Ali Alwan: Post-Quantum cryptography and McElliece Cryptosystem

Abstract.

The emergence of quantum computers threatens the security of many current public key cryptosystems (PKCs) by enabling quantum algorithms that can break them. Post-quantum cryptography (PQC) seeks to address this challenge with both innovative and time-tested cryptographic systems. Among these is the McEliece Key Encapsulation Mechanism (KEM), which utilizes Goppa codes, a type of error-correcting code with a long history of security. This paper will explore the construction of Goppa codes, the implementation of the McEliece KEM, and an analysis of information set decoding—the most extensively studied attack method against these systems. Additionally, we will discuss the implications of quantum algorithms on the security of McEliece KEM.