Lattice-Based Algorithms for Post-Quantum Cryptography

An in-depth introduction to lattice-based cryptography that traces how research advances led to NIST standards

NIST (National Institute of Standards and Technology) anticipates that beyond 2035, current encryption and signature schemes will be vulnerable to quantum attacks and recommends immediate transition to quantum-resistant algorithms. Lattice-Based Algorithms for Post-Quantum Cryptography traces the research path from computationally hard lattice problems to practical algorithms now standardized by NIST, presenting the mathematical principles and algorithm families that define this field.

Detailed treatments of NIST standards—including Dilithium, Kyber, and Falcon—accompany thorough analysis of Learning With Errors, Short Integer Solution, and their variants: Ring-LWE, Ring-SIS, Module-LWE, Module-SIS, LWR, and Order-LWE. The book presents key cryptographic schemes built on these problems alongside lattice structures, properties, and the seminal algorithms that established lattice-based cryptography as a credible solution.

Readers will also find:

• Security properties and categories of attacks on cryptographic schemes providing context for evaluating the resilience of lattice-based constructions against adversaries
• Coverage tracing how theoretical lattice research progressed into efficient practical algorithms suitable for NIST standardization processes
• An exploration of quantum algorithms—including Shor's and Grover's algorithms—revealing how sufficiently powerful quantum computers could challenge the security foundations of RSA, Diffie-Hellman key exchange, and elliptic-curve cryptographic systems
• Worked examples and problems throughout the mathematical foundations designed to facilitate self-directed study of core lattice concepts

Designed for graduate and senior undergraduate students in computer science, engineering, electrical engineering, and applied mathematics, this book also serves engineers and developers in industry and research institutions preparing to implement quantum-resistant cryptographic solutions in production systems.