Curve described in https://www.iso.org/standard/80241.html

Parameters

Sources

• ISO/IEC 15946-5:2013 - Information technology — Security techniques — Cryptographic techniques based on elliptic curves — Part 5: Elliptic curve generation

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  5192296858534689624111674181427015
• Discriminant:
  26959946667149205758383469736921695435015736735261155141423417420035
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  5192296858534689506442115857736067

SAGE

p = 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833
K = GF(p)
a = K(0x00)
b = K(0x03)
E = EllipticCurve(K, (a, b))
G = E(0x01, 0x02)
E.set_order(0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed * 0x01)

PARI/GP

p = 0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833
a = Mod(0x00, p)
b = Mod(0x03, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed * 0x01
G = [Mod(0x01, p), Mod(0x02, p)]

JSON

{
  "name": "Fp224BN",
  "desc": "Curve described in https://www.iso.org/standard/80241.html",
  "sources": [
    {
      "name": "ISO/IEC 15946-5:2013 - Information technology — Security techniques — Cryptographic techniques based on elliptic curves — Part 5: Elliptic curve generation",
      "url": "https://www.iso.org/standard/80241.html"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xfffffffffff107288ec29e602c4520db42180823bb907d1287127833",
    "bits": 224
  },
  "params": {
    "a": {
      "raw": "0x00"
    },
    "b": {
      "raw": "0x03"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01"
    },
    "y": {
      "raw": "0x02"
    }
  },
  "order": "0xfffffffffff107288ec29e602c4420db4218082b36c2accff76c58ed",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "26959946667149205758383469736921695435015736735261155141423417420035",
    "j_invariant": "0",
    "trace_of_frobenius": "5192296858534689624111674181427015",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "5192296858534689506442115857736067"
  }
}