RFC7836

Parameters

Characteristics

• j-invariant:
  3279526492516777515918714136866447726665055949835218722150114206701277040061277147122787695822725918855580899339255833327922367669454014389888618448520937
• Trace of Frobenius:
  -149097018916599106931901217895018650162542083271457414743815309640053273077069
• Discriminant:
  3168251429939329401500982659836128598832488836312881941454031137145329322102983037116860271709983280267186414249706141598349259183530624792370505272178517
• Supersingular:
  false
• Embedding degree:
  1117317327495216424964502083183820510623280485049366114810296786976813669172820430903308958031730602510485157957234261251691399803452850047142812962686538

SAGE

p = 0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F
K = GF(p)
a = K(0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C)
b = K(0x687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116)
E = EllipticCurve(K, (a, b))
G = E(0x02, 0x1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD)
E.set_order(0x00800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD * 0x1)

PARI/GP

p = 0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F
a = Mod(0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C, p)
b = Mod(0x687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116, p)
E = ellinit([a, b])
E[16][1] = 0x00800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD * 0x1
G = [Mod(0x02, p), Mod(0x1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD, p)]

JSON

{
  "name": "id-tc26-gost-3410-12-512-paramSetB",
  "desc": "RFC7836",
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006F",
    "bits": 512
  },
  "params": {
    "a": {
      "raw": "0x008000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000006C"
    },
    "b": {
      "raw": "0x687D1B459DC841457E3E06CF6F5E2517B97C7D614AF138BCBF85DC806C4B289F3E965D2DB1416D217F8B276FAD1AB69C50F78BEE1FA3106EFB8CCBC7C5140116"
    }
  },
  "generator": {
    "x": {
      "raw": "0x02"
    },
    "y": {
      "raw": "0x1A8F7EDA389B094C2C071E3647A8940F3C123B697578C213BE6DD9E6C8EC7335DCB228FD1EDF4A39152CBCAAF8C0398828041055F94CEEEC7E21340780FE41BD"
    }
  },
  "order": "0x00800000000000000000000000000000000000000000000000000000000000000149A1EC142565A545ACFDB77BD9D40CFA8B996712101BEA0EC6346C54374F25BD",
  "cofactor": "0x1",
  "characteristics": {
    "j_invariant": "3279526492516777515918714136866447726665055949835218722150114206701277040061277147122787695822725918855580899339255833327922367669454014389888618448520937",
    "discriminant": "3168251429939329401500982659836128598832488836312881941454031137145329322102983037116860271709983280267186414249706141598349259183530624792370505272178517",
    "embedding_degree": "1117317327495216424964502083183820510623280485049366114810296786976813669172820430903308958031730602510485157957234261251691399803452850047142812962686538",
    "supersingular": false,
    "trace_of_frobenius": "-149097018916599106931901217895018650162542083271457414743815309640053273077069"
  }
}