Multivariate Public Key Cryptosystem from Sidon Spaces

TL;DR

This paper introduces a new multivariate public key cryptosystem based on Sidon spaces, which leverages the hardness of the MinRank problem to achieve quantum-resistant security and demonstrates its robustness through theoretical analysis and software implementation.

Contribution

It proposes a novel cryptosystem using Sidon spaces that remains secure against quantum attacks and algebraic vulnerabilities, with experimental validation.

Findings

System is resilient to kernel and minor MinRank attacks

Security relies on the hardness of the MinRank problem

Experimental implementation confirms practical hardness

Abstract

A Sidon space is a subspace of an extension field over a base field in which the product of any two elements can be factored uniquely, up to constants. This paper proposes a new public-key cryptosystem of the multivariate type which is based on Sidon spaces, and has the potential to remain secure even if quantum supremacy is attained. This system, whose security relies on the hardness of the well-known MinRank problem, is shown to be resilient to several straightforward algebraic attacks. In particular, it is proved that the two popular attacks on the MinRank problem, the kernel attack, and the minor attack, succeed only with exponentially small probability. The system is implemented in software, and its hardness is demonstrated experimentally.