Parameters

Sources

• ANSI X9.63

Characteristics

• OID:
  1.3.132.0.25
• j-invariant:
  5053066381681102639885175237237616768683530047828961128529
• Trace of Frobenius:
  -214577892669885555631611261865
• Discriminant:
  4946476016329916785216072668156805272487483199688540362414

SAGE

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

JSON

{
  "name": "ansit193r2",
  "desc": "",
  "oid": "1.3.132.0.25",
  "sources": [
    {
      "name": "ANSI X9.63",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9632011r2017"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 193,
    "degree": 193,
    "poly": [
      {
        "power": 193,
        "coeff": "0x01"
      },
      {
        "power": 15,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x0163f35a5137c2ce3ea6ed8667190b0bc43ecd69977702709b"
    },
    "b": {
      "raw": "0x00c9bb9e8927d4d64c377e2ab2856a5b16e3efb7f61d4316ae"
    }
  },
  "generator": {
    "x": {
      "raw": "0x00d9b67d192e0367c803f39e1a7e82ca14a651350aae617e8f"
    },
    "y": {
      "raw": "0x01ce94335607c304ac29e7defbd9ca01f596f927224cdecf6c"
    }
  },
  "order": "0x010000000000000000000000015aab561b005413ccd4ee99d5",
  "cofactor": "0x2",
  "aliases": [
    "secg/sect193r2"
  ],
  "characteristics": {
    "discriminant": "4946476016329916785216072668156805272487483199688540362414",
    "j_invariant": "5053066381681102639885175237237616768683530047828961128529",
    "trace_of_frobenius": "-214577892669885555631611261865"
  }
}