Paper 2021/721
Index Calculus Attacks on Hyperelliptic Jacobians with Effective Endomorphisms
Sulamithe Tsakou and Sorina Ionica
Abstract
For a hyperelliptic curve defined over a finite field $\bbbf_{q^n}$ with $n>1$, the discrete logarithm problem is subject to index calculus attacks. We exploit the endomorphism of the curve to reduce the size of the factorization basis and hence improve the complexity of the index calculus attack for certain families of ordinary elliptic curves and genus 2 hyperelliptic Jacobians defined over finite fields. This approach adds an extra cost when performing operation on the factor basis, but the experiences show that reducing the size of the factor basis allows to have a gain on the total complexity of index calculus algorithm with respect to the generic attacks.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- elliptic curvesindex calculusattack
- Contact author(s)
-
sorina ionica @ u-picardie fr
sulamithe tsakou @ u-picardie fr - History
- 2021-05-31: received
- Short URL
- https://ia.cr/2021/721
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/721,
author = {Sulamithe Tsakou and Sorina Ionica},
title = {Index Calculus Attacks on Hyperelliptic Jacobians with Effective Endomorphisms},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/721},
year = {2021},
url = {https://eprint.iacr.org/2021/721}
}