Advanced Topics in Cryptography

Lecture 2: Doubly Efficient Interactive Proofs

Topics

• Definition
• Example of doubly efficient IP for counting triangles in a graph
• Low-degree extension
• Doubly efficient IP for all bounded depth computations (the GKR protocol)

Readings

• J. Thaler, “Proofs, Arguments, and Zero-Knowledge (PDF),” chapters 3.5, 4.3, 4.6 (2023).
•  S. Goldwasser, G. Rothblum, and Y. T. Kalai, “Delegating Computation: Interactive Proofs for Muggles.” Electronic Colloquium on Computational Complexity, Report No. 108 (2017), ECCC - TR17-108 (PDF).

Lecture Videos

Part 1

Part 2