Decoding supercodes of Gabidulin codes and applications to cryptanalysis

TL;DR

This paper extends decoding techniques for Gabidulin codes to supercodes, enabling polynomial-time cryptanalysis of certain rank-metric encryption schemes, revealing vulnerabilities in their security assumptions.

Contribution

It introduces a method to decode supercodes of Gabidulin codes with reduced radius and applies it to break specific rank-metric encryption schemes.

Findings

Polynomial-time attacks on RAMESSES and LIGA encryption schemes

Extended decoder for supercodes of Gabidulin codes

Decreased decoding radius for supercodes

Abstract

This article discusses the decoding of Gabidulin codes and shows how to extend the usual decoder to any supercode of a Gabidulin code at the cost of a significant decrease of the decoding radius. Using this decoder, we provide polynomial time attacks on the rank-metric encryption schemes RAMESSES and LIGA.