ADMM and Reproducing Sum-Product Decoding Algorithm Applied to QC-MDPC Code-based McEliece Cryptosystems

QC-MDPC (quasi cyclic moderate density parity check) code-based McEliece cryptosystems are considered to be one of the candidates for post-quantum cryptography. Decreasing DER (decoding error rate) is one of important factor for their security, since recent attacks to these cryptosystems effectively use DER information. In this paper, we pursue the possibility of optimization-base decoding, concretely we examine ADMM (alternating direction method of multipliers), a recent developing method in optimization theory. Further, RSPA (reproducing sum-product algorithm), which efficiently reuse outputs of SPA (sum-product algorithm) is proposed for the reduction of execution time in decoding. By numerical simulations, we show that the proposing scheme shows considerable decrement in DER compared to the conventional decoding methods such as BF (bit-flipping algorithm) variants or SPA

Improved iterative decoding of QC-MDPC codes in the McEliece public key cryptosystem

We improve iterative decoding of the moderate density parity-check codes, recently suggested as code candidates in the McEliece public key cryptosystem. In case of bit-flipping (BF) decoder failure, the code parity-check matrix is extended by adding auxiliary variable nodes based on reliability information from the BF decoder. Then iterative decoding is applied to the extended parity-check matrix. The proposed decoding algorithm is analyzed and its frame error rate performance is compared to the same performance of both the best implementations of BF decoding and its modifications. It is demonstrated an improved performance for the iterative decoding step in decryption, which allows to increase the resistance against recent attacks based on taking advantage of the somewhat large failure probability of the BF algorithm