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BADA55-VPR-224

224-bit prime field Weierstrass curve.

BADA55 curve from the https://bada55.cr.yp.to/bada55-20150927.pdf


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

Parameters

NameValue
p0xffffffffffffffffffffffffffffffff000000000000000000000001
a0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49
b0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2
n0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add
h0x01


SAGE

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
K = GF(p)
a = K(0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49)
b = K(0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add * 0x01)

PARI/GP

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
a = Mod(0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49, p)
b = Mod(0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add * 0x01
\\ No generator defined

JSON

{
"name": "BADA55-VPR-224",
"desc": "BADA55 curve from the https://bada55.cr.yp.to/bada55-20150927.pdf",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xffffffffffffffffffffffffffffffff000000000000000000000001",
"bits": 224
},
"params": {
"a": {
"raw": "0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49"
},
"b": {
"raw": "0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2"
}
},
"order": "0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add",
"cofactor": "0x01"
}

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