Parameters

Sources

• Elliptic Curve Cryptography (ECC) Nothing Up My Sleeve (NUMS) Curves and Curve Generation

Characteristics

• j-invariant:
  63443586882444752838319511351138587410933807550953792556950236171595237693864
• Trace of Frobenius:
  36904200015056198187214188655179355935
• Discriminant:
  115792089237316195423570985008687907853269984665640564039457583997805596472403
• Embedding degree:
  28948022309329048855892746252171976963308270116406376960317592454814487570953
• CM-discriminant:
  -461806436970513507795776071208962019617834464011805499237102336028251098834763
• Conductor:
  1

SAGE

p = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff43
K = GF(p)
a = K(0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff40)
b = K(0x25581)
E = EllipticCurve(K, (a, b))
G = E(0x01, 0x696f1853c1e466d7fc82c96cceeedd6bd02c2f9375894ec10bf46306c2b56c77)
E.set_order(0xffffffffffffffffffffffffffffffffe43c8275ea265c6020ab20294751a825 * 0x01)

PARI/GP

p = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff43
a = Mod(0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff40, p)
b = Mod(0x25581, p)
E = ellinit([a, b])
E[16][1] = 0xffffffffffffffffffffffffffffffffe43c8275ea265c6020ab20294751a825 * 0x01
G = [Mod(0x01, p), Mod(0x696f1853c1e466d7fc82c96cceeedd6bd02c2f9375894ec10bf46306c2b56c77, p)]

JSON

{
  "name": "numsp256d1",
  "desc": "",
  "sources": [
    {
      "name": "Elliptic Curve Cryptography (ECC) Nothing Up My Sleeve (NUMS) Curves and Curve Generation",
      "url": "https://tools.ietf.org/html/draft-black-numscurves-02"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff43",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff40"
    },
    "b": {
      "raw": "0x25581"
    }
  },
  "generator": {
    "x": {
      "raw": "0x01"
    },
    "y": {
      "raw": "0x696f1853c1e466d7fc82c96cceeedd6bd02c2f9375894ec10bf46306c2b56c77"
    }
  },
  "order": "0xffffffffffffffffffffffffffffffffe43c8275ea265c6020ab20294751a825",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-461806436970513507795776071208962019617834464011805499237102336028251098834763",
    "conductor": "1",
    "discriminant": "115792089237316195423570985008687907853269984665640564039457583997805596472403",
    "j_invariant": "63443586882444752838319511351138587410933807550953792556950236171595237693864",
    "embedding_degree": "28948022309329048855892746252171976963308270116406376960317592454814487570953",
    "trace_of_frobenius": "36904200015056198187214188655179355935"
  }
}