Poseidon2-KoalaBear Constants

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

MDS Matrix

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

\[\begin{split}\begin{bmatrix} 2 & 3 & 1 & 1 \\ 1 & 2 & 3 & 1 \\ 1 & 1 & 2 & 3 \\ 3 & 1 & 1 & 2 \\ \end{bmatrix}\end{split}\]

Width 16

External Round Constants

// clang-format off
__constant__ uint32_t kbp_external_rc_array_16[8][16] = {
    {2128964168, 288780357, 316938561, 2126233899, 426817493,
     1714118888, 1045008582, 1738510837, 889721787, 8866516, 681576474,
     419059826, 1596305521, 1583176088, 1584387047, 1529751136},
    {1863858111, 1072044075, 517831365, 1464274176, 1138001621,
     428001039, 245709561, 1641420379, 1365482496, 770454828, 693167409,
     757905735, 136670447, 436275702, 525466355, 1559174242},
    {1030087950, 869864998, 322787870, 267688717, 948964561,
     740478015, 679816114, 113662466, 2066544572, 1744924186, 367094720,
     1380455578, 1842483872, 416711434, 1342291586, 1692058446},
    {1493348999, 1113949088, 210900530, 1071655077, 610242121,
     1136339326, 2020858841, 1019840479, 678147278, 1678413261, 1361743414,
     61132629, 1209546658, 64412292, 1936878279, 1980661727},
    {1423960925, 2101391318, 1915532054, 275400051, 1168624859,
     1141248885, 356546469, 1165250474, 1320543726, 932505663, 1204226364,
     1452576828, 1774936729, 926808140, 1184948056, 1186493834},
    {843181003, 185193011, 452207447, 510054082, 1139268644,
     630873441, 669538875, 462500858, 876500520, 1214043330, 383937013,
     375087302, 636912601, 307200505, 390279673, 1999916485},
    {1518476730, 1606686591, 1410677749, 1581191572, 1004269969,
     143426723, 1747283099, 1016118214, 1749423722, 66331533, 1177761275,
     1581069649, 1851371119, 852520128, 1499632627, 1820847538},
    {150757557, 884787840, 619710451, 1651711087, 505263814,
     212076987, 1482432120, 1458130652, 382871348, 417404007, 2066495280,
     1996518884, 902934924, 582892981, 1337064375, 1199354861}
};

Internal Round Constants

__constant__ uint32_t kbp_internal_rc_array_16[20] = {
    2102596038, 1533193853, 1436311464, 2012303432, 839997195,
    1225781098, 2011967775, 575084315, 1309329169, 786393545,
    995788880, 1702925345, 1444525226, 908073383, 1811535085,
    1531002367, 1635653662, 1585100155, 867006515, 879151050
};

Internal Diagonal Constants

__constant__ uint32_t kbp_internal_diag_array_16[16] = {
    2130706431, 1, 2, 1065353217, 3, 4, 1065353216, 2130706430, 2130706429,
    2122383361, 1864368129, 2130706306, 8323072, 266338304, 133169152, 127
};

Width 24

External Round Constants

__constant__ uint32_t kbp_external_rc_array_24[8][24] = {
    {487143900, 1829048205, 1652578477, 646002781, 1044144830, 53279448,
     1519499836, 22697702, 1768655004, 230479744, 1484895689, 705130286,
     1429811285, 1695785093, 1417332623, 1115801016, 1048199020, 878062617,
     738518649, 249004596, 1601837737, 24601614, 245692625, 364803730},
    {1857019234, 1906668230, 1916890890, 835590867, 557228239, 352829675,
     515301498, 973918075, 954515249, 1142063750, 1795549558, 608869266,
     1850421928, 2028872854, 1197543771, 1027240055, 1976813168, 963257461,
     652017844, 2113212249, 213459679, 90747280, 1540619478, 324138382},
    {1377377119, 294744504, 512472871, 668081958, 907306515, 518526882,
     1907091534, 1152942192, 1572881424, 720020214, 729527057, 1762035789,
     86171731, 205890068, 453077400, 1201344594, 986483134, 125174298,
     2050269685, 1895332113, 749706654, 40566555, 742540942, 1735551813},
    {162985276, 1943496073, 1469312688, 703013107, 1979485151, 1278193166,
     548674995, 2118718736, 749596440, 1476142294, 1293606474, 918523452,
     890353212, 1691895663, 1932240646, 1180911992, 86098300, 1592168978,
     895077289, 724819849, 1697986774, 1608418116, 1083269213, 691256798},
    {328586442, 1572520009, 1375479591, 322991001, 967600467, 1172861548,
     1973891356, 1503625929, 1881993531, 40601941, 1155570620, 571547775,
     1361622243, 1495024047, 1733254248, 964808915, 763558040, 1887228519,
     994888261, 718330940, 213359415, 603124968, 1038411577, 2099454809},
    {949846777, 630926956, 1168723439, 222917504, 1527025973, 1009157017,
     2029957881, 805977836, 1347511739, 540019059, 589807745, 440771316,
     1530063406, 761076336, 87974206, 1412686751, 1230318064, 514464425,
     1469011754, 1770970737, 1510972858, 965357206, 209398053, 778802532},
    {40567006, 1984217577, 1545851069, 879801839, 1611910970, 1215591048,
     330802499, 1051639108, 321036, 511927202, 591603098, 1775897642,
     115598532, 278200718, 233743176, 525096211, 1335507608, 830017835,
     1380629279, 560028578, 598425701, 302162385, 567434115, 1859222575},
    {958294793, 1582225556, 1781487858, 1570246000, 1067748446, 526608119,
     1666453343, 1786918381, 348203640, 1860035017, 1489902626, 1904576699,
     860033965, 1954077639, 1685771567, 971513929, 1877873770, 137113380,
     520695829, 806829080, 1408699405, 1613277964, 793223662, 648443918}
};

Internal Round Constants

__constant__ uint32_t kbp_internal_rc_array_24[23] = {
    893435011, 403879071, 1363789863, 1662900517, 2043370, 2109755796,
    931751726, 2091644718, 606977583, 185050397, 946157136, 1350065230,
    1625860064, 122045240, 880989921, 145137438, 1059782436, 1477755661,
    335465138, 1640704282, 1757946479, 1551204074, 681266718
};

Internal Diagonal Constants

__constant__ uint32_t kbp_internal_diag_array_24[24] = {
    2130706431, 1, 2, 1065353217, 3, 4, 1065353216, 2130706430, 2130706429, 2122383361,
    1598029825, 1864368129, 1997537281, 2064121857, 2097414145, 2130706306, 8323072,
    266338304, 133169152, 66584576, 33292288, 16646144, 4161536, 127
};