RFC5832

Parameters

Characteristics

• j-invariant:
  47600942436259896686252565464037418196133049460809434901599611094145698194061
• Trace of Frobenius:
  -447942250905168602652181588181066248577
• Discriminant:
  7131076324798369740383976847735509623538161424877910620024627361000146746618
• Anomalous:
  false
• Supersingular:
  false
• Embedding degree:
  9649340769776349618630915417390658987847155763954241770396828932022938511603
• CM-discriminant:
  231584178474632390847141970017375815706987911582186296681567349604007325532741
• Conductor:
  1

SAGE

p = 0x8000000000000000000000000000000000000000000000000000000000000431
K = GF(p)
a = K(0x7)
b = K(0x5fbff498aa938ce739b8e022fbafef40563f6e6a3472fc2a514c0ce9dae23b7e)
E = EllipticCurve(K, (a, b))
G = E(0x2, 0x8e2a8a0e65147d4bd6316030e16d19c85c97f0a9ca267122b96abbcea7e8fc8)
E.set_order(0x8000000000000000000000000000000150fe8a1892976154c59cfc193accf5b3 * 0x1)

PARI/GP

p = 0x8000000000000000000000000000000000000000000000000000000000000431
a = Mod(0x7, p)
b = Mod(0x5fbff498aa938ce739b8e022fbafef40563f6e6a3472fc2a514c0ce9dae23b7e, p)
E = ellinit([a, b])
E[16][1] = 0x8000000000000000000000000000000150fe8a1892976154c59cfc193accf5b3 * 0x1
G = [Mod(0x2, p), Mod(0x8e2a8a0e65147d4bd6316030e16d19c85c97f0a9ca267122b96abbcea7e8fc8, p)]

JSON

{
  "name": "gost256",
  "desc": "RFC5832",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x8000000000000000000000000000000000000000000000000000000000000431",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0x7"
    },
    "b": {
      "raw": "0x5fbff498aa938ce739b8e022fbafef40563f6e6a3472fc2a514c0ce9dae23b7e"
    }
  },
  "generator": {
    "x": {
      "raw": "0x2"
    },
    "y": {
      "raw": "0x8e2a8a0e65147d4bd6316030e16d19c85c97f0a9ca267122b96abbcea7e8fc8"
    }
  },
  "order": "0x8000000000000000000000000000000150fe8a1892976154c59cfc193accf5b3",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "47600942436259896686252565464037418196133049460809434901599611094145698194061",
    "anomalous": false,
    "cm_disc": "231584178474632390847141970017375815706987911582186296681567349604007325532741",
    "conductor": "1",
    "discriminant": "7131076324798369740383976847735509623538161424877910620024627361000146746618",
    "embedding_degree": "9649340769776349618630915417390658987847155763954241770396828932022938511603",
    "torsion_degrees": [
      {
        "full": 3,
        "least": 3,
        "r": 2
      },
      {
        "full": 2,
        "least": 2,
        "r": 3
      },
      {
        "full": 10,
        "least": 2,
        "r": 5
      },
      {
        "full": 6,
        "least": 2,
        "r": 7
      },
      {
        "full": 10,
        "least": 10,
        "r": 11
      },
      {
        "full": 168,
        "least": 168,
        "r": 13
      },
      {
        "full": 288,
        "least": 288,
        "r": 17
      },
      {
        "full": 18,
        "least": 2,
        "r": 19
      }
    ],
    "supersingular": false,
    "trace_of_frobenius": "-447942250905168602652181588181066248577"
  }
}