Protograph-based Quasi-Cyclic MDPC Codes for McEliece Cryptosystems

TL;DR

This paper introduces protograph-based quasi-cyclic MDPC codes that enhance error correction in McEliece cryptosystems without increasing key size, improving security against decoding attacks.

Contribution

It presents new ensembles of MDPC codes based on protographs, analyzed both asymptotically and via simulations, with improved error correction and security features.

Findings

Significant error correction improvement over existing MDPC codes.

Enhanced robustness against decoding attacks.

Validated performance through density evolution and Monte Carlo simulations.

Abstract

In this paper, ensembles of quasi-cyclic moderate-density parity-check (MDPC) codes based on protographs are introduced and analyzed in the context of a McEliece-like cryptosystem. The proposed ensembles significantly improve the error correction capability of the regular MDPC code ensembles that are currently considered for post-quantum cryptosystems without increasing the public key size. The proposed ensembles are analyzed in the asymptotic setting via density evolution, both under the sum-product algorithm and a low-complexity (error-and-erasure) message passing algorithm. The asymptotic analysis is complemented at finite block lengths by Monte Carlo simulations. The enhanced error correction capability remarkably improves the scheme robustness with respect to (known) decoding attacks.