Explore an in-depth lecture on efficient zero-knowledge proof systems derived from interactive proofs. Delve into the fundamentals of zero-knowledge proofs, efficiency measures, and existing constructions. Examine the doubly efficient interactive proof system [GKR15] and the Sumcheck Protocol. Analyze prover time complexities for Sumcheck on multilinear polynomials and the GKR protocol. Discover a new algorithm for GKR Prover Phase 1, including performance matrices and protocol properties. Investigate leakage issues in GKR proof and compare prior approaches to achieving zero knowledge with the presenter's novel method. Study the argument system derived from GKR [ZGK+17] and learn how to remove trusted setup. Evaluate the complexity of the new polynomial commitment and see how all components fit together. Conclude with a comparison to other zero-knowledge proof systems, gaining a comprehensive understanding of state-of-the-art techniques in this critical area of cryptography and security. Read more