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Curve22103

221-bit prime field Weierstrass curve.

Curve from https://github.com/relic-toolkit/relic


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

Parameters

NameValue
p0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd
a0x155555555555555555555555555555555555555555555552174084FF
b0x1425ED097B425ED097B425ED097B425ED097B425ED0BBA9428427967
G(0xCB476FE081B61F56A60B1D1B34FB7207D072EF25DADF377731049B0, 0x36429404D97E1E217BAD2E5601F6551F95D8FE9481BD454D1F3E7B6)
n0x3FFFFFFFFFFFFFFFFFFFFFFFFFFF5CD04695A145C3067CF4AAE2025
h0x08


SAGE

p = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd
K = GF(p)
a = K(0x155555555555555555555555555555555555555555555552174084FF)
b = K(0x1425ED097B425ED097B425ED097B425ED097B425ED0BBA9428427967)
E = EllipticCurve(K, (a, b))
G = E(0xCB476FE081B61F56A60B1D1B34FB7207D072EF25DADF377731049B0, 0x36429404D97E1E217BAD2E5601F6551F95D8FE9481BD454D1F3E7B6)
E.set_order(0x3FFFFFFFFFFFFFFFFFFFFFFFFFFF5CD04695A145C3067CF4AAE2025 * 0x08)

PARI/GP

p = 0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd
a = Mod(0x155555555555555555555555555555555555555555555552174084FF, p)
b = Mod(0x1425ED097B425ED097B425ED097B425ED097B425ED0BBA9428427967, p)
E = ellinit([a, b])
E[16][1] = 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFF5CD04695A145C3067CF4AAE2025 * 0x08
G = [Mod(0xCB476FE081B61F56A60B1D1B34FB7207D072EF25DADF377731049B0, p), Mod(0x36429404D97E1E217BAD2E5601F6551F95D8FE9481BD454D1F3E7B6, p)]

JSON

{
"name": "Curve22103",
"desc": "Curve from https://github.com/relic-toolkit/relic",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffd",
"bits": 221
},
"params": {
"a": {
"raw": "0x155555555555555555555555555555555555555555555552174084FF"
},
"b": {
"raw": "0x1425ED097B425ED097B425ED097B425ED097B425ED0BBA9428427967"
}
},
"generator": {
"x": {
"raw": "0xCB476FE081B61F56A60B1D1B34FB7207D072EF25DADF377731049B0"
},
"y": {
"raw": "0x36429404D97E1E217BAD2E5601F6551F95D8FE9481BD454D1F3E7B6"
}
},
"order": "0x3FFFFFFFFFFFFFFFFFFFFFFFFFFF5CD04695A145C3067CF4AAE2025",
"cofactor": "0x08"
}

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