Lattice-Based Vulnerabilities in Lee Metric Post-Quantum Cryptosystems

TL;DR

This paper investigates potential vulnerabilities of Lee metric-based McEliece cryptosystems to lattice-based attacks, addressing security concerns in post-quantum cryptography with smaller key sizes.

Contribution

It provides the first analysis of lattice-based attack vulnerabilities on Lee metric McEliece cryptosystems, highlighting security considerations for alternative metrics.

Findings

Lee metric cryptosystems may be susceptible to lattice-based attacks

Smaller key sizes could compromise security

Analysis informs future cryptosystem design

Abstract

Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two prominent approaches, both heavily studied within the NIST standardization project. Code-based cryptography -- most prominently exemplified by the McEliece cryptosystem -- is based on the hardness of decoding random linear error-correcting codes. Despite the McEliece cryptosystem having been unbroken for several decades, it suffers from large key sizes, which has led to exploring variants using metrics than the Hamming metric, such as the Lee metric. This alternative metric may allow for smaller key sizes, but requires further analysis for potential vulnerabilities to lattice-based attack techniques. In this paper, we consider a generic Lee metric based McEliece type cryptosystem and evaluate its security against lattice-based attacks.