Curve from https://eprint.iacr.org/2013/325.pdf

Parameters

Sources

• Elligator: Elliptic-curve points indistinguishable from uniform random strings

Characteristics

• j-invariant:
  2690978671320507776905092275615806335130698438665513251393091481162114579959
• Trace of Frobenius:
  45330879683285730139092453152713398836
• Discriminant:
  1836333416361251496393519324128432846709347278129127493981795341638145579585
• Embedding degree:
  904625697166532776746648320380374280092339035279495474023489261773642975600
• CM-discriminant:
  -3104780625450999362585819446753918118449992865572619605369411600236483762515
• Conductor:
  2

SAGE

p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7
K = GF(p)
a = K(0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D)
b = K(0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6)
E = EllipticCurve(K, (a, b))
G = E(0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051, 0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0)
E.set_order(0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971 * 0x04)

PARI/GP

p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7
a = Mod(0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D, p)
b = Mod(0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6, p)
E = ellinit([a, b])
E[16][1] = 0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971 * 0x04
G = [Mod(0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051, p), Mod(0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0, p)]

JSON

{
  "name": "Curve1174",
  "desc": "Curve from https://eprint.iacr.org/2013/325.pdf",
  "sources": [
    {
      "name": "Elligator: Elliptic-curve points indistinguishable from uniform random strings",
      "url": "https://eprint.iacr.org/2013/325"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7",
    "bits": 251
  },
  "params": {
    "a": {
      "raw": "0x486BE25B34C8080922B969257EEB54C404F914A29067A5560BB9AEE0BC67A6D"
    },
    "b": {
      "raw": "0xE347A25BF875DD2F1F12D8A10334D417CC15E77893A99F4BF278CA563072E6"
    }
  },
  "generator": {
    "x": {
      "raw": "0x3BE821D63D2CD5AFE0504F452E5CF47A60A10446928CEAECFD5294F89B45051"
    },
    "y": {
      "raw": "0x66FE4E7B8B6FE152F743393029A61BFB839747C8FB00F7B27A6841C07532A0"
    }
  },
  "order": "0x1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF77965C4DFD307348944D45FD166C971",
  "cofactor": "0x04",
  "characteristics": {
    "cm_disc": "-3104780625450999362585819446753918118449992865572619605369411600236483762515",
    "conductor": "2",
    "discriminant": "1836333416361251496393519324128432846709347278129127493981795341638145579585",
    "j_invariant": "2690978671320507776905092275615806335130698438665513251393091481162114579959",
    "embedding_degree": "904625697166532776746648320380374280092339035279495474023489261773642975600",
    "trace_of_frobenius": "45330879683285730139092453152713398836"
  }
}