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numsp512d1

512-bit prime field Weierstrass curve.
y2x3+ax+by^2 \equiv x^3 + ax + b

Parameters

NameValue
p0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7
a0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc4
b0x1d99b
G(0x02, 0x1c282eb23327f9711952c250ea61ad53fcc13031cf6dd336e0b9328433afbdd8cc5a1c1f0c716fdc724dde537c2b0adb00bb3d08dc83755b205cc30d7f83cf28)
n0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff5b3ca4fb94e7831b4fc258ed97d0bdc63b568b36607cd243ce153f390433555d
h0x01


SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc4)
b = K(0x1d99b)
E = EllipticCurve(K, (a, b))
G = E(0x02, 0x1c282eb23327f9711952c250ea61ad53fcc13031cf6dd336e0b9328433afbdd8cc5a1c1f0c716fdc724dde537c2b0adb00bb3d08dc83755b205cc30d7f83cf28)
E.set_order(0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff5b3ca4fb94e7831b4fc258ed97d0bdc63b568b36607cd243ce153f390433555d * 0x01)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7
a = Mod(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc4, p)
b = Mod(0x1d99b, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff5b3ca4fb94e7831b4fc258ed97d0bdc63b568b36607cd243ce153f390433555d * 0x01
G = [Mod(0x02, p), Mod(0x1c282eb23327f9711952c250ea61ad53fcc13031cf6dd336e0b9328433afbdd8cc5a1c1f0c716fdc724dde537c2b0adb00bb3d08dc83755b205cc30d7f83cf28, p)]

JSON

{
"name": "numsp512d1",
"desc": "",
"form": "Weierstrass",
"field": {
"type": "Prime",
"p": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc7",
"bits": 512
},
"params": {
"a": {
"raw": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdc4"
},
"b": {
"raw": "0x1d99b"
}
},
"generator": {
"x": {
"raw": "0x02"
},
"y": {
"raw": "0x1c282eb23327f9711952c250ea61ad53fcc13031cf6dd336e0b9328433afbdd8cc5a1c1f0c716fdc724dde537c2b0adb00bb3d08dc83755b205cc30d7f83cf28"
}
},
"order": "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff5b3ca4fb94e7831b4fc258ed97d0bdc63b568b36607cd243ce153f390433555d",
"cofactor": "0x01"
}

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