On the Usage of LDPC Codes in the McEliece Cryptosystem

In this paper, a new variant of the McEliece cryptosystem, based on Low-Density Parity-Check (LDPC) codes, is studied. Random-based techniques allow to design large families of LDPC codes with equivalent error correction capability; therefore, in principle, such codes can substitute Goppa codes, originally used by McEliece in his cryptosystem. Furthermore, Quasi-Cyclic (QC) LDPC codes can be adopted in order to reduce the key length, thus overcoming the main drawbacks of the original cryptosystem. Their usage, however, must be subject to cryptanalytic evaluation to ensure sufficient system robustness. The author proves that some widespread families of QC-LDPC codes, based on circulant permutation matrices, are inapplicable in this context, due to security issues, whilst other families of codes, based on the “difference families” approach, are not exposed to the same risk. However, another attack is presented that obliges to adopt very large codes in order to ensure a good level of security against intrusions.