Foundations of cryptography :: basic tools /
Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cr...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, U.K. ; New York :
Cambridge University Press,
2001.
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs. The emphasis is on the clarification of fundamental concepts and on demonstrating the feasibility of solving cryptographic problems, rather than on describing ad-hoc approaches. The book is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful. |
| Beschreibung: | Title from title screen. |
| Beschreibung: | 1 online resource |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 1280430060 9781280430060 0511546890 9780511546891 9781461949176 1461949173 |
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| 245 | 1 | 0 | |a Foundations of cryptography : |b basic tools / |c Oded Goldreich. |
| 260 | |a Cambridge, U.K. ; |a New York : |b Cambridge University Press, |c 2001. | ||
| 300 | |a 1 online resource | ||
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| 500 | |a Title from title screen. | ||
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| 520 | |a Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs. The emphasis is on the clarification of fundamental concepts and on demonstrating the feasibility of solving cryptographic problems, rather than on describing ad-hoc approaches. The book is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful. | ||
| 505 | 0 | 0 | |g 1.1.1. |t Encryption Schemes |g 2 -- |g 1.1.2. |t Pseudorandom Generators |g 3 -- |g 1.1.3. |t Digital Signatures |g 4 -- |g 1.1.4. |t Fault-Tolerant Protocols and Zero-Knowledge Proofs |g 6 -- |g 1.2. |t Some Background from Probability Theory |g 8 -- |g 1.2.1. |t Notational Conventions |g 8 -- |g 1.2.2. |t Three Inequalities |g 9 -- |g 1.3. |t Computational Model |g 12 -- |g 1.3.1. |t P, NP, and NP-Completeness |g 12 -- |g 1.3.2. |t Probabilistic Polynomial Time |g 13 -- |g 1.3.3. |t Non-Uniform Polynomial Time |g 16 -- |g 1.3.4. |t Intractability Assumptions |g 19 -- |g 1.3.5. |t Oracle Machines |g 20 -- |g 1.4. |t Motivation to the Rigorous Treatment |g 21 -- |g 1.4.1. |t Need for a Rigorous Treatment |g 21 -- |g 1.4.2. |t Practical Consequences of the Rigorous Treatment |g 23 -- |g 1.4.3. |t Tendency to Be Conservative |g 24 -- |g 1.5.1. |t Historical Notes |g 25 -- |g 1.5.3. |t Open Problems |g 27 -- |g 2 |t Computational Difficulty |g 30 -- |g 2.1. |t One-Way Functions: Motivation |g 31 -- |g 2.2. |t One-Way Functions: Definitions |g 32 -- |g 2.2.1. |t Strong One-Way Functions |g 32 -- |g 2.2.2. |t Weak One-Way Functions |g 35 -- |g 2.2.3. |t Two Useful Length Conventions |g 35 -- |g 2.2.4. |t Candidates for One-Way Functions |g 40 -- |g 2.2.5. |t Non-Uniformly One-Way Functions |g 41 -- |g 2.3. |t Weak One-Way Functions Imply Strong Ones |g 43 -- |g 2.3.1. |t Construction and Its Analysis (Proof of Theorem 2.3.2) |g 44 -- |g 2.3.2. |t Illustration by a Toy Example |g 48 -- |g 2.4. |t One-Way Functions: Variations |g 51 -- |g 2.4.1. |t Universal One-Way Function |g 52 -- |g 2.4.2. |t One-Way Functions as Collections |g 53 -- |g 2.4.3. |t Examples of One-Way Collections |g 55 -- |g 2.4.4. |t Trapdoor One-Way Permutations |g 58 -- |g 2.4.5. |t Claw-Free Functions |g 60 -- |g 2.4.6. |t On Proposing Candidates |g 63 -- |g 2.5. |t Hard-Core Predicates |g 64 -- |g 2.5.2. |t Hard-Core Predicates for Any One-Way Function |g 65 -- |g 2.5.3. |t Hard-Core Functions |g 74 -- |g 2.6. |t Efficient Amplification of One-Way Functions |g 78 -- |g 2.6.1. |t Construction |g 80 -- |g 2.6.2. |t Analysis |g 81 -- |g 2.7.1. |t Historical Notes |g 89 -- |g 3 |t Pseudorandom Generators |g 101 -- |g 3.1. |t Motivating Discussion |g 102 -- |g 3.1.1. |t Computational Approaches to Randomness |g 102 -- |g 3.1.2. |t A Rigorous Approach to Pseudorandom Generators |g 103 -- |g 3.2. |t Computational Indistinguishability |g 103 -- |g 3.2.2. |t Relation to Statistical Closeness |g 106 -- |g 3.2.3. |t Indistinguishability by Repeated Experiments |g 107 -- |g 3.2.4. |t Indistinguishability by Circuits |g 111 -- |g 3.2.5. |t Pseudorandom Ensembles |g 112 -- |g 3.3. |t Definitions of Pseudorandom Generators |g 112 -- |g 3.3.1. |t Standard Definition of Pseudorandom Generators |g 113 -- |g 3.3.2. |t Increasing the Expansion Factor |g 114 -- |g 3.3.3. |t Variable-Output Pseudorandom Generators |g 118 -- |g 3.3.4. |t Applicability of Pseudorandom Generators |g 119 -- |g 3.3.5. |t Pseudorandomness and Unpredictability |g 119 -- |g 3.3.6. |t Pseudorandom Generators Imply One-Way Functions |g 123 -- |g 3.4. |t Constructions Based on One-Way Permutations |g 124 -- |g 3.4.1. |t Construction Based on a Single Permutation |g 124 -- |g 3.4.2. |t Construction Based on Collections of Permutations |g 131 -- |g 3.4.3. |t Using Hard-Core Functions Rather than Predicates |g 134 -- |g 3.5. |t Constructions Based on One-Way Functions |g 135 -- |g 3.5.1. |t Using 1-1 One-Way Functions |g 135 -- |g 3.5.2. |t Using Regular One-Way Functions |g 141 -- |g 3.5.3. |t Going Beyond Regular One-Way Functions |g 147 -- |g 3.6. |t Pseudorandom Functions |g 148 -- |g 3.6.3. |t Applications: A General Methodology |g 157 -- |g 3.7. |t Pseudorandom Permutations |g 164 -- |g 3.8.1. |t Historical Notes |g 169 -- |g 4 |t Zero-Knowledge Proof Systems |g 184 -- |g 4.1. |t Zero-Knowledge Proofs: Motivation |g 185 -- |g 4.1.1. |t Notion of a Proof |g 187 -- |g 4.1.2. |t Gaining Knowledge |g 189 -- |g 4.2. |t Interactive Proof Systems |g 190 -- |g 4.2.2. |t An Example (Graph Non-Isomorphism in IP) |g 195 -- |g 4.2.3. |t Structure of the Class IP |g 198 -- |g 4.2.4. |t Augmentation of the Model |g 199 -- |g 4.3. |t Zero-Knowledge Proofs: Definitions |g 200 -- |g 4.3.1. |t Perfect and Computational Zero-Knowledge |g 200 -- |g 4.3.2. |t An Example (Graph Isomorphism in PZK) |g 207 -- |g 4.3.3. |t Zero-Knowledge with Respect to Auxiliary Inputs |g 213 -- |g 4.3.4. |t Sequential Composition ofh Zero-Knowledge Proofs |g 216 -- |g 4.4. |t Zero-Knowledge Proofs for NP |g 223 -- |g 4.4.1. |t Commitment Schemes |g 223 -- |g 4.4.2. |t Zero-Knowledge Proof of Graph Coloring |g 228 -- |g 4.4.3. |t General Result and Some Applications |g 240 -- |g 4.4.4. |t Second-Level Considerations |g 243 -- |g 4.5. |t Negative Results |g 246 -- |g 4.5.1. |t On the Importance of Interaction and Randomness |g 247 -- |g 4.5.2. |t Limitations of Unconditional Results |g 248 -- |g 4.5.3. |t Limitations of Statistical ZK Proofs |g 250 -- |g 4.5.4. |t Zero-Knowledge and Parallel Composition |g 251 -- |g 4.6. |t Witness Indistinguishability and Hiding |g 254 -- |g 4.6.2. |t Parallel Composition |g 258 -- |g 4.7. |t Proofs of Knowledge |g 262 -- |g 4.7.2. |t Reducing the Knowledge Error |g 267 -- |g 4.7.3. |t Zero-Knowledge Proofs of Knowledge for NP |g 268 -- |g 4.7.5. |t Proofs of Identity (Identification Schemes) |g 270 -- |g 4.7.6. |t Strong Proofs of Knowledge |g 274 -- |g 4.8. |t