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This paper presents a review of module ring learning with errors-based (MLWE-based) public-key encryption and key-establishment algorithms. In particular, we introduce the preliminaries of public key cryptography, MLWE-based algorithms, and arithmetic operations in post-quantum cryptography. We then focus on analyzing the state-of-the-art hardware architecture designs of CRYSTALS-Kyber at different security levels, including hardware architectures for Kyber-512, Kyber-768, and Kyber-1024. This analysis is dedicated to providing complete guidelines for selecting the most suitable CRYSTALS-Kyber hardware architecture to apply in post-quantum cryptography-based security systems in reality, with different requirements of security levels and hardware efficiency.

An Analysis of Hardware Design of MLWE-Based Public-Key Encryption and Key-Establishment Algorithms