040930522,200685896}, 201 {2145466369,949804237,1809146322}, 202 {2145445889,1673903706,95316881}, 203 {2145390593,806941852,1428671135}, 204 {2145372161,1402525292,159350694}, 205 {2145361921,2124760298,1589134749}, 206 {2145359873,1217503067,1561543010}, 207 {2145355777,338341402,83865711}, 208 {2145343489,1381532164,641430002}, 209 {2145325057,1883895478,1528469895}, 210 {2145318913,1335370424,65809740}, 211 {2145312769,2000008042,1919775760}, 212 {2145300481,961450962,1229540578}, 213 {2145282049,910466767,1964062701}, 214 {2145232897,816527501,450152063}, 215 {2145218561,1435128058,1794509700}, 216 {2145187841,33505311,1272467582}, 217 {2145181697,269767433,1380363849}, 218 {2145175553,56386299,1316870546}, 219 {2145079297,2106880293,1391797340}, 220 {2145021953,1347906152,720510798}, 221 {2145015809,206769262,1651459955}, 222 {2145003521,1885513236,1393381284}, 223 {2144960513,1810381315,31937275}, 224 {2144944129,1306487838,2019419520}, 225 {2144935937,37304730,1841489054}, 226 {2144894977,1601434616,157985831}, 227 {2144888833,98749330,2128592228}, 228 {2144880641,1772327002,2076128344}, 229 {2144864257,1404514762,2029969964}, 230 {2144827393,801236594,406627220}, 231 {2144806913,349217443,1501080290}, 232 {2144796673,1542656776,2084736519}, 233 {2144778241,1210734884,1746416203}, 234 {2144759809,1146598851,716464489}, 235 {2144757761,286328400,1823728177}, 236 {2144729089,1347555695,1836644881}, 237 {2144727041,1795703790,520296412}, 238 {2144696321,1302475157,852964281}, 239 {2144667649,1075877614,504992927}, 240 {2144573441,198765808,1617144982}, 241 {2144555009,321528767,155821259}, 242 {2144550913,814139516,1819937644}, 243 {2144536577,571143206,962942255}, 244 {2144524289,1746733766,2471321}, 245 {2144512001,1821415077,124190939}, 246 {2144468993,917871546,1260072806}, 247 {2144458753,378417981,1569240563}, 248 {2144421889,175229668,1825620763}, 249 {2144409601,1699216963,351648117}, 250 {2144370689,1071885991,958186029}, 251 {2144348161,1763151227,540353574}, 252 {2144335873,1060214804,919598847}, 253 {2144329729,663515846,1448552668}, 254 {2144327681,1057776305,590222840}, 255 {2144309249,1705149168,1459294624}, 256 {2144296961,325823721,1649016934}, 257 {2144290817,738775789,447427206}, 258 {2144243713,962347618,893050215}, 259 {2144237569,1655257077,900860862}, 260 {2144161793,242206694,1567868672}, 261 {2144155649,769415308,1247993134}, 262 {2144137217,320492023,515841070}, 263 {2144120833,1639388522,770877302}, 264 {2144071681,1761785233,964296120}, 265 {2144065537,419817825,204564472}, 266 {2144028673,666050597,2091019760}, 267 {2144010241,1413657615,1518702610}, 268 {2143952897,1238327946,475672271}, 269 {2143940609,307063413,1176750846}, 270 {2143918081,2062905559,786785803}, 271 {2143899649,1338112849,1562292083}, 272 {2143891457,68149545,87166451}, 273 {2143885313,921750778,394460854}, 274 {2143854593,719766593,133877196}, 275 {2143836161,1149399850,1861591875}, 276 {2143762433,1848739366,1335934145}, 277 {2143756289,1326674710,102999236}, 278 {2143713281,808061791,1156900308}, 279 {2143690753,388399459,1926468019}, 280 {2143670273,1427891374,1756689401}, 281 {2143666177,1912173949,986629565}, 282 {2143645697,2041160111,371842865}, 283 {2143641601,1279906897,2023974350}, 284 {2143635457,720473174,1389027526}, 285 {2143621121,1298309455,1732632006}, 286 {2143598593,1548762216,1825417506}, 287 {2143567873,620475784,1073787233}, 288 {2143561729,1932954575,949167309}, 289 {2143553537,354315656,1652037534}, 290 {2143541249,577424288,1097027618}, 291 {2143531009,357862822,478640055}, 292 {2143522817,2017706025,1550531668}, 293 {2143506433,2078127419,1824320165}, 294 {2143488001,613475285,1604011510}, 295 {2143469569,1466594987,502095196}, 296 {2143426561,1115430331,1044637111}, 297 {2143383553,9778045,1902463734}, 298 {2143377409,1557401276,2056861771}, 299 {2143363073,652036455,1965915971}, 300 {2143260673,1464581171,1523257541}, 301 {2143246337,1876119649,764541916}, 302 {2143209473,1614992673,1920672844}, 303 {2143203329,981052047,2049774209}, 304 {2143160321,1847355533,728535665}, 305 {2143129601,965558457,603052992}, 306 {2143123457,2140817191,8348679}, 307 {2143100929,1547263683,694209023}, 