Computationally Sound Proofs (Arguments) |g 277 -- |g 4.8.2. |t Perfectly Hiding Commitment Schemes |g 278 -- |g 4.8.3. |t Perfect Zero-Knowledge Arguments for NP |g 284 -- |g 4.8.4. |t Arguments of Poly-Logarithmic Efficiency |g 286 -- |g 4.9. |t Constant-Round Zero-Knowledge Proofs |g 288 -- |g 4.9.1. |t Using Commitment Schemes with Perfect Secrecy |g 289 -- |g 4.9.2. |t Bounding the Power of Cheating Provers |g 294 -- |g 4.10. |t Non-Interactive Zero-Knowledge Proofs |g 298 -- |g 4.10.3. |t Extensions |g 306 -- |g 4.11. |t Multi-Prover Zero-Knowledge Proofs |g 311 -- |g 4.11.2. |t Two-Sender Commitment Schemes |g 313 -- |g 4.11.3. |t Perfect Zero-Knowledge for NP |g 317 -- |g 4.12.1. |t Historical Notes |g 320 -- |g Appendix |t A Background in Computational Number Theory |g 331 -- |g A.1. |t Prime Numbers |g 331 -- |g A.1.1. |t Quadratic Residues Modulo a Prime |g 331 -- |g A.1.2. |t Extracting Square Roots Modulo a Prime |g 332 -- |g A.1.3. |t Primality Testers |g 332 -- |g A.1.4. |t On Uniform Selection of Primes |g 333 -- |g A.2. |t Composite Numbers |g 334 -- |g A.2.1. |t Quadratic Residues Modulo a Composite |g 335 -- |g A.2.2. |t Extracting Square Roots Modulo a Composite |g 335 -- |g A.2.3. |t Legendre and Jacobi Symbols |g 336 -- |g A.2.4. |t Blum Integers and Their Quadratic-Residue Structure |g 337 -- |g Appendix B |t Brief Outline of Volume |g 338 -- |g B.1. |t Encryption: Brief Summary |g 338 -- |g B.1.3. |t Beyond Eavesdropping Security |g 343 -- |g B.2. |t Signatures: Brief Summary |g 345 -- |g B.3. |t Cryptographic Protocols: Brief Summary |g 350. |
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| 650 | 0 | |a Cryptography |x Mathematics. | |
| 650 | 6 | |a Cryptographie |x Mathématiques. | |
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Datensatz im Suchindex
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| author | Goldreich, Oded |
| author_facet | Goldreich, Oded |
| author_role | |
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| contents | Encryption Schemes Pseudorandom Generators Digital Signatures Fault-Tolerant Protocols and Zero-Knowledge Proofs Some Background from Probability Theory Notational Conventions Three Inequalities Computational Model P, NP, and NP-Completeness Probabilistic Polynomial Time Non-Uniform Polynomial Time Intractability Assumptions Oracle Machines Motivation to the Rigorous Treatment Need for a Rigorous Treatment Practical Consequences of the Rigorous Treatment Tendency to Be Conservative Historical Notes Open Problems 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 Construction and Its Analysis (Proof of Theorem 2.3.2) Illustration by a Toy Example 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 Hard-Core Predicates for Any One-Way Function Hard-Core Functions Efficient Amplification of One-Way Functions Construction Analysis Motivating Discussion Computational Approaches to Randomness A Rigorous Approach to Pseudorandom Generators Computational Indistinguishability 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 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 Applications: A General Methodology Pseudorandom Permutations Zero-Knowledge Proof Systems Zero-Knowledge Proofs: Motivation Notion of a Proof Gaining Knowledge Interactive Proof Systems An Example (Graph Non-Isomorphism in IP) 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 ofh Zero-Knowledge Proofs Zero-Knowledge Proofs for NP Commitment Schemes