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

TL;DR

This paper proposes a method to optimize the density of parity-check matrices in QC-LDPC code-based McEliece cryptosystems, balancing security and decryption complexity to improve cryptographic efficiency.

Contribution

It introduces a novel procedure for selecting the parity-check matrix density tailored to security and complexity requirements in QC-LDPC McEliece systems.

Findings

Optimized parity-check matrix densities improve security and efficiency.

Examples demonstrate practical parameter settings for the proposed method.

The approach fills a gap in the design of QC-LDPC-based cryptosystems.

Abstract

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.