Multivariate Public Key Cryptosystem from Sidon Spaces
This addresses the need for secure cryptography in a post-quantum era, though it appears incremental as it builds on existing multivariate and MinRank frameworks.
The paper tackles the problem of designing a quantum-resistant public-key cryptosystem by proposing a new multivariate cryptosystem based on Sidon spaces, which is shown to be resilient to algebraic attacks and experimentally validated for hardness.
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.