Poseidon2-BabyBear Constants

This document provides the round constant arrays and Maximum Distance Separable (MDS) matrix used in the Poseidon2-BabyBear algorithm.

MDS Matrix

The Maximum Distance Separable (MDS) matrix used in the algorithm is:

\[\begin{split}\begin{bmatrix} 5 & 7 & 1 & 3 \\ 4 & 6 & 1 & 1 \\ 1 & 3 & 5 & 7 \\ 1 & 1 & 4 & 6 \\ \end{bmatrix}\end{split}\]

Width 16

External Round Constants

// clang-format off
__constant__ uint32_t external_rc_array_16[8][16] = {
    {1774958255, 1185780729, 1621102414, 1796380621, 588815102, 1932426223, 1925334750, 747903232,
     89648862, 360728943, 977184635, 1425273457, 256487465, 1200041953, 572403254, 448208942},
    {1215789478, 944884184, 953948096, 547326025, 646827752, 889997530, 1536873262, 86189867,
     1065944411, 32019634, 333311454, 456061748, 1963448500, 1827584334, 1391160226, 1348741381},
    {88424255, 104111868, 1763866748, 79691676, 1988915530, 1050669594, 359890076, 573163527,
     222820492, 159256268, 669703072, 763177444, 889367200, 256335831, 704371273, 25886717},
    {51754520, 1833211857, 454499742, 1384520381, 777848065, 1053320300, 1851729162, 344647910,
     401996362, 1046925956, 5351995, 1212119315, 754867989, 36972490, 751272725, 506915399},
    {1922082829, 1870549801, 1502529704, 1990744480, 1700391016, 1702593455, 321330495, 528965731,
     183414327, 1886297254, 1178602734, 1923111974, 744004766, 549271463, 1781349648, 542259047},
    {1536158148, 715456982, 503426110, 340311124, 1558555932, 1226350925, 742828095, 1338992758,
     1641600456, 1843351545, 301835475, 43203215, 386838401, 1520185679, 1235297680, 904680097},
    {1491801617, 1581784677, 913384905, 247083962, 532844013, 107190701, 213827818, 1979521776,
     1358282574, 1681743681, 1867507480, 1530706910, 507181886, 695185447, 1172395131, 1250800299},
    {1503161625, 817684387, 498481458, 494676004, 1404253825, 108246855, 59414691, 744214112,
     890862029, 1342765939, 1417398904, 1897591937, 1066647396, 1682806907, 1015795079, 1619482808}
};

Internal Round Constants

__constant__ uint32_t internal_rc_array_16[13] = {
    1518359488, 1765533241, 945325693, 422793067, 311365592,
    1311448267, 1629555936, 1009879353, 190525218, 786108885,
    557776863,  212616710,  605745517
};

Internal Diagonal Constants

__constant__ uint32_t internal_diag_array_16[16] = {
    174271892,  1840666551, 1459346590, 86719882,
    863261185,  1543704716, 199992187,  629943947,
    302161721,  1766394318, 1831016228, 566473250,
    1007223973, 30846170,  661675139,  1378994178
};

Width 24

External Round Constants

__constant__ uint32_t external_rc_array_24[8][24] = {
    {262278199,  127253399,  314968988,  246143118,  157582794,  118043943,  454905424,  815798990,
     1004040026, 1773108264, 1066694495, 1930780904, 1180307149, 1464793095, 1660766320, 1389166148,
     343354132,  1307439985, 638242172,  525458520,  1964135730, 1751797115, 1421525369, 831813382},
    {695835963,  1845603984, 540703332,  1333667262, 1917861751, 1170029417, 1989924532, 1518763784,
     1339793538, 622609176,  686842369,  1737016378, 1282239129, 897025192,  716894289,  1997503974,
     395622276,  1201063290, 1917549072, 1150912935, 1687379185, 1507936940, 241306552,  989176635},
    {1147522062, 27129487,   1257820264, 142102402,  217046702,  1664590951, 855276054, 1215259350,
     946500736,  552696906,  1424297384, 538103555,  1608853840, 162510541,  623051854, 1549062383,
     1908416316, 1622328571, 1079030649, 1584033957, 1099252725, 1910423126, 447555988, 862495875},
    {128479034, 1587822577, 608401422,  1290028279, 342857858,  825405577,  427731030,  1718628547,
     588764636, 204228775,  1454563174, 1740472809, 1338899225, 1269493554, 53007114,   1647670797,
     306391314, 172614232,  51256176,   1221257987, 1239734761, 273790406,  1781980094, 1291790245},
    {53041581,   723038058,  1439947916, 1136469704, 205609311,  1883820770, 14387587,   720724951,
     1854174607, 1629316321, 530151394,  1679178250, 1549779579, 48375137,   976057819,  463976218,
     875839332,  1946596189, 434078361,  1878280202, 1363837384, 1470845646, 1792450386, 1040977421},
    {1209164052, 714957516, 390340387,  1213686459, 790726260,  117294666,  140621810,  993455846,
     1889603648, 78845751,  925018226,  708123747,  1647665372, 1649953458, 942439428,  1006235079,
     238616145,  930036496, 1401020792, 989618631,  1545325389, 1715719711, 755691969,  150307788},
    {1567618575, 1663353317, 1950429111, 1891637550, 192082241,  1080533265, 1463323727, 890243564,
     158646617,  1402624179, 59510015,   1198261138, 1065075039, 1150410028, 1293938517, 76770019,
     1478577620, 1748789933, 457372011,  1841795381, 760115692,  1042892522, 1507649755, 1827572010},
    {1206940496, 1896271507, 1003792297, 738091882, 1124078057, 1889898,     813674331,  228520958,
     1832911930, 781141772,  459826664,  202271745, 1296144415, 1111203133, 1090783436,  641665156,
     1393671120, 1303271640, 809508074,  162506101, 1262312258, 1672219447, 1608891156,  1380248020}
};

Internal Round Constants

__constant__ uint32_t internal_rc_array_24[21] = {
    497520322,  1930103076, 1052077299, 1540960371, 924863639,  1365519753,
    1726563304, 440300254,  1891545577, 822033215,  1111544260, 308575117,
    1708681573, 1240419708, 1199068823, 1186174623, 1551596046, 1886977120,
    1327682690, 1210751726, 1810596765
};

Internal Diagonal Constants

__constant__ uint32_t internal_diag_array_24[24] = {
    1083257840, 375892129,  111593398,  1867716110, 658182609,  51866717,
    1928969209, 1942928017, 1558116381, 20525701,   1188752902, 106789798,
    1389833583, 98371040,   1001081699, 1792686146, 801504236,  1997365680,
    1461037801, 65998480,   1974912880, 606789471,  13683276,   918610824
};