BADA55 curve from the https://bada55.cr.yp.to/bada55-20150927.pdf

Parameters

Sources

• How to manipulate curve standards: a white paper for the black hat

Characteristics

• j-invariant:
  20035387721920485348400481045400108781349066688510057321890440459113
• Trace of Frobenius:
  661950337966252150745153098997235
• Discriminant:
  2243161245327399348031772367113162507429929629715722183863459097477
• Embedding degree:
  13479973333575319897333507543509815005803789146887078699178483650823
• CM-discriminant:
  -107401608418668923735108959339263260485069539573549549469677727550299
• Conductor:
  1

SAGE

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
K = GF(p)
a = K(0x8f0ff20e1e3cf4905d492e04110683948bfc236790bbb59e6e6b33f24f348ed2e16c64ee79f9fd27e9a367ff6415b41189e4fb6bada555455dc44c4f87011eef)
b = K(0xe85067a95547e30661c854a43ed80f36289043ffc73da78a97e37fb96a2717009088656b948865a660ff3959330d8a1ca1e4de31b7b7d496a4cde555e57d05c)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xffffffffffffffffffffffffffffdf5c0319f61dc6ccebe902bc220f * 0x01)

PARI/GP

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
a = Mod(0x8f0ff20e1e3cf4905d492e04110683948bfc236790bbb59e6e6b33f24f348ed2e16c64ee79f9fd27e9a367ff6415b41189e4fb6bada555455dc44c4f87011eef, p)
b = Mod(0xe85067a95547e30661c854a43ed80f36289043ffc73da78a97e37fb96a2717009088656b948865a660ff3959330d8a1ca1e4de31b7b7d496a4cde555e57d05c, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffffdf5c0319f61dc6ccebe902bc220f * 0x01
\\ No generator defined

JSON

{
  "name": "BADA55-VPR2-224",
  "desc": "BADA55 curve from the https://bada55.cr.yp.to/bada55-20150927.pdf",
  "sources": [
    {
      "name": "How to manipulate curve standards: a white paper for the black hat",
      "url": "https://bada55.cr.yp.to/bada55-20150927.pdf"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xffffffffffffffffffffffffffffffff000000000000000000000001",
    "bits": 224
  },
  "params": {
    "a": {
      "raw": "0x8f0ff20e1e3cf4905d492e04110683948bfc236790bbb59e6e6b33f24f348ed2e16c64ee79f9fd27e9a367ff6415b41189e4fb6bada555455dc44c4f87011eef"
    },
    "b": {
      "raw": "0xe85067a95547e30661c854a43ed80f36289043ffc73da78a97e37fb96a2717009088656b948865a660ff3959330d8a1ca1e4de31b7b7d496a4cde555e57d05c"
    }
  },
  "order": "0xffffffffffffffffffffffffffffdf5c0319f61dc6ccebe902bc220f",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-107401608418668923735108959339263260485069539573549549469677727550299",
    "conductor": "1",
    "discriminant": "2243161245327399348031772367113162507429929629715722183863459097477",
    "j_invariant": "20035387721920485348400481045400108781349066688510057321890440459113",
    "embedding_degree": "13479973333575319897333507543509815005803789146887078699178483650823",
    "trace_of_frobenius": "661950337966252150745153098997235"
  }
}