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:
  96352772434343068284941752698741343881529619471464934096633633307958507507507
• Trace of Frobenius:
  381257165022567524325218360739058995869
• Discriminant:
  33024497026253337160729626824031371799586170046501504160073511830729782933196
• Embedding degree:
  36484857110565759539223575010245042715196030827615390210958701731818987799330
• CM-discriminant:
  -11698450377829753151182841061045172603605934816251805048442847406795581220411
• Conductor:
  5

SAGE

p = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03
K = GF(p)
a = K(0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00)
b = K(0xbada55bada55bada55bada55bada55bada55bada55bada55bada55bada55bd48)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xf1fd178c0b3ad58f10126de8ce42435a1a8e3837861aa0efa0e52aec7379c967 * 0x01)

PARI/GP

p = 0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03
a = Mod(0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00, p)
b = Mod(0xbada55bada55bada55bada55bada55bada55bada55bada55bada55bada55bd48, p)
E = ellinit([a, b])
E[16][1] = 0xf1fd178c0b3ad58f10126de8ce42435a1a8e3837861aa0efa0e52aec7379c967 * 0x01
\\ No generator defined

JSON

{
  "name": "BADA55-R-256",
  "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": "0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0xf1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00"
    },
    "b": {
      "raw": "0xbada55bada55bada55bada55bada55bada55bada55bada55bada55bada55bd48"
    }
  },
  "order": "0xf1fd178c0b3ad58f10126de8ce42435a1a8e3837861aa0efa0e52aec7379c967",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-11698450377829753151182841061045172603605934816251805048442847406795581220411",
    "conductor": "5",
    "discriminant": "33024497026253337160729626824031371799586170046501504160073511830729782933196",
    "j_invariant": "96352772434343068284941752698741343881529619471464934096633633307958507507507",
    "embedding_degree": "36484857110565759539223575010245042715196030827615390210958701731818987799330",
    "trace_of_frobenius": "381257165022567524325218360739058995869"
  }
}