Foundations and Trends® in Theoretical Computer Science > Vol 3 > Issue 1

Probabilistic Proof Systems: A Primer

Oded Goldreich, Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Israel, oded.goldreich@weizmann.ac.il
 
Suggested Citation
Oded Goldreich (2008), "Probabilistic Proof Systems: A Primer", Foundations and TrendsĀ® in Theoretical Computer Science: Vol. 3: No. 1, pp 1-91. http://dx.doi.org/10.1561/0400000023

Published: 08 Aug 2008
© 2008 O. Goldreich
 
Subjects
Cryptography and information security,  Randomness in Computation
 

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In this article:
Conventions and Organization
1 Interactive Proof Systems
2 Zero-Knowledge Proof Systems
3 Probabilistically Checkable Proof Systems
Bibliographic Notes
Acknowledgments
References

Abstract

Various types of probabilistic proof systems have played a central role in the development of computer science in the last couple of decades. These proof systems deviate from the traditional concept of a proof by introducing randomization and interaction into the verification process. Probabilistic proof systems carry an error probability (which is explicitly bounded and can be decreased by repetitions), but they offer various advantages over deterministic proof systems.

This primer concentrates on three types of probabilistic proof systems: interactive proofs, zero-knowledge proofs, and Probabilistically Checkable Proofs (PCP). Surveying the basic results regarding these proof systems, we stress the essential role of randomness in each of them.

DOI:10.1561/0400000023
ISBN: 978-1-60198-152-3
104 pp. $75.00
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ISBN: 978-1-60198-153-0
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Table of contents:
Preface
Conventions and Organization
1: Interactive Proof Systems
2: Zero-Knowledge Proof Systems
3: Probabilistically Checkable Proof Systems
Bibliographic Notes
Bibliography

Probabilistic Proof Systems

Various types of probabilistic proof systems have played a central role in the development of computer science in the last couple of decades. These proof systems deviate from the traditional concept of a proof by introducing randomization and interaction into the verification process. Probabilistic proof systems carry an error probability (which is explicitly bounded and can be decreased by repetitions), but they offer various advantages over deterministic proof systems. This primer concentrates on three types of probabilistic proof systems: interactive proofs, zero-knowledge proofs, and probabilistically checkable proofs (PCP). Surveying the basic results regarding these proof systems, the primer stresses the essential role of randomness in each of them.

 
TCS-023