  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.
