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:
  46176913415558528862592191480069677879287716767964574463655728463603723997370
• Trace of Frobenius:
  161780446515958999764292222349558067737
• Discriminant:
  57896044618658097711785492504343953926634992332820282019728792003767411190931
• Embedding degree:
  28948022309329048855892746252171976963236605943152161509982249890803503375733
• CM-discriminant:
  -205411265599729320381766099367521569945690409339341388813247842067801178975643
• Conductor:
  1

SAGE

p = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03
K = GF(p)
a = K(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd00)
b = K(-0x51bd)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x7fffffffffffffffffffffffffffffff864a38283ad2b3dfab8fac983c594aeb * 0x01)

PARI/GP

p = 0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03
a = Mod(0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd00, p)
b = Mod(-0x51bd, p)
E = ellinit([a, b])
E[16][1] = 0x7fffffffffffffffffffffffffffffff864a38283ad2b3dfab8fac983c594aeb * 0x01
\\ No generator defined

JSON

{
  "name": "w-255-mers",
  "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": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd03",
    "bits": 255
  },
  "params": {
    "a": {
      "raw": "0x7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffd00"
    },
    "b": {
      "raw": "-0x51bd"
    }
  },
  "order": "0x7fffffffffffffffffffffffffffffff864a38283ad2b3dfab8fac983c594aeb",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-205411265599729320381766099367521569945690409339341388813247842067801178975643",
    "conductor": "1",
    "discriminant": "57896044618658097711785492504343953926634992332820282019728792003767411190931",
    "j_invariant": "46176913415558528862592191480069677879287716767964574463655728463603723997370",
    "embedding_degree": "28948022309329048855892746252171976963236605943152161509982249890803503375733",
    "trace_of_frobenius": "161780446515958999764292222349558067737"
  }
}