Optimization of the parity-check matrix density in QC-LDPC code-based McEliece cryptosystems
This work addresses a gap in cryptographic design for post-quantum security, offering incremental improvements in parameter selection for code-based cryptosystems.
The paper tackles the problem of optimizing parity-check matrix density in QC-LDPC code-based McEliece cryptosystems, proposing a procedure to select density based on security level and decryption complexity, and provides examples of resulting system parameters.
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.