Parameters

Sources

• RFC4357

Characteristics

• j-invariant:
  6652745622926419573233155027295391061028493201567049670637289133556058620731
• Trace of Frobenius:
  -467140827435544800340052492131167243509
• Discriminant:
  25086829932126800311652180130828872457575393184303739951923669692579300879855
• Embedding degree:
  28948022309329048855892746252171976963551066580127913410034422248043866033351
• CM-discriminant:
  -619
• Conductor:
  4646402506017662432554672533504826433

SAGE

p = 0x8000000000000000000000000000000000000000000000000000000000000c99
K = GF(p)
a = K(0x8000000000000000000000000000000000000000000000000000000000000c96)
b = K(0x3e1af419a269a5f866a7d3c25c3df80ae979259373ff2b182f49d4ce7e1bbc8b)
E = EllipticCurve(K, (a, b))
G = E(0x01, 0x3fa8124359f96680b83d1c3eb2c070e5c545c9858d03ecfb744bf8d717717efc)
E.set_order(0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198f * 0x1)

PARI/GP

p = 0x8000000000000000000000000000000000000000000000000000000000000c99
a = Mod(0x8000000000000000000000000000000000000000000000000000000000000c96, p)
b = Mod(0x3e1af419a269a5f866a7d3c25c3df80ae979259373ff2b182f49d4ce7e1bbc8b, p)
E = ellinit([a, b])
E[16][1] = 0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198f * 0x1
G = [Mod(0x01, p), Mod(0x3fa8124359f96680b83d1c3eb2c070e5c545c9858d03ecfb744bf8d717717efc, p)]

JSON

{
  "name": "id-GostR3410-2001-CryptoPro-B-ParamSet",
  "desc": "",
  "sources": [
    {
      "name": "RFC4357",
      "url": "https://datatracker.ietf.org/doc/html/rfc4357"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x8000000000000000000000000000000000000000000000000000000000000c99",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0x8000000000000000000000000000000000000000000000000000000000000c96"
    },
    "b": {
      "raw": "0x3e1af419a269a5f866a7d3c25c3df80ae979259373ff2b182f49d4ce7e1bbc8b"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01"
    },
    "y": {
      "raw": "0x3fa8124359f96680b83d1c3eb2c070e5c545c9858d03ecfb744bf8d717717efc"
    }
  },
  "order": "0x800000000000000000000000000000015f700cfff1a624e5e497161bcc8a198f",
  "cofactor": "0x1",
  "characteristics": {
    "cm_disc": "-619",
    "conductor": "4646402506017662432554672533504826433",
    "discriminant": "25086829932126800311652180130828872457575393184303739951923669692579300879855",
    "j_invariant": "6652745622926419573233155027295391061028493201567049670637289133556058620731",
    "embedding_degree": "28948022309329048855892746252171976963551066580127913410034422248043866033351",
    "trace_of_frobenius": "-467140827435544800340052492131167243509"
  }
}