Zero-Knowledge Proof of Graph Coloring 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 Parallel Composition Proofs of Knowledge Reducing the Knowledge Error Zero-Knowledge Proofs of Knowledge for NP Proofs of Identity (Identification Schemes) Strong Proofs of Knowledge Computationally Sound Proofs (Arguments) 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 Extensions Multi-Prover Zero-Knowledge Proofs Two-Sender Commitment Schemes Perfect Zero-Knowledge for NP A 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 Legendre and Jacobi Symbols Blum Integers and Their Quadratic-Residue Structure Brief Outline of Volume Encryption: Brief Summary Beyond Eavesdropping Security Signatures: Brief Summary Cryptographic Protocols: Brief Summary |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 652 - Processes of written communication |
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| dewey-search | 652/.8 |
| dewey-sort | 3652 18 |
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| discipline | Informatik Wirtschaftswissenschaften |
| format | Electronic eBook |
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code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from title screen.</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and indexes.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs. The emphasis is on the clarification of fundamental concepts and on demonstrating the feasibility of solving cryptographic problems, rather than on describing ad-hoc approaches. The book is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="g">1.1.1.</subfield><subfield code="t">Encryption Schemes</subfield><subfield code="g">2 --</subfield><subfield code="g">1.1.2.</subfield><subfield code="t">Pseudorandom Generators</subfield><subfield code="g">3 --</subfield><subfield code="g">1.1.3.</subfield><subfield code="t">Digital Signatures</subfield><subfield code="g">4 --</subfield><subfield code="g">1.1.4.</subfield><subfield code="t">Fault-Tolerant Protocols and Zero-Knowledge Proofs</subfield><subfield code="g">6 --</subfield><subfield code="g">1.2.</subfield><subfield code="t">Some Background from Probability Theory</subfield><subfield code="g">8 --</subfield><subfield code="g">1.2.1.</subfield><subfield code="t">Notational Conventions</subfield><subfield code="g">8 --</subfield><subfield code="g">1.2.2.</subfield><subfield code="t">Three Inequalities</subfield><subfield code="g">9 --</subfield><subfield code="g">1.3.</subfield><subfield code="t">Computational Model</subfield><subfield code="g">12 --</subfield><subfield code="g">1.3.1.</subfield><subfield code="t">P, NP, and NP-Completeness</subfield><subfield code="g">12 --</subfield><subfield code="g">1.3.2.</subfield><subfield code="t">Probabilistic Polynomial Time</subfield><subfield code="g">13 --</subfield><subfield code="g">1.3.3.</subfield><subfield code="t">Non-Uniform Polynomial Time</subfield><subfield code="g">16 --</subfield><subfield code="g">1.3.4.</subfield><subfield code="t">Intractability Assumptions</subfield><subfield code="g">19 --</subfield><subfield code="g">1.3.5.</subfield><subfield code="t">Oracle Machines</subfield><subfield code="g">20 --</subfield><subfield code="g">1.4.</subfield><subfield code="t">Motivation to the Rigorous Treatment</subfield><subfield code="g">21 --</subfield><subfield code="g">1.4.1.</subfield><subfield code="t">Need for a Rigorous Treatment</subfield><subfield code="g">21 --</subfield><subfield code="g">1.4.2.