Interactive Proofs: The Power of Interaction

This lecture explores the concept of interactive proofs, focusing on topics such as zero-knowledge proofs, parallel composition, sequential composition, and the Goldreich-Micali-Wigderson protocol. It delves into the complexities of cryptographic protocols, soundness, zero-knowledge levels, and the relationship between complexity classes. The instructor discusses the Goldwasser-Micali-Rackoff protocol, graph coloring, and the Graph Isomorphism problem. The lecture also covers the Sigma Protocol, ZK Trick, and the notion of a malicious prover. Additionally, it examines the properties of E-protocols, proof of knowledge, and the implications of protocols as proof of knowledge.