McEliece cryptosystem based on Plotkin construction with QC-MDPC and QC-LDPC codes

TL;DR

This paper introduces a novel McEliece cryptosystem variant that combines QC-LDPC and QC-MDPC codes using Plotkin construction, enhancing security against dual code attacks while reducing public key size.

Contribution

It proposes a new cryptosystem design using concatenated QC-LDPC and QC-MDPC codes with Plotkin construction, addressing vulnerabilities and key size issues.

Findings

Resists dual code and generic decoding attacks

Reduces public key size using quasi-cyclic and Plotkin construction

Demonstrates feasibility of secure code-based cryptography

Abstract

In this paper, we propose a new variant of the McEliece cryptosystem using two families of quasi-cyclic codes: low density parity check codes (QC-LDPC) and moderate density parity check codes (QC-MDPC). Due to the low weight codewords in the dual of LDPC codes, this family of codes is vulnerable to dual code attacks, making it unsuitable for use with the McEliece cryptosystem. However, this is not the case in our proposal, and it is possible by using the (U |U + V ) construction to concatenate LDPC codes with MDPC codes. We will demonstrate that our proposed cryptosystem can withstand dual code and generic decoding attacks, and that the public key can be reduced by leveraging the quasi-cyclic property and the Plotkin construction.