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Pallas

255-bit prime field Weierstrass curve.

Pallas curve from the Pasta curves.


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

Parameters

NameValue
p0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
a0x00
b0x05
G(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000, 0x02)
n0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001
h0x01


SAGE

p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
K = GF(p)
a = K(0x00)
b = K(0x05)
E = EllipticCurve(K, (a, b))
G = E(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000, 0x02)
E.set_order(0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001 * 0x01)

PARI/GP

p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
a = Mod(0x00, p)
b = Mod(0x05, p)
E = ellinit([a, b])
E[16][1] = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001 * 0x01
G = [Mod(0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000, p), Mod(0x02, p)]

JSON

{
"name": "Pallas",
"desc": "Pallas curve from the [Pasta curves](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/).",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001",
"bits": 255
},
"params": {
"a": {
"raw": "0x00"
},
"b": {
"raw": "0x05"
}
},
"generator": {
"x": {
"raw": "0x40000000000000000000000000000000224698fc094cf91b992d30ed00000000"
},
"y": {
"raw": "0x02"
}
},
"order": "0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001",
"cofactor": "0x01"
}

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