Low communication 2 prover zero knowledge proofs for NP 1st edition by Cynthia Dwork, Uri Feige, Joe Kilian, Moni Naor, Muli Safra ISBN 3540573401 9783540573401

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ISBN 10:       3540573401
ISBN 13: 978-3540573401
Author:         Cynthia Dwork, Uri Feige, Joe Kilian, Moni Naor, Muli Safra

We exhibit a two-prover perfect zero-knowledge proof system for 3-SAT. In this protocol, the verifier asks a single message to each prover, whose size grows logarithmically in the size of the 3-SAT formula. Each prover’s answer consists of only a constant number of bits. The verifier will always accept correct proofs. Given an unsatisfiable formula S the verifier will reject with probability at least Ω((|S|-max-sat(S))/|S|, where max-sat(S) denotes the maximum number of clauses of S that may be simultaneously satisfied, and |S| denotes the total number of clauses of S. Using a recent result by Arora et al [2], we can construct for any language in NP a protocol with the property that any non-member of the language be rejected with constant probability.

Low communication 2-prover zero-knowledge proofs for NP 1st Table of contents:

Chapter 1: Introduction

• Overview of Zero-Knowledge Proofs
• Importance of Low Communication Protocols
• Prover-Verifier Interactions
• Applications and Use Cases of Zero-Knowledge Proofs

Chapter 2: Background Concepts

• Complexity Classes and NP
• Cryptographic Protocols
• The Zero-Knowledge Property
• Interactive Proofs and Provers
• Definitions and Terminology

Chapter 3: Zero-Knowledge Proofs

• Classical Zero-Knowledge Proofs
• Soundness, Completeness, and Zero-Knowledge
• The Concept of Perfect, Statistical, and Computational Zero-Knowledge
• Protocols for NP Problems

Chapter 4: The 2-Prover Setting

• The Role of Two Provers
• Simultaneous Interaction Model
• Soundness and Zero-Knowledge in Two-Prover Systems
• The Role of a Common Reference String

Chapter 5: Low Communication Complexity

• Communication Complexity in Cryptographic Protocols
• Techniques for Reducing Communication in Zero-Knowledge Proofs
• The Challenge of Low Communication in NP Problems
• Trade-offs Between Communication and Security

Chapter 6: Protocol Design for 2-Prover Zero-Knowledge Proofs

• Constructing Low Communication Protocols
• Approaches to Minimizing Message Exchange
• Analysis of Efficiency and Security
• Case Studies of NP Problems in Low Communication Settings

Chapter 7: Results and Theoretical Insights

• Proven Bounds for Communication Complexity
• Performance of Low Communication 2-Prover Protocols
• Comparison with Other Zero-Knowledge Protocols
• Implications for Cryptographic Efficiency

Chapter 8: Applications of Low Communication Zero-Knowledge Proofs

• Privacy-Preserving Cryptographic Protocols
• Authentication Systems
• Secure Voting Systems
• Blockchain and Cryptocurrencies

Chapter 9: Challenges and Open Problems

• Limitations of Current Techniques
• Improvements for Real-World Applications
• Potential Research Directions
• Future of Low Communication Protocols for NP

Chapter 10: Conclusion

• Summary of Key Findings
• Impact on Cryptography and Security
• The Future of Zero-Knowledge Proofs in Practical Systems

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