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224-bit Random ECP Group

224-bit prime field Weierstrass curve.

Defined in IETF in RFC5114


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

Parameters

NameValue
p0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001
a0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE
b0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4
G(0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21, 0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34)
n0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D
h0x01


SAGE

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001
K = GF(p)
a = K(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE)
b = K(0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4)
E = EllipticCurve(K, (a, b))
G = E(0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21, 0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34)
E.set_order(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D * 0x01)

PARI/GP

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001
a = Mod(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE, p)
b = Mod(0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4, p)
E = ellinit([a, b])
E[16][1] = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D * 0x01
G = [Mod(0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21, p), Mod(0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34, p)]

JSON

{
"name": "224-bit Random ECP Group",
"desc": "Defined in IETF in RFC5114",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
"bits": 224
},
"params": {
"a": {
"raw": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE"
},
"b": {
"raw": "0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"
}
},
"generator": {
"x": {
"raw": "0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"
},
"y": {
"raw": "0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"
}
},
"order": "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
"cofactor": "0x01"
}

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