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Tom-521

521-bit prime field Weierstrass curve.

Tom-521 curve from https://eprint.iacr.org/2021/1183.pdf


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

Parameters

NameValue
p0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249
a0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2
b0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d
n0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
h0x01


SAGE

p = 0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249
K = GF(p)
a = K(0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2)
b = K(0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff * 0x01)

PARI/GP

p = 0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249
a = Mod(0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2, p)
b = Mod(0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d, p)
E = ellinit([a, b])
E[16][1] = 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff * 0x01
\\ No generator defined

JSON

{
"name": "Tom-521",
"desc": "Tom-521 curve from https://eprint.iacr.org/2021/1183.pdf",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249",
"bits": 521
},
"params": {
"a": {
"raw": "0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2"
},
"b": {
"raw": "0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d"
}
},
"order": "0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
"cofactor": "0x01"
}

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