Paper 2017/1236 Original: eprint.iacr.org/2017/1236 ↗
Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
Abstract
In August 2015 the cryptographic world was shaken by a sudden and surprising announcement by the US National Security Agency (NSA) concerning plans to transition to post-quantum algorithms. Since this announcement post-quantum cryptography has become a topic of primary interest for several standardization bodies. The transition from the currently deployed public-key algorithms to post-quantum algorithms has been found to be challenging in many aspects. In particular the problem of evaluating the quantum-bit security of such post-quantum cryptosystems remains vastly open. Of course this question is of primarily concern in the process of standardizing the post-quantum cryptosystems. In this paper we consider the quantum security of the problem of solving a system of $m$ Boolean multivariate quadratic equations in $n$ variables (MQ$_2$); a central problem in post-quantum cryptography. When $n=m$, under a natural algebraic assumption, we present a Las-Vegas quantum algorithm solving MQ$_2$ that requires the evaluation of, on average, $O(2^{0.462n})$ quantum gates. To our knowledge this is the fastest algorithm for solving MQ$_2$.
Metadata
- Available format(s)
PDF- Publication info
- Preprint.
- History
- 2017-12-22: last updated
- 2017-12-22: published
- Short URL
- https://ia.cr/2017/1236
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2017/1236,
author = {Jean-Charles Faugère and Kelsey Horan and Delaram Kahrobaei and Marc Kaplan and Elham Kashefi and Ludovic Perret},
title = {Fast Quantum Algorithm for Solving Multivariate Quadratic Equations},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/1236},
year = {2017},
url = {https://eprint.iacr.org/2017/1236}
}