Code-Based Cryptography in Different Metrics

Speaker: Dr Anna-Lena Horlemann
Affiliation: University of St. Gallen

Abstract

Code-based cryptography is a leading candidate for post-quantum cryptography, relying on the hardness of decoding problems of linear error-correcting codes (over finite fields or finite rings). Traditionally, these systems have employed the Hamming metric to measure the error weights. However, alternative metrics—such as the rank, Lee, and sum-rank metrics—offer new perspectives and potential advantages. Among these, the rank metric is the most extensively studied, with a rich theory and several cryptographic constructions. More recently, the Lee and sum-rank metrics have garnered significant attention, both for their structural properties and cryptographic applications. In this talk, we will give a brief introduction to code-based cryptography and discuss known results and open problems for the different metrics.