Quasi-Cyclic Low-Density Parity-Check Codes in the McEliece Cryptosystem

In this paper, a new variant of the McEliece cryptosystem, based on quasi-cyclic low-density parity-check (QC-LDPC) codes, is studied. In principle, such codes can substitute Goppa codes, originally used by McEliece; their adoption, however, is subject to cryptanalytic evaluation to ensure sufficient system robustness. The authors conclude that some families of QC-LDPC codes, based on circulant permutation matrices, are inapplicable in this context, due to security issues, whilst other codes, based on the "difference families" approach, can be able to ensure a good level of security against intrusions, even if very large lengths are needed.