Security in Post-Quantum Era: A Comprehensive Survey on Lattice-Based Algorithms

Lattice-based post-quantum cryptography (PQC) has attracted significant attention as a promising solution to the security challenges posed by quantum computing. Unlike traditional cryptographic algorithms, lattice-based schemes are expected to remain secure even in the presence of quantum attacks, making them essential for securing future data. Despite their strong theoretical foundations, lattice-based schemes face several practical challenges, particularly in optimizing performance and scalability for real-world applications. This survey provides a novel taxonomy that categorizes lattice-based PQC designs, with an emphasis on computational paradigms and security considerations. We systematically evaluate lattice-based PQC implementations across both software platforms, including central processing units and graphics processing units, as well as hardware platforms like field-programmable gate arrays and application-specific integrated circuits, highlighting their strengths and limitations. In addition, we explore the practical applications of lattice-based cryptography in fields such as secure communication, critical infrastructure, privacy-preserving data analytics, artificial intelligence, and trust and authentication systems. By offering a comprehensive overview of the current state of lattice-based PQC, this survey aims to provide valuable insights into the ongoing advancements and future research directions in the field as we transition to a post-quantum era.