Parameters

Sources

• A Family of Implementation-Friendly BN Elliptic Curves

Characteristics

• j-invariant:
  0
• Trace of Frobenius:
  800995136978371572363525747477255032258950408689114271367829691469194143147501961435441086332935
• Discriminant:
  641593209463000238284923228689168801117629789043238356871360716989515584497239494051781991794253619096481315470262367432019698642631650152075067922231951354925301839708740457083469793688592055
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  12
• CM-discriminant:
  -3
• Conductor:
  800995136978371572363525747477255032258950408690575773003799464919714074125184154404652534726667

SAGE

p = 0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55C00086520021E55BFFFFF51FFFF4EB800000004C80015ACDFFFFFFFFFFFFECE00000000000000067
K = GF(p)
a = K(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
b = K(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101)
E = EllipticCurve(K, (a, b))
G = E(0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55C00086520021E55BFFFFF51FFFF4EB800000004C80015ACDFFFFFFFFFFFFECE00000000000000066, 0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010)
E.set_order(0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55600086550021E555FFFFF54FFFF4EAC000000049800154D9FFFFFFFFFFFFEDA00000000000000061 * 0x01)

PARI/GP

p = 0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55C00086520021E55BFFFFF51FFFF4EB800000004C80015ACDFFFFFFFFFFFFECE00000000000000067
a = Mod(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, p)
b = Mod(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101, p)
E = ellinit([a, b])
E[16][1] = 0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55600086550021E555FFFFF54FFFF4EAC000000049800154D9FFFFFFFFFFFFEDA00000000000000061 * 0x01
G = [Mod(0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55C00086520021E55BFFFFF51FFFF4EB800000004C80015ACDFFFFFFFFFFFFECE00000000000000066, p), Mod(0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010, p)]

JSON

{
  "name": "bn638",
  "desc": "",
  "sources": [
    {
      "name": "A Family of Implementation-Friendly BN Elliptic Curves",
      "url": "https://eprint.iacr.org/2010/429"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55C00086520021E55BFFFFF51FFFF4EB800000004C80015ACDFFFFFFFFFFFFECE00000000000000067",
    "bits": 638
  },
  "params": {
    "a": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    },
    "b": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101"
    }
  },
  "generator": {
    "x": {
      "raw": "0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55C00086520021E55BFFFFF51FFFF4EB800000004C80015ACDFFFFFFFFFFFFECE00000000000000066"
    },
    "y": {
      "raw": "0x0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010"
    }
  },
  "order": "0x23FFFFFDC000000D7FFFFFB8000001D3FFFFF942D000165E3FFF94870000D52FFFFDD0E00008DE55600086550021E555FFFFF54FFFF4EAC000000049800154D9FFFFFFFFFFFFEDA00000000000000061",
  "cofactor": "0x01",
  "characteristics": {
    "discriminant": "641593209463000238284923228689168801117629789043238356871360716989515584497239494051781991794253619096481315470262367432019698642631650152075067922231951354925301839708740457083469793688592055",
    "j_invariant": "0",
    "trace_of_frobenius": "800995136978371572363525747477255032258950408689114271367829691469194143147501961435441086332935",
    "embedding_degree": "12",
    "anomalous": false,
    "supersingular": false,
    "cm_disc": "-3",
    "conductor": "800995136978371572363525747477255032258950408690575773003799464919714074125184154404652534726667"
  }
}