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 $Y sup 2 = X sup 5 + u X sup 3 + v X$ 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 curvepoint 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},
note = {\url{https://eprint.iacr.org/2008/398}},
url = {https://eprint.iacr.org/2008/398}
}
