Review of quantum theories for the design of post-quantum cryptosystems: CRYSTALS-Kyber as a case study
Yaser Alkurdi, Qasem S. Abu Al-Haija, Mustafa A. Al-Fayoumi · IET conference proceedings. · 2025
Powerful new computers based on the principles of quantum mechanics could crack the codes that safeguard our information today. The National Institute of Standards and Technology is running a competition to find more secure encryption methods to address this future challenge. CRYSTALS-Kyber is a messaging scramble Algorithm built with a complex structure called a lattice. This design is considered secure against powerful quantum computers because there is no known shortcut for them to break the code efficiently, unlike some other classical encryption Algorithms. In this paper, we introduce primitive information about quantum characteristics, computation, and main gate circuits, as well as the quantum theories for the design of post-quantum cryptosystems. Then, we listed the main key players in the quantum field and their achievements. We also compared the programming platforms used in developing programs in a quantum environment. Finally, we focused on cryptography applications and showed some of the mathematics background required to build knowledge for post-quantum cryptography algorithms, especially the CRYSTALS-Kyber algorithms and its core block Number Theoretic Transformation (NTT).