Information Security and Cryptography

With Additional Background by Oded Goldreich

By: Alon Rosen

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Hardcover | 21 August 2006

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200 Pages

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22.86 x 15.24 x 1.27

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Zero-knowledge proofs are fascinating and extremely useful constructs. Their fascinating nature is due to their seemingly contradictory de?nition; ze- knowledge proofs are convincing and yet yield nothing beyond the validity of the assertion being proved. Their applicability in the domain of cryptography is vast; they are typically used to force malicious parties to behave according to a predetermined protocol. In addition to their direct applicability in cr- tography, zero-knowledge proofs serve as a good benchmark for the study of variousproblemsregardingcryptographicprotocols(e.g.,"securecomposition of protocols"). A fundamental question regarding zero-knowledge protocols refers to the preservation of security (i.e., of the zero-knowledge feature) when many - stances are executed concurrently, and in particular under a purely as- chronous model. The practical importance of this question, in the days of extensive Internet communication, seems clear. It turned out that this qu- tion is also very interesting from a theoretical point of view. In particular, this question served as a benchmark for the study of the security of concurrent executions of protocols and led to the development of techniques for coping with the problems that arise in that setting.

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"Protocols that remain zero-knowledge when many instances are executed concurrently are called concurrent zero-knowledge. This book is very well suited for the reader who wants to know the state of the art of concurrent zero-knowledge proofs. ... The book could be used as a textbook on advanced topics in cryptography. It is highly recommended to the newcomer in the field who wants technical information, and to the researcher in the area who would like a survey on concurrent zero-knowledge." (Yongge Wang, Mathematical Reviews, Issue 2007 m)

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You Can Find This Book In

Non-Fiction Reference, Information & Interdisciplinary Subjects Interdisciplinary Studies Communication Studies Computing & I.T.Computer Security Data Encryption Computer Programming & Software Development Algorithms & Data Structures Research & Information Information theory Computer Science

Mathematical Theory of Computation Databases

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Paperback

Published: 25th November 2010

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A Brief Introduction to Zero-Knowledge (by O.G.)	p. 1
Preliminaries	p. 3
Interactive Proofs and Argument Systems	p. 4
Computational Difficulty and One-Way Functions	p. 6
Computational Indistinguishability	p. 7
Definitional Issues	p. 8
The Simulation Paradigm	p. 9
The Basic Definition	p. 10
Variants	p. 11
Zero-Knowledge Proofs for Every NP-set	p. 15
Constructing Zero-Knowledge Proofs for NP-sets	p. 15
Using Zero-Knowledge Proofs for NP-sets	p. 17
Composing Zero-Knowledge Protocols	p. 18
Sequential Composition	p. 19
Parallel Composition	p. 20
Concurrent Composition (With and Without Timing)	p. 22
Introduction to Concurrent Zero-Knowledge	p. 25
Zero-Knowledge Proof Systems	p. 26
Concurrent Composition of ZK	p. 26
On the Feasibility of cZK	p. 27
The Round-Complexity of cZK	p. 27
From Repetition to Composition	p. 28
A "Typical" ZK Protocol for NP	p. 29
Composition of ZK Protocols	p. 32
A Second Look at the Feasibility of cZK	p. 33
A Troublesome Scheduling	p. 33
The Richardson-Kilian Protocol and Its Analysis	p. 35
Improving the Analysis of the RK Protocol	p. 36
What About Non-Black-Box Simulation?	p. 36
Organization and the Rest of This Book	p. 37
Preliminaries	p. 39
General	p. 39
Basic Notation	p. 39
Probabilistic Notation	p. 39
Computational Indistinguishability	p. 39
Interactive Proofs	p. 40
Zero-Knowledge	p. 41
Witness Indistinguishability	p. 41
Concurrent Zero-Knowledge	p. 42
Black-Box Concurrent Zero-Knowledge	p. 43
Conventions Used in Construction of Simulators	p. 44
Commitment Schemes	p. 46
cZK Proof Systems for NP	p. 49
Blum's Hamiltonicity Protocol	p. 50
The Richardson-Kilian cZK Protocol	p. 51
The Prabhakharan-Rosen-Sahai cZK Protocol	p. 53
Simulating the RK and PRS Protocols - Outline	p. 55
Analyzing the Simulation - Outline	p. 58
The Simulator Runs in Polynomial Time	p. 59
The Simulator's Output is "Correctly" Distributed	p. 59
The Simulator (Almost) Never Gets "Stuck"	p. 59
cZK in Logarithmically Many Rounds	p. 67
Detailed Description of the Simulator	p. 67
The Main Procedure and Ideas	p. 68
The Actual Simulator	p. 74
The Simulator's Running Time	p. 75
The Simulator's Output Distribution	p. 75
The Probability of Getting "Stuck"	p. 77
Counting Bad Random Tapes	p. 83
Special Intervals Are Visited Many Times	p. 90
Extensions	p. 95
Applicability to Other Protocols	p. 95
cZK Arguments Based on Any One-Way Function	p. 96
Applicability to Resettable Zero-Knowledge	p. 98
cZK Arguments with Poly-Logarithmic Efficiency	p. 99
A Simple Lower Bound	p. 101
Proof of Theorem 6.1	p. 101
Schedule, Adversary Verifiers and Decision Procedure	p. 102
Proof of Lemma 6.1.5	p. 105
Existence of Useful Initiation Prefixes	p. 107
The Structure of Good Subtrees	p. 109
Black-Box cZK Requires Logarithmically Many Rounds	p. 111
Proof Outline	p. 112
The High-Level Framework	p. 112
The Schedule and Additional Ideas	p. 114
The Actual Analysis	p. 119
The Actual Proof	p. 119
The Concurrent Adversarial Verifier	p. 119
The Actual Verifier Strategy V_g,h	p. 126
The Decision Procedure for L	p. 130
Performance on no-instances	p. 132
The Cheating Prover	p. 133
The Success Probability of the Cheating Prover	p. 137
Legal Transcripts Yield Useful Block Prefixes	p. 142
Existence of Potentially Useful Block Prefixes	p. 144
Existence of Useful Block Prefixes	p. 152
Conclusions and Open Problems	p. 161
Avoiding the Lower Bounds of Chapter 7	p. 161
Open Problems	p. 162
A Brief Account of Other Developments (by O.G.)	p. 165
Using the Adversary's Program in the Proof of Security	p. 167
Witness Indistinguishability and the FLS-Technique	p. 169
Proofs of Knowledge	p. 171
How to Define Proofs of Knowledge	p. 171
How to Construct Proofs of Knowledge	p. 172
Non-interactive Zero-Knowledge	p. 173
Statistical Zero-Knowledge	p. 174
Transformations	p. 175
Complete Problems and Structural Properties	p. 176
Resettability of a Party's Random-Tape (rZK and rsZK)	p. 176
Zero-Knowledge in Other Models	p. 177
References	p. 179
Table of Contents provided by Publisher. All Rights Reserved.

Information Security and Cryptography

With Additional Background by Oded Goldreich

At a Glance

Hardcover

Industry Reviews

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You Can Find This Book In

Other Editions and Formats

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