Paper 2017/372
A crossbred algorithm for solving Boolean polynomial systems
Antoine Joux and Vanessa Vitse
Abstract
We consider the problem of solving multivariate systems of Boolean polynomial equations: starting from a system of $m$ polynomials of degree at most $d$ in $n$ variables, we want to find its solutions over $\F_2$. Except for $d=1$, the problem is known to be NP-hard, and its hardness has been used to create public cryptosystems; this motivates the search for faster algorithms to solve this problem. After reviewing the state of the art, we describe a new algorithm and show that it outperforms previously known methods in a wide range of relevant parameters. In particular, the first named author has been able to solve all the Fukuoka Type~I MQ challenges, culminating with the resolution of a system of 148 quadratic equations in 74 variables in less than a day (and with a lot of luck).
Metadata
- Available format(s)
-
PDF
- Publication info
- Preprint.
- Keywords
- multivariate polynomial systemsGroebner basisXLmultivariate cryptographyalgebraic cryptanalysis
- Contact author(s)
- vanessa vitse @ univ-grenoble-alpes fr
- History
- 2017-04-28: received
- Short URL
- https://ia.cr/2017/372
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2017/372,
author = {Antoine Joux and Vanessa Vitse},
title = {A crossbred algorithm for solving Boolean polynomial systems},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/372},
year = {2017},
url = {https://eprint.iacr.org/2017/372}
}
