Hindering reaction attacks by using monomial codes in the McEliece cryptosystem

TL;DR

This paper proposes using monomial codes in the McEliece cryptosystem to prevent reaction attacks that exploit the distance spectrum of private codes, enhancing cryptographic security.

Contribution

It introduces monomial codes with unique distance spectra and proves their resistance to existing reaction attacks in the McEliece cryptosystem.

Findings

Monomial codes have a unique and complete distance spectrum.

Recovery of secret keys reduces to a clique-finding problem.

Current reaction attacks are ineffective against monomial codes.

Abstract

In this paper we study recent reaction attacks against QC-LDPC and QC-MDPC code-based cryptosystems, which allow an opponent to recover the private parity-check matrix through its distance spectrum by observing a sufficiently high number of decryption failures. We consider a special class of codes, known as monomial codes, to form private keys with the desirable property of having a unique and complete distance spectrum. We verify that for these codes the problem of recovering the secret key from the distance spectrum is equivalent to that of finding cliques in a graph, and use this equivalence to prove that current reaction attacks are not applicable when codes of this type are used in the McEliece cryptosystem.