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 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.Comment: 5 page

About Low DFR for QC-MDPC Decoding

International audienceMcEliece-like code-based key exchange mechanisms using QC-MDPC codes can reach IND-CPA security under hardness assumptions from coding theory, namely quasi-cyclic syndrome decoding and quasi-cyclic codeword finding. To reach higher security requirements, like IND-CCA security, it is necessary in addition to prove that the decoding failure rate (DFR) is negligible, for some decoding algorithm and a proper choice of parameters. Getting a formal proof of a low DFR is a difficult task. Instead, we propose to ensure this low DFR under some additional security assumption on the decoder. This assumption relates to the asymptotic behavior of the decoder and is supported by several other works. We define a new decoder, Backflip, which features a low DFR. We evaluate the Backflip decoder by simulation and extrapolate its DFR under the decoder security assumption. We also measure the accuracy of our simulation data, in the form of confidence intervals, using standard techniques from communication systems

Protograph-based Quasi-Cyclic MDPC Codes for McEliece Cryptosystems

In this paper, ensembles of quasi-cyclic moderatedensity 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 (errorand-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