Comparative Study on the McEliece Public-Key Cryptosystem Based on Goppa and QC-MDPC Codes

In recent years, much research has been conducted on quantum computers – machine that exploit the phenomena of quantum mechanics to solve difficult or insoluble mathematical problems for conventional computers. If large-scale quantum computers are built, they will be able to break many of the public key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the internet. Post-quantum cryptography aims to develop secure cryptographic systems against both conventional as well as quantum computers for interacting with existing protocols and communication networks. In this paper we present a public key cryptosystem of McEliece based on the correcting codes, using two types of correcting codes; QC-MDPC and Goppa correcting codes. This latter seems very interesting considering its two characteristics, namely the power of correction and the efficient decoding algorithm which resistant to quantum attacks due to difficulty of decoding a linear code. On the other hand, QC-MDPC cryptosystem code is rapid and more secure than Goppa cryptosystem. © 2021, Springer Nature Switzerland AG.