Randomized Decoding of Gabidulin Codes Beyond the Unique Decoding Radius

TL;DR

This paper presents a novel randomized decoding method for Gabidulin codes that extends decoding capabilities beyond the unique decoding radius by using erasures, significantly enhancing decoding efficiency and impacting cryptographic security assessments.

Contribution

It introduces a randomized decoding approach that employs erasures to decode beyond the traditional radius, improving decoding efficiency exponentially over generic methods.

Findings

Decoding beyond the unique radius is feasible with erasures.

The proposed method improves decoding efficiency exponentially.

Implications for cryptosystem security are significant.

Abstract

We address the problem of decoding Gabidulin codes beyond their unique error-correction radius. The complexity of this problem is of importance to assess the security of some rank-metric code-based cryptosystems. We propose an approach that introduces row or column erasures to decrease the rank of the error in order to use any proper polynomial-time Gabidulin code error-erasure decoding algorithm. This approach improves on generic rank-metric decoders by an exponential factor.