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Curve383187

283-bit prime field Montgomery curve.
By2x3+Ax2+xBy^2 \equiv x^3 + Ax^2 + x

Parameters

NameValue
p0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45
a0x38251
b0x01
G(0x5, 0x1eebe07dc1871896732b12d5504a32370471965c7a11f2c89865f855ab3cbd7c224e3620c31af3370788457dd5ce46df)
n0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21
h0x8


SAGE

p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45
K = GF(p)
A = K(0x38251)
B = K(0x01)
E = EllipticCurve(K, ((3 - A^2)/(3 * B^2), (2 * A^3 - 9 * A)/(27 * B^3)))
def to_weierstrass(A, B, x, y):
return (x/B + A/(3*B), y/B)
def to_montgomery(A, B, u, v):
return (B * (u - A/(3*B)), B*v)
G = E(*to_weierstrass(A, B, K(0x5), K(0x1eebe07dc1871896732b12d5504a32370471965c7a11f2c89865f855ab3cbd7c224e3620c31af3370788457dd5ce46df)))
E.set_order(0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21 * 0x8)
# This curve is a Weierstrass curve (SAGE does not support Montgomery curves) birationally equivalent to the intended curve.
# You can use the to_weierstrass and to_montgomery functions to convert the points.


JSON

{
"name": "Curve383187",
"desc": "",
"form": "Montgomery",
"field": {
"type": "Prime",
"p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff45",
"bits": 283
},
"params": {
"a": {
"raw": "0x38251"
},
"b": {
"raw": "0x01"
}
},
"generator": {
"x": {
"raw": "0x5"
},
"y": {
"raw": "0x1eebe07dc1871896732b12d5504a32370471965c7a11f2c89865f855ab3cbd7c224e3620c31af3370788457dd5ce46df"
}
},
"order": "0x1000000000000000000000000000000000000000000000000e85a85287a1488acd41ae84b2b7030446f72088b00a0e21",
"cofactor": "0x8"
}

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