Securing the Quantum Era: A Comprehensive Review of Post-Quantum Cryptography, Threat Models, Algorithmic Foundations, and Standardization Pathways

Abstract

The advent of fault-tolerant quantum computing precipitates a foundational threat to the security of global digital infrastructure by rendering obsolete the mathematical assumptions underlying classical public-key cryptography. Widely deployed algorithms, including RSA, ECDSA, and Diffie-Hellman, which rely on the computational intractability of integer factorization and discrete logarithm problems, are vulnerable to polynomial-time attacks via Shor's algorithm. Concurrently, Grover's algorithm imposes a quadratic reduction in the security strength of symmetric primitives. In response, Post-Quantum Cryptography (PQC) has emerged as a critical field of research, dedicated to developing cryptographic systems secure against both classical and quantum attacks, while remaining deployable on existing classical hardware. This paper presents a comprehensive and in-depth examination of PQC, analyzing the five principal families: lattice-based, code-based, multivariate, hash-based, and isogeny-based cryptography. Each family is scrutinized through rigorous mathematical exposition, conceptual analysis, comparative performance evaluations, and contemporary security assessments. The study situates PQC within the evolving global threat landscape, provides a detailed analysis of the National Institute of Standards and Technology (NIST) PQC standardization process, and addresses critical implementation challenges such as constrained environments, migration strategies, hybrid cryptographic modes, and the imperative for cryptographic agility. The paper concludes by delineating essential future research directions vital for constructing a robust, quantum-resilient global cryptographic infrastructure.