Protograph-based Quasi-Cyclic MDPC Codes for McEliece Cryptosystems

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 ensembles are obtained by threshold optimization (via density evolution analysis), both under the sum-product algorithm and a low-complexity (error-and-erasure) message passing algorithm. The enhanced error correction capability remarkably improves the scheme robustness with respect to (known) decoding attacks.