  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.
