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Curve1174

251-bit prime field Weierstrass curve.

Curve from https://eprint.iacr.org/2013/325.pdf


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

Parameters

NameValue
p0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7
a0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D
b0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6
G(0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051, 0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0)
n0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971
h0x04


SAGE

p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7
K = GF(p)
a = K(0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D)
b = K(0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6)
E = EllipticCurve(K, (a, b))
G = E(0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051, 0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0)
E.set_order(0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971 * 0x04)

PARI/GP

p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7
a = Mod(0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D, p)
b = Mod(0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6, p)
E = ellinit([a, b])
E[16][1] = 0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971 * 0x04
G = [Mod(0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051, p), Mod(0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0, p)]

JSON

{
"name": "Curve1174",
"desc": "Curve from https://eprint.iacr.org/2013/325.pdf",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7",
"bits": 251
},
"params": {
"a": {
"raw": "0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D"
},
"b": {
"raw": "0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6"
}
},
"generator": {
"x": {
"raw": "0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051"
},
"y": {
"raw": "0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0"
}
},
"order": "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971",
"cofactor": "0x04"
}

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