sect131r1
131-bit binary field Weierstrass curve.
y2+xy≡x3+ax2+b Parameters
| Name | Value |
|---|
| m | 131 |
| f(x) | x^131 + x^8 + x^3 + x^2 + 1 |
| a | 0x07a11b09a76b562144418ff3ff8c2570b8 |
| b | 0x0217c05610884b63b9c6c7291678f9d341 |
| G | (0x0081baf91fdf9833c40f9c181343638399, 0x078c6e7ea38c001f73c8134b1b4ef9e150) |
| n | 0x0400000000000000023123953a9464b54d |
| h | 0x2 |
SAGE
F.<x> = GF(2)[]
K = GF(2^131, name="x", modulus= x^131 + x^8 + x^3 + x^2 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x07a11b09a76b562144418ff3ff8c2570b8), 0, 0, K.fetch_int(0x0217c05610884b63b9c6c7291678f9d341)))
E.set_order(0x0400000000000000023123953a9464b54d * 0x2)
G = E(K.fetch_int(0x0081baf91fdf9833c40f9c181343638399), K.fetch_int(0x078c6e7ea38c001f73c8134b1b4ef9e150))
JSON
{
"name": "sect131r1",
"desc": "",
"oid": "1.3.132.0.22",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 131,
"degree": 131,
"poly": [
{
"coeff": "0x01",
"power": 131
},
{
"coeff": "0x01",
"power": 8
},
{
"coeff": "0x01",
"power": 3
},
{
"coeff": "0x01",
"power": 2
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x07a11b09a76b562144418ff3ff8c2570b8"
},
"b": {
"raw": "0x0217c05610884b63b9c6c7291678f9d341"
}
},
"generator": {
"x": {
"raw": "0x0081baf91fdf9833c40f9c181343638399"
},
"y": {
"raw": "0x078c6e7ea38c001f73c8134b1b4ef9e150"
}
},
"order": "0x0400000000000000023123953a9464b54d",
"cofactor": "0x2"
}