Parameters

Sources

• ANSI X9.62

Characteristics

• OID:
  1.2.840.10045.3.0.5
• Seed:
  4E13CA542744D696E67687561517552F279A8C84
• j-invariant:
  1592290136509610664567829827251242588540222540739152629723
• Trace of Frobenius:
  -2867709611233468671243809609
• Discriminant:
  1134615152941088452485133098472963493214560786404446668268

SAGE

F.<x> = GF(2)[]
K = GF(2^191, name="x", modulus=u^191 +  u^9 + 1)
E = EllipticCurve(K, (1, K.from_integer(0x2866537b676752636a68f56554e12640276b649ef7526267), 0, 0, K.from_integer(0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec)))
E.set_order(0x40000000000000000000000004a20e90c39067c893bbb9a5 * 0x2)
G = E(K.from_integer(0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d), K.from_integer(0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb))

JSON

{
  "name": "c2tnb191v1",
  "desc": "",
  "oid": "1.2.840.10045.3.0.5",
  "sources": [
    {
      "name": "ANSI X9.62",
      "url": "https://webstore.ansi.org/standards/ascx9/ansix9621998"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Binary",
    "bits": 191,
    "degree": 191,
    "poly": [
      {
        "power": 191,
        "coeff": "0x01"
      },
      {
        "power": 9,
        "coeff": "0x01"
      },
      {
        "power": 0,
        "coeff": "0x01"
      }
    ],
    "basis": "poly"
  },
  "params": {
    "a": {
      "raw": "0x2866537b676752636a68f56554e12640276b649ef7526267"
    },
    "b": {
      "raw": "0x2e45ef571f00786f67b0081b9495a3d95462f5de0aa185ec"
    }
  },
  "generator": {
    "x": {
      "raw": "0x36b3daf8a23206f9c4f299d7b21a9c369137f2c84ae1aa0d"
    },
    "y": {
      "raw": "0x765be73433b3f95e332932e70ea245ca2418ea0ef98018fb"
    }
  },
  "order": "0x40000000000000000000000004a20e90c39067c893bbb9a5",
  "cofactor": "0x2",
  "characteristics": {
    "seed": "4E13CA542744D696E67687561517552F279A8C84",
    "discriminant": "1134615152941088452485133098472963493214560786404446668268",
    "j_invariant": "1592290136509610664567829827251242588540222540739152629723",
    "trace_of_frobenius": "-2867709611233468671243809609"
  }
}