Lecture 1. Introduction (The Mathematics of Lattice-Based Cryptography

Video lectures for Alfred Menezes's introductory course on the mathematics of lattice-based cryptography. Kyber (ML-KEM) and Dilithium (ML-DSA) are lattice-based cryptosystems that are resistant to attacks by quantum computers. Hardness of the Module-SIS and Module-LWE problems is the basis for the security of Kyber and Dilithium . These lectures describe the connection between lattices and the Module-SIS and Module-LWE problems, thus explaining why Kyber and Dilithium are considered to be lattice-based cryptosystems. Topics covered: Post-quantum cryptography, NIST's PQC standards, Kyber and Dilithium, SIS and LWE problems. Lecture playlist: https://www.youtube.com/playlist?list=PLA1qgQLL41STNFDvPJRqrHtuz0PIEJ4a8 Course web page: https://cryptography101.ca/lattice-based-cryptography/ The slides are available on the course web page. Other cryptography courses: https://cryptography101.ca Slides 00:00 Introduction 00:19 Slide 2: NIST's PQC standards 01:29 Slide 3: Kyber and Dilithium 02:26 Slide 4: Lattice-based cryptosystems 03:33 Slide 5: Course outline 05:05 Slide 6: Course material