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ansit193r2

193-bit binary field Weierstrass curve.
Also known as: sect193r2
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m193
f(x) x^193 + x^15 + 1
a0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b
b0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae
G(0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f, 0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c)
n0x010000000000000000000000015aab561b005413ccd4ee99d5
h0x2

Characteristics

  • OID:
    1.3.132.0.25

SAGE

F.<x> = GF(2)[]
K = GF(2^193, name="x", modulus= x^193 + x^15 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b), 0, 0, K.fetch_int(0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae)))
E.set_order(0x010000000000000000000000015aab561b005413ccd4ee99d5 * 0x2)
G = E(K.fetch_int(0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f), K.fetch_int(0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c))


JSON

{
"name": "ansit193r2",
"desc": "",
"oid": "1.3.132.0.25",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 193,
"degree": 193,
"poly": [
{
"coeff": "0x01",
"power": 193
},
{
"coeff": "0x01",
"power": 15
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b"
},
"b": {
"raw": "0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae"
}
},
"generator": {
"x": {
"raw": "0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f"
},
"y": {
"raw": "0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c"
}
},
"order": "0x010000000000000000000000015aab561b005413ccd4ee99d5",
"cofactor": "0x2",
"aliases": [
"secg/sect193r2"
]
}

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