Tutorial: Privacy 101, with Trumpets and Truffles - An Introduction to Differential Privacy and Homomorphic Encryption, and Applications in Federated Learning

In an age where data privacy has become a paramount concern, understanding the mechanisms that protect personal information is essential. This 3-hour tutorial offers a comprehensive introduction to two of the most promising tools in privacy-preserving technologies: Differential Privacy and Homomorphic Encryption, with practical applications in Federated Learning. Designed for individuals who are new to the field, this course provides a structured overview that combines theoretical foundations with practical insights, making complex concepts accessible and relevant. The tutorial begins with an introduction and motivation for why privacy matters and why it is difficult to achieve with seemingly sound approaches like anonymization. Then, it presents differential privacy as a statistical indistinguishability problem, which can be achieved through randomization algorithms. We will also discuss how standard DP must face some practical challenges of utility and satisfiability, and introduce approximate-DP as a mitigation strategy. Following this, the tutorial introduces lattice-based Homomorphic Encryption. We will discuss why solving approximate problems in lattices is hard, giving raise to the Learning with Errors paradigm. This leads to explaining some cryptographic primitives that allow us to perform mathematical operations with encrypted data. The tutorial concludes with a discussion on the application of these privacy techniques in Federated Learning, highlighting real-world projects such as TRUMPET and TRUFFLES, which demonstrate the benefits of these privacy-preserving technologies.