Defined in IETF in RFC5114

Parameters

Sources

• RFC5114

Characteristics

• j-invariant:
  20781977079628996477063007379734849057519732242287194936686605794677
• Trace of Frobenius:
  4733100108545601916421827343930821
• Discriminant:
  8133954887115844930654026312464158747844254983800706208418026371607
• Embedding degree:
  8986648889050213264889005029006541980152602571474797240560907456020
• CM-discriminant:
  -9493061114565352281698673660738078664961855212656825491744070162387
• Conductor:
  3

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 * 0x01)

PARI/GP

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001
a = Mod(0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE, p)
b = Mod(0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4, p)
E = ellinit([a, b])
E[16][1] = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D * 0x01
G = [Mod(0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21, p), Mod(0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34, p)]

JSON

{
  "name": "224-bit Random ECP Group",
  "desc": "Defined in IETF in RFC5114",
  "sources": [
    {
      "name": "RFC5114",
      "url": "https://tools.ietf.org/html/rfc5114"
    }
  ],
  "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": "0x01",
  "characteristics": {
    "cm_disc": "-9493061114565352281698673660738078664961855212656825491744070162387",
    "conductor": "3",
    "discriminant": "8133954887115844930654026312464158747844254983800706208418026371607",
    "j_invariant": "20781977079628996477063007379734849057519732242287194936686605794677",
    "embedding_degree": "8986648889050213264889005029006541980152602571474797240560907456020",
    "trace_of_frobenius": "4733100108545601916421827343930821"
  }
}