Generating genus two hyperelliptic curves over large characteristic finite fields

Takakazu Satoh

Paper 2008/398

Generating genus two hyperelliptic curves over large characteristic finite fields

Takakazu Satoh

Abstract

In hyperelliptic curve cryptography, finding a suitable hyperelliptic curve is an important fundamental problem. One of necessary conditions is that the order of its Jacobian is a product of a large prime number and a small number. In the paper, we give a probabilistic polynomial time algorithm to test whether the Jacobian of the given hyperelliptic curve of the form satisfies the condition and, if so, gives the largest prime factor. Our algorithm enables us to generate random curves of the form until the order of its Jacobian is almost prime in the above sense. A key idea is to obtain candidates of its zeta function over the base field from its zeta function over the extension field where the Jacobian splits.

Note: Results of numerical experiments with cryptographic size parameters are added. Some new references are added.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: hyperelliptic curve point counting
Contact author(s): satohaar @ mathpc-satoh math titech ac jp
History: 2008-10-31: last of 2 revisions; 2008-09-24: received; See all versions
Short URL: https://ia.cr/2008/398
License: CC BY

BibTeX

@misc{cryptoeprint:2008/398,
      author = {Takakazu Satoh},
      title = {Generating genus two hyperelliptic curves over large characteristic finite fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/398},
      year = {2008},
      url = {https://eprint.iacr.org/2008/398}
}