Tom-384 curve from https://eprint.iacr.org/2021/1183.pdf

Parameters

Sources

• ZKAttest: Ring and Group Signatures for existing ECDSA keys

Characteristics

• j-invariant:
  326462434825228256235579647892697736227757759368012541919936456457937698577614429313939851016653953232755169675813
• Trace of Frobenius:
  -8254077619909260646185522759808830509245368802333014026297
• Discriminant:
  13076868080412601760417078185553024353771265319943610679946121181768375298310931100780088601623229035448248142310378
• Embedding degree:
  39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112318
• CM-discriminant:
  -619
• Conductor:
  380201093441490505678902542719199835054253522446560116525

SAGE

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5
K = GF(p)
a = K(0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba)
b = K(0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff * 0x01)

PARI/GP

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5
a = Mod(0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba, p)
b = Mod(0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b, p)
E = ellinit([a, b])
E[16][1] = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff * 0x01
\\ No generator defined

JSON

{
  "name": "Tom-384",
  "desc": "Tom-384 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": "0xfffffffffffffffffffffffffffffffffffffffffffffffeaf5f689f8669fb41b08d5f5edffd26599c434bbd978917c5",
    "bits": 384
  },
  "params": {
    "a": {
      "raw": "0x821dfdc940e7f074ac481f8b2870c48962cce56abd72dfc42813a944cea15df78dc0a2d97fbf031ed26c9076826940ba"
    },
    "b": {
      "raw": "0x9b5b584b655fdcb087d37f8c4fee893c0499223db5e004c674ea0dee48a4ec0c9e9f684099f2a51c62a2cce400cb1e4b"
    }
  },
  "order": "0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-619",
    "conductor": "380201093441490505678902542719199835054253522446560116525",
    "discriminant": "13076868080412601760417078185553024353771265319943610679946121181768375298310931100780088601623229035448248142310378",
    "j_invariant": "326462434825228256235579647892697736227757759368012541919936456457937698577614429313939851016653953232755169675813",
    "embedding_degree": "39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112318",
    "trace_of_frobenius": "-8254077619909260646185522759808830509245368802333014026297"
  }
}