An Overview of Post-Quantum Cryptography Families

Quantum computing is a distinct field of computational science that uses principles from quantum mechanics to tackle problems that traditional computing struggles with in speed, size, and complexity. Classical cryptography relies on the complexity of mathematical problems such as large-number factorization, but quantum systems can solve them much faster. This threat necessitates the development and implementation of cryptographic methods resistant to attacks from both classical and quantum systems, known as Post-Quantum Cryptography (PQC). Strong cryptographic algorithms are crucial to counter vulnerabilities in pre-quantum systems. This paper reviews the challenges and solutions for securing communication amid advances in quantum computing. It stresses the urgent need to shift from classical cryptographic systems, which are susceptible to quantum threats, to PQC. The discussion includes theoretical frameworks and practical implementations, covering quantum principles, Quantum Key Distribution (QKD), and standard PQC algorithms. Additionally, it briefly introduces Number Theoretic Transform (NTT) concepts, which enhance polynomial multiplication speed—an essential operation in PQC—by reducing computational complexity from $O\left(n^2\right)$ to $O\left(n\log n\right)$ . The paper demonstrates the NTT/Inverse Number Theoretic Transform (INTT) hardware core in Python, focusing on its application to ML-KEM Polynomial arithmetic. Results indicate that NTT outperforms INTT in execution time and throughput. The paper concludes with an overview of security assumptions, cryptanalysis, and the current status of standardization.