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K-409

409-bit binary field Weierstrass curve.

Koblitz curve.


Also known as: sect409k1ansit409k1
y2+xyx3+ax2+by^2 + xy \equiv x^3 + ax^2 + b

Parameters

NameValue
m409
f(x) x^409 + x^87 + 1
a0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
b0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
G(0x060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746, 0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b)
n0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf
h0x4

Characteristics

  • OID:
    1.3.132.0.36
  • j-invariant:
    1
  • Trace of Frobenius:
    10457288737315625927447685387048320737638796957687575791173829
  • Discriminant:
    1
  • Anomalous:
    false
  • Supersingular:
    false

SAGE

F.<x> = GF(2)[]
K = GF(2^409, name="x", modulus= x^409 + x^87 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000), 0, 0, K.fetch_int(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001)))
E.set_order(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf * 0x4)
G = E(K.fetch_int(0x060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746), K.fetch_int(0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b))


JSON

{
"name": "K-409",
"desc": "Koblitz curve.",
"oid": "1.3.132.0.36",
"form": "Weierstrass",
"field": {
"type": "Binary",
"bits": 409,
"degree": 409,
"poly": [
{
"coeff": "0x01",
"power": 409
},
{
"coeff": "0x01",
"power": 87
},
{
"coeff": "0x01",
"power": 0
}
],
"basis": "poly"
},
"params": {
"a": {
"raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
},
"b": {
"raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
}
},
"generator": {
"x": {
"raw": "0x060f05f658f49c1ad3ab1890f7184210efd0987e307c84c27accfb8f9f67cc2c460189eb5aaaa62ee222eb1b35540cfe9023746"
},
"y": {
"raw": "0x1e369050b7c4e42acba1dacbf04299c3460782f918ea427e6325165e9ea10e3da5f6c42e9c55215aa9ca27a5863ec48d8e0286b"
}
},
"order": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffe5f83b2d4ea20400ec4557d5ed3e3e7ca5b4b5c83b8e01e5fcf",
"cofactor": "0x4",
"aliases": [
"secg/sect409k1",
"x963/ansit409k1"
],
"characteristics": {
"j_invariant": "1",
"anomalous": false,
"discriminant": "1",
"supersingular": false,
"trace_of_frobenius": "10457288737315625927447685387048320737638796957687575791173829"
}
}

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