Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.20
• j-invariant:
  362269574762838995737133591261772891474603564643532771622226534618542191574924515217892206723079875799554062492802321892720276946
• Trace of Frobenius:
  1799562222397931009847908291975708857846270858398803555164615329
• Discriminant:
  730009817878589157105698105019566508793654980277815234786385618476547478165875682356826528735875627658295798257985650015095170584

SAGE

F.<x> = GF(2)[]
K = GF(2^431, name="x", modulus=u^431 +  u^120 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x1a827ef00dd6fc0e234caf046c6a5d8a85395b236cc4ad2cf32a0cadbdc9ddf620b0eb9906d0957f6c6feacd615468df104de296cd8f), 0, 0, K.from_integer(0x10d9b4a3d9047d8b154359abfb1b7f5485b04ceb868237ddc9deda982a679a5a919b626d4e50a8dd731b107a9962381fb5d807bf2618)))
E.set_order(0x0340340340340340340340340340340340340340340340340340340323c313fab50589703b5ec68d3587fec60d161cc149c1ad4a91 * 0x2760)
G = E(K.from_integer(0x120fc05d3c67a99de161d2f4092622feca701be4f50f4758714e8a87bbf2a658ef8c21e7c5efe965361f6c2999c0c247b0dbd70ce6b7), K.from_integer(0x20d0af8903a96f8d5fa2c255745d3c451b302c9346d9b7e485e7bce41f6b591f3e8f6addcbb0bc4c2f947a7de1a89b625d6a598b3760))

JSON

{
  "name": "c2tnb431r1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.20",
  "sources": [
    {
      "name": "ANSI X9.62",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9621998"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 431,
    "degree": 431,
    "poly": [
      {
        "power": 431,
        "coeff": "0x01"
      },
      {
        "power": 120,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x1a827ef00dd6fc0e234caf046c6a5d8a85395b236cc4ad2cf32a0cadbdc9ddf620b0eb9906d0957f6c6feacd615468df104de296cd8f"
    },
    "b": {
      "raw": "0x10d9b4a3d9047d8b154359abfb1b7f5485b04ceb868237ddc9deda982a679a5a919b626d4e50a8dd731b107a9962381fb5d807bf2618"
    }
  },
  "generator": {
    "x": {
      "raw": "0x120fc05d3c67a99de161d2f4092622feca701be4f50f4758714e8a87bbf2a658ef8c21e7c5efe965361f6c2999c0c247b0dbd70ce6b7"
    },
    "y": {
      "raw": "0x20d0af8903a96f8d5fa2c255745d3c451b302c9346d9b7e485e7bce41f6b591f3e8f6addcbb0bc4c2f947a7de1a89b625d6a598b3760"
    }
  },
  "order": "0x0340340340340340340340340340340340340340340340340340340323c313fab50589703b5ec68d3587fec60d161cc149c1ad4a91",
  "cofactor": "0x2760",
  "characteristics": {
    "discriminant": "730009817878589157105698105019566508793654980277815234786385618476547478165875682356826528735875627658295798257985650015095170584",
    "j_invariant": "362269574762838995737133591261772891474603564643532771622226534618542191574924515217892206723079875799554062492802321892720276946",
    "trace_of_frobenius": "1799562222397931009847908291975708857846270858398803555164615329"
  }
}