On the Post-Quantum Understanding of Lattice Problems

Abstract

This thesis explores key literature on lattice-based post-quantum cryptography and its elements. Chapter 2 introduces key computational concepts, including complexity theory and various models of computation, to establish the theoretical basis for cryptographic security. Chapter 3 provides an overview of classical cryptographic techniques, setting the stage for the transition to quantum-resistant approaches. Chapters 4 and 5 investigate lattice theory and its associated hard problems. Chapter 6 focuses on classical algorithms for lattice reduction that are relevant to both analyzing and solving lattice-based cryptographic problems. Appendices A and B supplement the main content with relevant mathematical back- ground and introductory concepts in quantum computing.