Skip to main content

Standard curve database

Search

Tom-256

256-bit prime field Weierstrass curve.

Tom-256 curve from https://eprint.iacr.org/2021/1183.pdf


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

Parameters

NameValue
p0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117
a0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114
b0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56
G(0x03, 0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d)
n0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
h0x01


SAGE

p = 0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117
K = GF(p)
a = K(0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114)
b = K(0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56)
E = EllipticCurve(K, (a, b))
G = E(0x03, 0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d)
E.set_order(0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff * 0x01)

PARI/GP

p = 0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117
a = Mod(0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114, p)
b = Mod(0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56, p)
E = ellinit([a, b])
E[16][1] = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff * 0x01
G = [Mod(0x03, p), Mod(0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d, p)]

JSON

{
"name": "Tom-256",
"desc": "Tom-256 curve from https://eprint.iacr.org/2021/1183.pdf",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117",
"bits": 256
},
"params": {
"a": {
"raw": "0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114"
},
"b": {
"raw": "0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56"
}
},
"generator": {
"x": {
"raw": "0x03"
},
"y": {
"raw": "0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d"
}
},
"order": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
"cofactor": "0x01"
}

© 2020 Jan Jancar | Built with Dox theme for Gatsby