Lattice-Based Post-Quantum Cryptography: A Comprehensive Guide

The podcast collectively offers a comprehensive overview of lattice-based post-quantum cryptography (PQC), detailing its fundamental principles and practical applications. It explains how traditional cryptographic methods are vulnerable to quantum computers and introduce lattices as a quantum-resistant solution. It discusses the mathematical foundations of lattices, focusing on their "hard problems" like the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP), which form the basis of security. Key algorithms such as Learning With Errors (LWE) and Short Integer Solution (SIS), including their Ring-LWE (RLWE) and Module-LWE (MLWE) variants, are presented as core engines for constructing secure systems. Finally, we discuss the standardisation efforts by NIST, highlighting chosen schemes like CRYSTALS-Kyber (ML-KEM) for key exchange and CRYSTALS-Dilithium (ML-DSA) for digital signatures, alongside implementation challenges like performance, key sizes, and side-channel attacks.