BLS12-638
638-bit prime field Weierstrass curve.Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.
Parameters
SAGE
p = 0x3cb868653d300b3fe80015554dd25db0fc01dcde95d4000000631bbd421715013955555555529c005c75d6c2ab00000000000ac79600d2abaaaaaaaaaaaaaa93eaf3ff000aaaaaaaaaaaaaaabeab000bK = GF(p)a = K(0x00)b = K(0x04)E = EllipticCurve(K, (a, b))G = E(0x160F63A3A3B297F113075ED79466138E85B025F7FE724B78E32D7AFC4D734BDD54F871092B8D1966D491C0F45A48A8BBA5586095DFFCC1410B7E26ED16BAF98C1117959134C24A17A7BE31E1AFBF844F, 0x2D340B33877480A9785E86ED2EDCAFC170B82568CB21B708B79FC6DA3748461FCD80697E486695F3CAE76FCB1781E784F6812F57BE05DFC850426650DED8B40A464B00A35718228EC8E02B52B59D876E)E.set_order(0x50F94035FF4000FFFFFFFFFFF9406BFDC0040000000000000035FB801DFFBFFFFFFFFFFFFFFF401BFF80000000000000000000FFC01 * 0xBFF8001555555555555555554D957EAAAAAAAAAAAAAAAAAAAABEB)
PARI/GP
p = 0x3cb868653d300b3fe80015554dd25db0fc01dcde95d4000000631bbd421715013955555555529c005c75d6c2ab00000000000ac79600d2abaaaaaaaaaaaaaa93eaf3ff000aaaaaaaaaaaaaaabeab000ba = Mod(0x00, p)b = Mod(0x04, p)E = ellinit([a, b])E[16][1] = 0x50F94035FF4000FFFFFFFFFFF9406BFDC0040000000000000035FB801DFFBFFFFFFFFFFFFFFF401BFF80000000000000000000FFC01 * 0xBFF8001555555555555555554D957EAAAAAAAAAAAAAAAAAAAABEBG = [Mod(0x160F63A3A3B297F113075ED79466138E85B025F7FE724B78E32D7AFC4D734BDD54F871092B8D1966D491C0F45A48A8BBA5586095DFFCC1410B7E26ED16BAF98C1117959134C24A17A7BE31E1AFBF844F, p), Mod(0x2D340B33877480A9785E86ED2EDCAFC170B82568CB21B708B79FC6DA3748461FCD80697E486695F3CAE76FCB1781E784F6812F57BE05DFC850426650DED8B40A464B00A35718228EC8E02B52B59D876E, p)]
JSON
{"name": "BLS12-638","desc": "Curve from https://github.com/relic-toolkit/relic. Also in https://eprint.iacr.org/2012/232.pdf.","form": "Weierstrass","field": {"type": "Prime","p": "0x3cb868653d300b3fe80015554dd25db0fc01dcde95d4000000631bbd421715013955555555529c005c75d6c2ab00000000000ac79600d2abaaaaaaaaaaaaaa93eaf3ff000aaaaaaaaaaaaaaabeab000b","bits": 638},"params": {"a": {"raw": "0x00"},"b": {"raw": "0x04"}},"generator": {"x": {"raw": "0x160F63A3A3B297F113075ED79466138E85B025F7FE724B78E32D7AFC4D734BDD54F871092B8D1966D491C0F45A48A8BBA5586095DFFCC1410B7E26ED16BAF98C1117959134C24A17A7BE31E1AFBF844F"},"y": {"raw": "0x2D340B33877480A9785E86ED2EDCAFC170B82568CB21B708B79FC6DA3748461FCD80697E486695F3CAE76FCB1781E784F6812F57BE05DFC850426650DED8B40A464B00A35718228EC8E02B52B59D876E"}},"order": "0x50F94035FF4000FFFFFFFFFFF9406BFDC0040000000000000035FB801DFFBFFFFFFFFFFFFFFF401BFF80000000000000000000FFC01","cofactor": "0xBFF8001555555555555555554D957EAAAAAAAAAAAAAAAAAAAABEB"}