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Foundations of Cryptography Basic Tools

ISBN-10: 0521791723
ISBN-13: 9780521791724
Edition: 2001
Authors: Oded Goldreich
List price: $83.99
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Description: Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. This text presents a systematic treatment of the foundational issues.

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Book details

List price: $83.99
Copyright year: 2001
Publisher: Cambridge University Press
Publication date: 8/6/2001
Binding: Hardcover
Pages: 392
Size: 7.00" wide x 10.50" long x 0.75" tall
Weight: 1.848
Language: English

Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. This text presents a systematic treatment of the foundational issues.

List of Figures
Preface
Introduction
Cryptography: Main Topics
Encryption Schemes
Pseudorandom Generators
Digital Signatures
Fault-Tolerant Protocols and Zero-Knowledge Proofs
Some Background from Probability Theory
Notational Conventions
Three Inequalities
The Computational Model
P, NP, and NP-Completeness
Probabilistic Polynomial Time
Non-Uniform Polynomial Time
Intractability Assumptions
Oracle Machines
Motivation to the Rigorous Treatment
The Need for a Rigorous Treatment
Practical Consequences of the Rigorous Treatment
The Tendency to Be Conservative
Miscellaneous
Historical Notes
Suggestions for Further Reading
Open Problems
Exercises
Computational Difficulty
One-Way Functions: Motivation
One-Way Functions: Definitions
Strong One-Way Functions
Weak One-Way Functions
Two Useful Length Conventions
Candidates for One-Way Functions
Non-Uniformly One-Way Functions
Weak One-Way Functions Imply Strong Ones
The Construction and Its Analysis (Proof of Theorem 2.3.2)
Illustration by a Toy Example
Discussion
One-Way Functions: Variations
Universal One-Way Function
One-Way Functions as Collections
Examples of One-Way Collections
Trapdoor One-Way Permutations
Claw-Free Functions
On Proposing Candidates
Hard-Core Predicates
Definition
Hard-Core Predicates for Any One-Way Function
Hard-Core Functions
Efficient Amplification of One-Way Functions
The Construction
Analysis
Miscellaneous
Historical Notes
Suggestions for Further Reading
Open Problems
Exercises
Pseudorandom Generators
Motivating Discussion
Computational Approaches to Randomness
A Rigorous Approach to Pseudorandom Generators
Computational Indistinguishability
Definition
Relation to Statistical Closeness
Indistinguishability by Repeated Experiments
Indistinguishability by Circuits
Pseudorandom Ensembles
Definitions of Pseudorandom Generators
Standard Definition of Pseudorandom Generators
Increasing the Expansion Factor
Variable-Output Pseudorandom Generators
The Applicability of Pseudorandom Generators
Pseudorandomness and Unpredictability
Pseudorandom Generators Imply One-Way Functions
Constructions Based on One-Way Permutations
Construction Based on a Single Permutation
Construction Based on Collections of Permutations
Using Hard-Core Functions Rather than Predicates
Constructions Based on One-Way Functions
Using 1-1 One-Way Functions
Using Regular One-Way Functions
Going Beyond Regular One-Way Functions
Pseudorandom Functions
Definitions
Construction
Applications: A General Methodology
Generalizations
Pseudorandom Permutations
Definitions
Construction
Miscellaneous
Historical Notes
Suggestions for Further Reading
Open Problems
Exercises
Zero-Knowledge Proof Systems
Zero-Knowledge Proofs: Motivation
The Notion of a Proof
Gaining Knowledge
Interactive Proof Systems
Definition
An Example (Graph Non-Isomorphism in IP)
The Structure of the Class IP
Augmentation of the Model
Zero-Knowledge Proofs: Definitions
Perfect and Computational Zero-Knowledge
An Example (Graph Isomorphism in PZK)
Zero-Knowledge with Respect to Auxiliary Inputs
Sequential Composition of Zero-Knowledge Proofs
Zero-Knowledge Proofs for NP
Commitment Schemes
Zero-Knowledge Proof of Graph Coloring
The General Result and Some Applications
Second-Level Considerations
Negative Results
On the Importance of Interaction and Randomness
Limitations of Unconditional Results
Limitations of Statistical ZK Proofs
Zero-Knowledge and Parallel Composition
Witness Indistinguishability and Hiding
Definitions
Parallel Composition
Constructions
Applications
Proofs of Knowledge
Definition
Reducing the Knowledge Error
Zero-Knowledge Proofs of Knowledge for NP
Applications
Proofs of Identity (Identification Schemes)
Strong Proofs of Knowledge
Computationally Sound Proofs (Arguments)
Definition
Perfectly Hiding Commitment Schemes
Perfect Zero-Knowledge Arguments for NP
Arguments of Poly-Logarithmic Efficiency
Constant-Round Zero-Knowledge Proofs
Using Commitment Schemes with Perfect Secrecy
Bounding the Power of Cheating Provers
Non-Interactive Zero-Knowledge Proofs
Basic Definitions
Constructions
Extensions
Multi-Prover Zero-Knowledge Proofs
Definitions
Two-Sender Commitment Schemes
Perfect Zero-Knowledge for NP
Applications
Miscellaneous
Historical Notes
Suggestions for Further Reading
Open Problems
Exercises
Background in Computational Number Theory
Prime Numbers
Quadratic Residues Modulo a Prime
Extracting Square Roots Modulo a Prime
Primality Testers
On Uniform Selection of Primes
Composite Numbers
Quadratic Residues Modulo a Composite
Extracting Square Roots Modulo a Composite
The Legendre and Jacobi Symbols
Blum Integers and Their Quadratic-Residue Structure
Brief Outline of Volume
Encryption: Brief Summary
Definitions
Constructions
Beyond Eavesdropping Security
Some Suggestions
Signatures: Brief Summary
Definitions
Constructions
Some Suggestions
Cryptographic Protocols: Brief Summary
Definitions
Constructions
Some Suggestions
Bibliography
Index

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