Overview of McEliece cryptosystem and its security

Abstract

McEliece cryptosystem (MECS) is one of the oldest public key
cryptosystems, and the oldest PKC that is conjectured to be post-quantum secure.
In this paper we survey the current state of the implementation issues and
security of MECS, and its variants. In the first part we focus on general decoding
problem, structural attacks, and the selection of parameters in general. We
summarize the details of MECS based on irreducible binary Goppa codes, and
review some of the implementation challenges for this system. Furthermore, we
survey various proposals that use alternative codes for MECS, and point out some
attacks on modified systems. Finally, we review notable existing implementations
on low-resource platforms, and conclude with the topic of side channels in the
implementations of MECS.