Tom-256 curve from https://eprint.iacr.org/2021/1183.pdf

Parameters

Sources

• ZKAttest: Ring and Group Signatures for existing ECDSA keys

Characteristics

• j-invariant:
  4656549606992696232289689989187499370423815418410623725246197941727346939837
• Trace of Frobenius:
  508360670408157092636158920390626029849
• Discriminant:
  80247434141677083092230988426308837398413450568362539892535226351061612564180
• Embedding degree:
  38597363070118749587565815649802524510028714471763438065177877102955699284650
• CM-discriminant:
  -4155
• Conductor:
  7019618127640898221939468283479924503

SAGE

p = 0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117
K = GF(p)
a = K(0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114)
b = K(0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56)
E = EllipticCurve(K, (a, b))
G = E(0x03, 0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d)
E.set_order(0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff * 0x01)

PARI/GP

p = 0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117
a = Mod(0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114, p)
b = Mod(0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56, p)
E = ellinit([a, b])
E[16][1] = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff * 0x01
G = [Mod(0x03, p), Mod(0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d, p)]

JSON

{
  "name": "Tom-256",
  "desc": "Tom-256 curve from https://eprint.iacr.org/2021/1183.pdf",
  "sources": [
    {
      "name": "ZKAttest: Ring and Group Signatures for existing ECDSA keys",
      "url": "https://eprint.iacr.org/2021/1183"
    }
  ],
  "form": "Weierstrass",
  "field": {
    "type": "Prime",
    "p": "0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b117",
    "bits": 256
  },
  "params": {
    "a": {
      "raw": "0xffffffff0000000100000000000000017e72b42b30e7317793135661b1c4b114"
    },
    "b": {
      "raw": "0xb441071b12f4a0366fb552f8e21ed4ac36b06aceeb354224863e60f20219fc56"
    }
  },
  "generator": {
    "x": {
      "raw": "0x03"
    },
    "y": {
      "raw": "0x5a6dd32df58708e64e97345cbe66600decd9d538a351bb3c30b4954925b1f02d"
    }
  },
  "order": "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-4155",
    "conductor": "7019618127640898221939468283479924503",
    "discriminant": "80247434141677083092230988426308837398413450568362539892535226351061612564180",
    "j_invariant": "4656549606992696232289689989187499370423815418410623725246197941727346939837",
    "embedding_degree": "38597363070118749587565815649802524510028714471763438065177877102955699284650",
    "trace_of_frobenius": "508360670408157092636158920390626029849"
  }
}