Cryptanalysis of a Public Key Encryption Scheme Based on QC-LDPC and QC-MDPC Codes

This letter presents a cryptanalysis of the modified McEliece cryptosystem recently proposed by Moufek et al.. 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 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.