Paper 2007/428
Isogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves
Benjamin Smith
Abstract
We describe the use of explicit isogenies to reduce Discrete Logarithm Problems (DLPs) on Jacobians of hyperelliptic genus~$3$ curves to Jacobians of non-hyperelliptic genus~$3$ curves, which are vulnerable to faster index calculus attacks. We provide algorithms which compute an isogeny with kernel isomorphic to $(\mathbb{Z}/2\mathbb{Z})^3$ for any hyperelliptic genus~$3$ curve. These algorithms provide a rational isogeny for a positive fraction of all hyperelliptic genus~$3$ curves defined over a finite field of characteristic $p > 3$. Subject to reasonable assumptions, our algorithms provide an explicit and efficient reduction from hyperelliptic DLPs to non-hyperelliptic DLPs for around $18.57\%$ of all hyperelliptic genus~$3$ curves over a given finite field.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- discrete logarithm problemnumber theory
- Contact author(s)
- smith @ lix polytechnique fr
- History
- 2007-11-18: received
- Short URL
- https://ia.cr/2007/428
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/428,
author = {Benjamin Smith},
title = {Isogenies and the Discrete Logarithm Problem on Jacobians of Genus 3 Hyperelliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2007/428},
year = {2007},
note = {\url{https://eprint.iacr.org/2007/428}},
url = {https://eprint.iacr.org/2007/428}
}
