### Huff's Model for Elliptic Curves

Marc Joye, Mehdi Tibouchi, and Damien Vergnaud

##### Abstract

This paper revisits a model for elliptic curves over Q introduced by Huff in 1948 to study a diophantine problem. Huff's model readily extends over fields of odd characteristic. Every elliptic curve over such a field and containing a copy of Z/4Z×Z/2Z is birationally equivalent to a Huff curve over the original field. This paper extends and generalizes Huff's model. It presents fast explicit formulas for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff curves. Remarkably, the formulas we obtain feature some useful properties, including completeness and independence of the curve parameters.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Contact author(s)
mehdi tibouchi @ normalesup org
History
Short URL
https://ia.cr/2010/383

CC BY

BibTeX

@misc{cryptoeprint:2010/383,
author = {Marc Joye and Mehdi Tibouchi and Damien Vergnaud},
title = {Huff's Model for Elliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2010/383},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/383}},
url = {https://eprint.iacr.org/2010/383}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.