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

TL;DR

This paper explores using irregular LDPC codes in the McEliece cryptosystem to enhance error correction and reduce key size, marking a novel approach in post-quantum cryptography.

Contribution

It introduces the first application of irregular LDPC codes and irregular transformation matrices to improve efficiency and key size in the McEliece cryptosystem.

Findings

Irregular LDPC codes outperform regular ones in error correction.

Irregular transformation matrices further reduce public key size.

Enhanced system efficiency demonstrated through simulations.

Abstract

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.