Parameters

Characteristics

• OID:
  1.3.132.0.37

SAGE

F.<x> = GF(2)[]
K = GF(2^409, name="x", modulus= x^409 +  x^87 + 1)
E = EllipticCurve(K, (1, K.fetch_int(0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001), 0, 0, K.fetch_int(0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f)))
E.set_order(0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173 * 0x2)
G = E(K.fetch_int(0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7), K.fetch_int(0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706))

JSON

{
  "name": "ansit409r1",
  "desc": "",
  "oid": "1.3.132.0.37",
  "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": "0x00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001"
    },
    "b": {
      "raw": "0x0021a5c2c8ee9feb5c4b9a753b7b476b7fd6422ef1f3dd674761fa99d6ac27c8a9a197b272822f6cd57a55aa4f50ae317b13545f"
    }
  },
  "generator": {
    "x": {
      "raw": "0x015d4860d088ddb3496b0c6064756260441cde4af1771d4db01ffe5b34e59703dc255a868a1180515603aeab60794e54bb7996a7"
    },
    "y": {
      "raw": "0x0061b1cfab6be5f32bbfa78324ed106a7636b9c5a7bd198d0158aa4f5488d08f38514f1fdf4b4f40d2181b3681c364ba0273c706"
    }
  },
  "order": "0x010000000000000000000000000000000000000000000000000001e2aad6a612f33307be5fa47c3c9e052f838164cd37d9a21173",
  "cofactor": "0x2",
  "aliases": [
    "nist/B-409",
    "secg/sect409r1"
  ]
}