308 {2143092737,643459066,1979934533}, 309 {2143082497,188603778,2026175670}, 310 {2143062017,1657329695,377451099}, 311 {2143051777,114967950,979255473}, 312 {2143025153,1698431342,1449196896}, 313 {2143006721,1862741675,1739650365}, 314 {2142996481,756660457,996160050}, 315 {2142976001,927864010,1166847574}, 316 {2142965761,905070557,661974566}, 317 {2142916609,40932754,1787161127}, 318 {2142892033,1987985648,675335382}, 319 {2142885889,797497211,1323096997}, 320 {2142871553,2068025830,1411877159}, 321 {2142861313,1217177090,1438410687}, 322 {2142830593,409906375,1767860634}, 323 {2142803969,1197788993,359782919}, 324 {2142785537,643817365,513932862}, 325 {2142779393,1717046338,218943121}, 326 {2142724097,89336830,416687049}, 327 {2142707713,5944581,1356813523}, 328 {2142658561,887942135,2074011722}, 329 {2142638081,151851972,1647339939}, 330 {2142564353,1691505537,1483107336}, 331 {2142533633,1989920200,1135938817}, 332 {2142529537,959263126,1531961857}, 333 {2142527489,453251129,1725566162}, 334 {2142502913,1536028102,182053257}, 335 {2142498817,570138730,701443447}, 336 {2142416897,326965800,411931819}, 337 {2142363649,1675665410,1517191733}, 338 {2142351361,968529566,1575712703}, 339 {2142330881,1384953238,1769087884}, 340 {2142314497,1977173242,1833745524}, 341 {2142289921,95082313,1714775493}, 342 {2142283777,109377615,1070584533}, 343 {2142277633,16960510,702157145}, 344 {2142263297,553850819,431364395}, 345 {2142208001,241466367,2053967982}, 346 {2142164993,1795661326,1031836848}, 347 {2142097409,1212530046,712772031}, 348 {2142087169,1763869720,822276067}, 349 {2142078977,644065713,1765268066}, 350 {2142074881,112671944,643204925}, 351 {2142044161,1387785471,1297890174}, 352 {2142025729,783885537,1000425730}, 353 {2142011393,905662232,1679401033}, 354 {2141974529,799788433,468119557}, 355 {2141943809,1932544124,449305555}, 356 {2141933569,1527403256,841867925}, 357 {2141931521,1247076451,743823916}, 358 {2141902849,1199660531,401687910}, 359 {2141890561,150132350,1720336972}, 360 {2141857793,1287438162,663880489}, 361 {2141833217,618017731,1819208266}, 362 {2141820929,999578638,1403090096}, 363 {2141786113,81834325,1523542501}, 364 {2141771777,120001928,463556492}, 365 {2141759489,122455485,2124928282}, 366 {2141749249,141986041,940339153}, 367 {2141685761,889088734,477141499}, 368 {2141673473,324212681,1122558298}, 369 {2141669377,1175806187,1373818177}, 370 {2141655041,1113654822,296887082}, 371 {2141587457,991103258,1585913875}, 372 {2141583361,1401451409,1802457360}, 373 {2141575169,1571977166,712760980}, 374 {2141546497,1107849376,1250270109}, 375 {2141515777,196544219,356001130}, 376 {2141495297,1733571506,1060744866}, 377 {2141483009,321552363,1168297026}, 378 {2141458433,505818251,733225819}, 379 {2141360129,1026840098,948342276}, 380 {2141325313,945133744,2129965998}, 381 {2141317121,1871100260,1843844634}, 382 {2141286401,1790639498,1750465696}, 383 {2141267969,1376858592,186160720}, 384 {2141255681,2129698296,1876677959}, 385 {2141243393,2138900688,1340009628}, 386 {2141214721,1933049835,1087819477}, 387 {2141212673,1898664939,1786328049}, 388 {2141202433,990234828,940682169}, 389 {2141175809,1406392421,993089586}, 390 {2141165569,1263518371,289019479}, 391 {2141073409,1485624211,507864514}, 392 {2141052929,1885134788,311252465}, 393 {2141040641,1285021247,280941862}, 394 {2141028353,1527610374,375035110}, 395 {2141011969,1400626168,164696620}, 396 {2140999681,632959608,966175067}, 397 {2140997633,2045628978,1290889438}, 398 {2140993537,1412755491,375366253}, 399 {2140942337,719477232,785367828}, 400 {2140925953,45224252,836552317}, 401 {2140917761,1157376588,1001839569}, 402 {2140887041,278480752,2098732796}, 403 {2140837889,1663139953,924094810}, 404 {2140788737,802501511,2045368990}, 405 {2140766209,1820083885,1800295504}, 406 {2140764161,1169561905,2106792035}, 407 {2140696577,127781498,1885987531}, 408 {2140684289,16014477,1098116827}, 409 {2140653569,665960598,1796728247}, 410 {2140594177,1043085491,377310938}, 411 {2140579841,1732838211,1504505945}, 412 {2140569601,302071939,358291016}, 413 {2140567553,192393733,1909137143},

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