New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem

TL;DR

This paper introduces new decoding algorithms for rank metric codes utilizing additional linear information, and demonstrates an effective attack on an LRPC-based cryptosystem by combining these algorithms with a folding technique.

Contribution

It presents novel algorithms for decoding rank metric codes with improved complexity and applies them to break a specific LRPC cryptosystem parameter set.

Findings

Enhanced decoding algorithms for rank metric codes

Feasible attack on LRPC cryptosystem parameters

Improved understanding of code-based cryptosystem vulnerabilities

Abstract

We consider the decoding problem or the problem of finding low weight codewords for rank metric codes. We show how additional information about the codeword we want to find under the form of certain linear combinations of the entries of the codeword leads to algorithms with a better complexity. This is then used together with a folding technique for attacking a McEliece scheme based on LRPC codes. It leads to a feasible attack on one of the parameters suggested in \cite{GMRZ13}.