Tom-521 curve from https://eprint.iacr.org/2021/1183.pdf

Parameters

Sources

• ZKAttest: Ring and Group Signatures for existing ECDSA keys

Characteristics

• j-invariant:
  482529792883044310381432738387810625973078366292242962568956589104155231443755832772934786096417507926471853972969222895968837733475850875577301467133664272
• Trace of Frobenius:
  5133182737093516966116292369105062158447915857038956549678982449484591328997963
• Discriminant:
  1991109211791184129566756845238735752114572928978384575053636733088398919379083870089176650703950781274147959163206701237649193373256789970473572867968393144
• Embedding degree:
  2288265886710203238327300266360464405756478433381101803131487819728514394465885350707519880220484851659098770463826952679040662666572214604191342763705019050
• CM-discriminant:
  -28243
• Conductor:
  6268055400574841440667156810254912726834973227558374885183820779126439865891

SAGE

p = 0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249
K = GF(p)
a = K(0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2)
b = K(0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d)
E = EllipticCurve(K, (a, b))
# No generator defined
E.set_order(0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff * 0x01)

PARI/GP

p = 0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249
a = Mod(0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2, p)
b = Mod(0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d, p)
E = ellinit([a, b])
E[16][1] = 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff * 0x01
\\ No generator defined

JSON

{
  "name": "Tom-521",
  "desc": "Tom-521 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": "0x200000000000000000000000000000000000000000000000000000000000000002c54be78524c33584f734a266748b2063accf5028e6778dc5056476d0690853249",
    "bits": 521
  },
  "params": {
    "a": {
      "raw": "0xef6432c21701cc48c63fb9263e14ba76d4a94ba14d173b134e3032b0e2e543180eb6725125992a7d00162a5f57d21918b0766364eeb53c53bb12f405dac1d527e2"
    },
    "b": {
      "raw": "0x3cbc65d1e0245d79703b18e9aaea1ac6d67f87a2cd4bd84b9e6df6a45a979c481825ca5a857270fc890352f9fac7fd6020deaabb28d099718f0f77a4eec222871d"
    }
  },
  "order": "0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
  "cofactor": "0x01",
  "characteristics": {
    "cm_disc": "-28243",
    "conductor": "6268055400574841440667156810254912726834973227558374885183820779126439865891",
    "discriminant": "1991109211791184129566756845238735752114572928978384575053636733088398919379083870089176650703950781274147959163206701237649193373256789970473572867968393144",
    "j_invariant": "482529792883044310381432738387810625973078366292242962568956589104155231443755832772934786096417507926471853972969222895968837733475850875577301467133664272",
    "embedding_degree": "2288265886710203238327300266360464405756478433381101803131487819728514394465885350707519880220484851659098770463826952679040662666572214604191342763705019050",
    "trace_of_frobenius": "5133182737093516966116292369105062158447915857038956549678982449484591328997963"
  }
}