Cryptanalysis of a public key encryption scheme based on QC-LDPC and QC-MDPC codes

TL;DR

This paper presents a cryptanalysis of a modified McEliece cryptosystem based on QC-LDPC and QC-MDPC codes, demonstrating that it is vulnerable due to high weak key probability, thus questioning its security.

Contribution

The paper introduces an effective cryptanalysis method revealing vulnerabilities in a recent QC-LDPC/QC-MDPC based cryptosystem, showing its insecurity.

Findings

High probability of weak keys in the scheme

Ability to decode ciphertext with high probability using the attack

Scheme can be considered insecure due to vulnerabilities

Abstract

This letter presents a cryptanalysis of the modified McEliece cryptosystem recently proposed by Moufek, Guenda and Gulliver [24]. The system is based on the juxtaposition of quasi-cyclic LDPC and quasi-cyclic MDPC codes. The idea of our attack is to find an alternative permutation matrix together with an equivalent LDPC code which allow the decoding of any cipher-text with a very high probability. We also apply a recent technique to determine weak keys [4] for this scheme. The results show that the probability of weak keys is high enough that this variant can be ruled out as a possible secure encryption scheme.