Improving the efficiency of the LDPC code-based McEliece cryptosystem through irregular codes

We consider the framework of the McEliece cryptosystem based on LDPC codes, which is a promising post-quantum alternative to classical public key cryptosystems. The use of LDPC codes in this context allows to achieve good security levels with very compact keys, which is an important advantage over the classical McEliece cryptosystem based on Goppa codes. However, only regular LDPC codes have been considered up to now, while some further improvement can be achieved by using irregular LDPC codes, which are known to achieve better error correction performance than regular LDPC codes. This is shown in this paper, for the first time at our knowledge. The possible use of irregular transformation matrices is also investigated, which further increases the efficiency of the system, especially in regard to the public key size.Comment: 6 pages, 3 figures, presented at ISCC 201

Optimization of the parity-check matrix density in QC-LDPC code-based McEliece cryptosystems

Low-density parity-check (LDPC) codes are one of the most promising families of codes to replace the Goppa codes originally used in the McEliece cryptosystem. In fact, it has been shown that by using quasi-cyclic low-density parity-check (QC-LDPC) codes in this system, drastic reductions in the public key size can be achieved, while maintaining fixed security levels. Recently, some proposals have appeared in the literature using codes with denser parity-check matrices, named moderate-density parity-check (MDPC) codes. However, the density of the parity-check matrices to be used in QC-LDPC code-based variants of the McEliece cryptosystem has never been optimized. This paper aims at filling such gap, by proposing a procedure for selecting the density of the private parity-check matrix, based on the security level and the decryption complexity. We provide some examples of the system parameters obtained through the proposed technique.Comment: 10 pages, 4 figures. To be presented at IEEE ICC 2013 - Workshop on Information Security over Noisy and Lossy Communication Systems. Copyright transferred to IEE