Cryptanalysis: Decorrelation & Proving Security

This lecture covers the topics of cryptanalysis, specifically focusing on decorrelation techniques and proving security in the context of conventional cryptography. The instructor explains distinguishing random functions, examples of distinguishing problems, decorrelation, first and second orders of decorrelation, matrices, matrix norms, and the random oracle model. The lecture delves into the concept of proving security, including the use of real matrices, matrix norms, and the relationship between vector norms and matrix norms. Various theorems and proofs related to decorrelation, distinguishers, and the Luby-Rackoff theorem are discussed. The lecture concludes with practical examples, such as the Full-Domain Hash (FDH) signature and the Fiat-Shamir signature paradigm.