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192-bit Random ECP Group

192-bit prime field Weierstrass curve.

Defined in IETF in RFC5114


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

Parameters

NameValue
p0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
a0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC
b0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1
G(0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012, 0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811)
n0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831
h0x01


SAGE

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
K = GF(p)
a = K(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC)
b = K(0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1)
E = EllipticCurve(K, (a, b))
G = E(0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012, 0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811)
E.set_order(0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831 * 0x01)

PARI/GP

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF
a = Mod(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC, p)
b = Mod(0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1, p)
E = ellinit([a, b])
E[16][1] = 0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831 * 0x01
G = [Mod(0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012, p), Mod(0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811, p)]

JSON

{
"name": "192-bit Random ECP Group",
"desc": "Defined in IETF in RFC5114",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
"bits": 192
},
"params": {
"a": {
"raw": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC"
},
"b": {
"raw": "0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"
}
},
"generator": {
"x": {
"raw": "0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"
},
"y": {
"raw": "0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"
}
},
"order": "0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
"cofactor": "0x01"
}

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