On the equivalence of two post-quantum cryptographic families
Computational Complexity
2024-10-21 v2 Discrete Mathematics
Abstract
The Maximum Likelihood Decoding Problem (MLD) is known to be NP-hard and its complexity is strictly related to the security of some post-quantum cryptosystems, that is, the so-called code-based primitives. Analogously, the Multivariate Quadratic System Problem (MQ) is NP-hard and its complexity is necessary for the security of the so-called multivariate-based primitives. In this paper we present a closed formula for a polynomial-time reduction from any instance of MLD to an instance of MQ, and viceversa. We also show a polynomial-time isomorphism between MQ and MLD, thus demonstrating the direct link between the two post-quantum cryptographic families.
Keywords
Cite
@article{arxiv.2109.05806,
title = {On the equivalence of two post-quantum cryptographic families},
author = {Alessio Meneghetti and Alex Pellegrini and Massimiliano Sala},
journal= {arXiv preprint arXiv:2109.05806},
year = {2024}
}
Comments
Accepted for publication in Annali di Matematica Pura ed Applicata (1923 -)