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Tom-384

384-bit prime field Weierstrass curve.

Tom-384 curve from https://eprint.iacr.org/2021/1183.pdf


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

Parameters

NameValue
p0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5
a0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba
b0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b
n0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
h0x01


SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5
K = GF(p)
a = K(0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba)
b = K(0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff * 0x01)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5
a = Mod(0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba, p)
b = Mod(0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff * 0x01
\\ No generator defined

JSON

{
"name": "Tom-384",
"desc": "Tom-384 curve from https://eprint.iacr.org/2021/1183.pdf",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5",
"bits": 384
},
"params": {
"a": {
"raw": "0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba"
},
"b": {
"raw": "0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b"
}
},
"order": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff",
"cofactor": "0x01"
}

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