A Comparison of Point Counting methods for Hyperelliptic Curves over Prime Fields and Fields of Characteristic 2

Colm O hEigeartaigh

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Paper 2004/241

A Comparison of Point Counting methods for Hyperelliptic Curves over Prime Fields and Fields of Characteristic 2

Colm O hEigeartaigh

Abstract

Computing the order of the Jacobian of a hyperelliptic curve remains a hard problem. It is usually essential to calculate the order of the Jacobian to prevent certain sub-exponential attacks on the cryptosystem. This paper reports on the viability of implementations of various point-counting techniques. We also report on the scalability of the algorithms as the fields grow larger.

Note: Faulty submission title

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Hyperelliptic Curve Cryptography lattices point counting Jacobian
Contact author(s): coheigeartaigh @ computing dcu ie
History: 2004-09-27: revised; 2004-09-20: received; See all versions
Short URL: https://ia.cr/2004/241
License: CC BY

BibTeX

@misc{cryptoeprint:2004/241,
      author = {Colm O hEigeartaigh},
      title = {A Comparison of Point Counting methods for Hyperelliptic Curves over Prime Fields and Fields of Characteristic 2},
      howpublished = {Cryptology ePrint Archive, Paper 2004/241},
      year = {2004},
      note = {\url{https://eprint.iacr.org/2004/241}},
      url = {https://eprint.iacr.org/2004/241}
}