On the equivalence of two post-quantum cryptographic families

Alessio Meneghetti; Alex Pellegrini; Massimiliano Sala

doi:10.1007/s10231-022-01267-x

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arXiv · 2109.05806

On the equivalence of two post-quantum cryptographic families

Alessio Meneghetti·Alex Pellegrini·Massimiliano Sala

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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.

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Alessio Meneghetti, Alex Pellegrini, Massimiliano Sala. 2021-09-13. On the equivalence of two post-quantum cryptographic families. https://doi.org/10.1007/s10231-022-01267-x

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