Moderate Classical McEliece Keys from Quasi-Centrosymmetric Goppa Codes

Abstract

As the development of quantum machines is booming and would threaten our standard cryptography algorithms, a transition period is necessary for the protection of the data processed by our classical machines as well before the arrival of theses machines as after. Recently, to get ahead of the curve, the National Institute of Standards and Technology (NIST) launched the Post Quantum Cryptography Standardization Project, started since late 2016. Among finalists, 3 promising code-theoretic finalist candidates, Classic McEliece, BIKE, and HQC are sent to the fourth round. In this work, to reduce classical McEliece key size without loss of security, we present a new key generation algorithm by introducing new family of codes called quasi-centrosymmetric Goppa codes with a moderate key size for storage optimisation. We also have characterized these codes in the case where the parity matrix is in Cauchy form by giving an algorithm to build them. We ended up giving a detailed analysis of the security against the most known structural attacks by giving the new complexities.