Protograph-based Quasi-Cyclic MDPC Codes for McEliece Cryptosystems
This work addresses security vulnerabilities in post-quantum cryptography for applications requiring efficient encryption.
The paper tackles the problem of improving error correction in McEliece cryptosystems by introducing protograph-based quasi-cyclic MDPC code ensembles, which enhance robustness against decoding attacks without increasing public key size.
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.