Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.

Parameters

Sources

• Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis

Characteristics

• j-invariant:
  1193904783842132576461800304849826730280618418511274336391995846834170990765840242224465394003336793409392233750372
• Trace of Frobenius:
  2184274201430630331829688577284583194017827823101929639907
• Discriminant:
  9847495414592669296538061489872013099874893943953759017552568018617869215322155954045933029003296406254048508042239
• Embedding degree:
  2461873853648167324134515372468003274968723485988439754387595936104109646247581566367162111452319644609668547791879
• CM-discriminant:
  -34618927871335259336999487706342085293022596660341578048304804428035468331396355251253170573929364508633533796261043
• Conductor:
  1

SAGE

p = 0x3ffaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
a = K(0x3ffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc)
b = K(-0x20a72)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x3ffaffffffffffffffffffffffffffffffffffffffffffffa6eb1cff4bde214d73b321ffd8e82cd160ab86803ebb301d * 0x01)

PARI/GP

p = 0x3ffaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
a = Mod(0x3ffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc, p)
b = Mod(-0x20a72, p)
E = ellinit([a, b])
E[16][1] = 0x3ffaffffffffffffffffffffffffffffffffffffffffffffa6eb1cff4bde214d73b321ffd8e82cd160ab86803ebb301d * 0x01
\\ No generator defined

JSON

{
  "name": "w-382-mont",
  "desc": "Curve from https://eprint.iacr.org/2014/130.pdf. No generator present.",
  "sources": [
    {
      "name": "Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis",
      "url": "https://eprint.iacr.org/2014/130"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x3ffaffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
    "bits": 382
  },
  "params": {
    "a": {
      "raw": "0x3ffafffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc"
    },
    "b": {
      "raw": "-0x20a72"
    }
  },
  "order": "0x3ffaffffffffffffffffffffffffffffffffffffffffffffa6eb1cff4bde214d73b321ffd8e82cd160ab86803ebb301d",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-34618927871335259336999487706342085293022596660341578048304804428035468331396355251253170573929364508633533796261043",
    "conductor": "1",
    "discriminant": "9847495414592669296538061489872013099874893943953759017552568018617869215322155954045933029003296406254048508042239",
    "j_invariant": "1193904783842132576461800304849826730280618418511274336391995846834170990765840242224465394003336793409392233750372",
    "embedding_degree": "2461873853648167324134515372468003274968723485988439754387595936104109646247581566367162111452319644609668547791879",
    "trace_of_frobenius": "2184274201430630331829688577284583194017827823101929639907"
  }
}