Parameters

Characteristics

• OID:
  1.3.132.0.33
• Seed:
  BD71344799D5C7FCDC45B59FA3B9AB8F6A948BC5
• j-invariant:
  20781977079628996477063007379734849057519732242287194936686605794677
• Trace of Frobenius:
  4733100108545601916421827343930821
• Discriminant:
  8133954887115844930654026312464158747844254983800706208418026371607
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  8986648889050213264889005029006541980152602571474797240560907456020
• CM-discriminant:
  107839786668602559178668060348078517961131556494503316152212921264703
• Conductor:
  1

SAGE

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
K = GF(p)
a = K(0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe)
b = K(0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4)
E = EllipticCurve(K, (a, b))
G = E(0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34)
E.set_order(0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d * 0x1)

PARI/GP

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
a = Mod(0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe, p)
b = Mod(0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d * 0x1
G = [Mod(0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21, p), Mod(0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34, p)]

JSON

{
  "name": "P-224",
  "desc": "",
  "oid": "1.3.132.0.33",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xffffffffffffffffffffffffffffffff000000000000000000000001",
    "bits": 224
  },
  "params": {
    "a": {
      "raw": "0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe"
    },
    "b": {
      "raw": "0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4"
    }
  },
  "generator": {
    "x": {
      "raw": "0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21"
    },
    "y": {
      "raw": "0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34"
    }
  },
  "order": "0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d",
  "cofactor": "0x1",
  "aliases": [
    "secg/secp224r1",
    "wtls/wap-wsg-idm-ecid-wtls12",
    "x963/ansip224r1"
  ],
  "characteristics": {
    "seed": "BD71344799D5C7FCDC45B59FA3B9AB8F6A948BC5",
    "j_invariant": "20781977079628996477063007379734849057519732242287194936686605794677",
    "anomalous": false,
    "cm_disc": "107839786668602559178668060348078517961131556494503316152212921264703",
    "conductor": "1",
    "discriminant": "8133954887115844930654026312464158747844254983800706208418026371607",
    "embedding_degree": "8986648889050213264889005029006541980152602571474797240560907456020",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 2,
        "least": 2,
        "r": 3
      },
      {
        "full": 6,
        "least": 6,
        "r": 5
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "4733100108545601916421827343930821"
  }
}