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In this paper, we propose a new variant of the McEliece cryptosystem usingtwo families of quasi-cyclic codes: low density parity check codes (QC-LDPC)and moderate density parity check codes (QC-MDPC). Due to the low weightcodewords in the dual of LDPC codes, this family of codes is vulnerable to dualcode attacks, making it unsuitable for use with the McEliece cryptosystem.However, this is not the case in our proposal, and it is possible by using the(U |U + V ) construction to concatenate LDPC codes with MDPC codes. We willdemonstrate that our proposed cryptosystem can withstand dual code and genericdecoding attacks, and that the public key can be reduced by leveraging thequasi-cyclic property and the Plotkin construction.

McEliece cryptosystem based on Plotkin construction with QC-MDPC and QC-LDPC codes