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:
  8970331276724101928998400188039414218090359635692591697732517465752
• Trace of Frobenius:
  3747123853060838272219601178637605
• Discriminant:
  18554481562680642436629910092114564632157928853044658558796075403180
• Embedding degree:
  26959946667150639794667015087019626926434063199188035923908887661276
• CM-discriminant:
  -93798849498425056487645609391472088921124359957609087271436345059499
• Conductor:
  1

SAGE

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
K = GF(p)
a = K(0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49)
b = K(0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add * 0x01)

PARI/GP

p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
a = Mod(0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49, p)
b = Mod(0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add * 0x01
\\ No generator defined

JSON

{
  "name": "BADA55-VPR-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": "0x7144ba12ce8a0c3befa053edbada555a42391fc64f052376e041c7d4af23195ebd8d83625321d452e8a0c3bb0a048a26115704e45dceb346a9f4bd9741d14d49"
    },
    "b": {
      "raw": "0x5c32ec7fc48ce1802d9b70dbc3fa574eaf015fce4e99b43ebe3468d6efb2276ba3669aff6ffc0f4c6ae4ae2e5d74c3c0af97dce17147688dda89e734b56944a2"
    }
  },
  "order": "0xffffffffffffffffffffffffffff473fa5d3e9bf40a95a8d3f014add",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-93798849498425056487645609391472088921124359957609087271436345059499",
    "conductor": "1",
    "discriminant": "18554481562680642436629910092114564632157928853044658558796075403180",
    "j_invariant": "8970331276724101928998400188039414218090359635692591697732517465752",
    "embedding_degree": "26959946667150639794667015087019626926434063199188035923908887661276",
    "trace_of_frobenius": "3747123853060838272219601178637605"
  }
}