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BLS12-455

455-bit prime field Weierstrass curve.

Curve from https://github.com/relic-toolkit/relic.


y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0x55555955557955572aa00e0f95b49203003f665e3a5b1d56234bd93954fcb314b8b3db9994ace86d1ba6c589556b2aa956aaa00001800002ab
a0x00
b0x0a
G(0x03018DF4C2336D178E6EA61540353ABA01923E3890B3295848906DFC90E0C43008E4751FFC913DC1FF3DF33D11DB57BADA7A9297195ACFB2FA, 0x19A8A9C4C3AC2FFB4C6B380D17B8282E029615052EAA6416C16C8F36F251D87C272657F0702CC58C4E072628D7BAD3C0E9B3A8AEBFC6B2357C)
n0x10000080000380002E0000F10004F00025E000750001D1000A00000400001C00007FFFFC00001
h0x555556AAAAB15555B54AAB6A9557FFAABFFAAB


SAGE

p = 0x55555955557955572aa00e0f95b49203003f665e3a5b1d56234bd93954fcb314b8b3db9994ace86d1ba6c589556b2aa956aaa00001800002ab
K = GF(p)
a = K(0x00)
b = K(0x0a)
E = EllipticCurve(K, (a, b))
G = E(0x03018DF4C2336D178E6EA61540353ABA01923E3890B3295848906DFC90E0C43008E4751FFC913DC1FF3DF33D11DB57BADA7A9297195ACFB2FA, 0x19A8A9C4C3AC2FFB4C6B380D17B8282E029615052EAA6416C16C8F36F251D87C272657F0702CC58C4E072628D7BAD3C0E9B3A8AEBFC6B2357C)
E.set_order(0x10000080000380002E0000F10004F00025E000750001D1000A00000400001C00007FFFFC00001 * 0x555556AAAAB15555B54AAB6A9557FFAABFFAAB)

PARI/GP

p = 0x55555955557955572aa00e0f95b49203003f665e3a5b1d56234bd93954fcb314b8b3db9994ace86d1ba6c589556b2aa956aaa00001800002ab
a = Mod(0x00, p)
b = Mod(0x0a, p)
E = ellinit([a, b])
E[16][1] = 0x10000080000380002E0000F10004F00025E000750001D1000A00000400001C00007FFFFC00001 * 0x555556AAAAB15555B54AAB6A9557FFAABFFAAB
G = [Mod(0x03018DF4C2336D178E6EA61540353ABA01923E3890B3295848906DFC90E0C43008E4751FFC913DC1FF3DF33D11DB57BADA7A9297195ACFB2FA, p), Mod(0x19A8A9C4C3AC2FFB4C6B380D17B8282E029615052EAA6416C16C8F36F251D87C272657F0702CC58C4E072628D7BAD3C0E9B3A8AEBFC6B2357C, p)]

JSON

{
"name": "BLS12-455",
"desc": "Curve from https://github.com/relic-toolkit/relic.",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x55555955557955572aa00e0f95b49203003f665e3a5b1d56234bd93954fcb314b8b3db9994ace86d1ba6c589556b2aa956aaa00001800002ab",
"bits": 455
},
"params": {
"a": {
"raw": "0x00"
},
"b": {
"raw": "0x0a"
}
},
"generator": {
"x": {
"raw": "0x03018DF4C2336D178E6EA61540353ABA01923E3890B3295848906DFC90E0C43008E4751FFC913DC1FF3DF33D11DB57BADA7A9297195ACFB2FA"
},
"y": {
"raw": "0x19A8A9C4C3AC2FFB4C6B380D17B8282E029615052EAA6416C16C8F36F251D87C272657F0702CC58C4E072628D7BAD3C0E9B3A8AEBFC6B2357C"
}
},
"order": "0x10000080000380002E0000F10004F00025E000750001D1000A00000400001C00007FFFFC00001",
"cofactor": "0x555556AAAAB15555B54AAB6A9557FFAABFFAAB"
}

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