</subfield><subfield code="t">Practical Consequences of the Rigorous Treatment</subfield><subfield code="g">23 --</subfield><subfield code="g">1.4.3.</subfield><subfield code="t">Tendency to Be Conservative</subfield><subfield code="g">24 --</subfield><subfield code="g">1.5.1.</subfield><subfield code="t">Historical Notes</subfield><subfield code="g">25 --</subfield><subfield code="g">1.5.3.</subfield><subfield code="t">Open Problems</subfield><subfield code="g">27 --</subfield><subfield code="g">2</subfield><subfield code="t">Computational Difficulty</subfield><subfield code="g">30 --</subfield><subfield code="g">2.1.</subfield><subfield code="t">One-Way Functions: Motivation</subfield><subfield code="g">31 --</subfield><subfield code="g">2.2.</subfield><subfield code="t">One-Way Functions: Definitions</subfield><subfield code="g">32 --</subfield><subfield code="g">2.2.1.</subfield><subfield code="t">Strong One-Way Functions</subfield><subfield code="g">32 --</subfield><subfield code="g">2.2.2.</subfield><subfield code="t">Weak One-Way Functions</subfield><subfield code="g">35 --</subfield><subfield code="g">2.2.3.</subfield><subfield code="t">Two Useful Length Conventions</subfield><subfield code="g">35 --</subfield><subfield code="g">2.2.4.</subfield><subfield code="t">Candidates for One-Way Functions</subfield><subfield code="g">40 --</subfield><subfield code="g">2.2.5.</subfield><subfield code="t">Non-Uniformly One-Way Functions</subfield><subfield code="g">41 --</subfield><subfield code="g">2.3.</subfield><subfield code="t">Weak One-Way Functions Imply Strong Ones</subfield><subfield code="g">43 --</subfield><subfield code="g">2.3.1.</subfield><subfield code="t">Construction and Its Analysis (Proof of Theorem 2.3.2)</subfield><subfield code="g">44 --</subfield><subfield code="g">2.3.2.</subfield><subfield code="t">Illustration by a Toy Example</subfield><subfield code="g">48 --</subfield><subfield code="g">2.4.</subfield><subfield code="t">One-Way Functions: Variations</subfield><subfield code="g">51 --</subfield><subfield code="g">2.4.1.</subfield><subfield code="t">Universal One-Way Function</subfield><subfield code="g">52 --</subfield><subfield code="g">2.4.2.</subfield><subfield code="t">One-Way Functions as Collections</subfield><subfield code="g">53 --</subfield><subfield code="g">2.4.3.</subfield><subfield code="t">Examples of One-Way Collections</subfield><subfield code="g">55 --</subfield><subfield code="g">2.4.4.</subfield><subfield code="t">Trapdoor One-Way Permutations</subfield><subfield code="g">58 --</subfield><subfield code="g">2.4.5.</subfield><subfield code="t">Claw-Free Functions</subfield><subfield code="g">60 --</subfield><subfield code="g">2.4.6.</subfield><subfield code="t">On Proposing Candidates</subfield><subfield code="g">63 --</subfield><subfield code="g">2.5.</subfield><subfield code="t">Hard-Core Predicates</subfield><subfield code="g">64 --</subfield><subfield code="g">2.5.2.</subfield><subfield code="t">Hard-Core Predicates for Any One-Way Function</subfield><subfield code="g">65 --</subfield><subfield code="g">2.5.3.</subfield><subfield code="t">Hard-Core Functions</subfield><subfield code="g">74 --</subfield><subfield code="g">2.6.</subfield><subfield code="t">Efficient Amplification of One-Way Functions</subfield><subfield code="g">78 --</subfield><subfield code="g">2.6.1.</subfield><subfield code="t">Construction</subfield><subfield code="g">80 --</subfield><subfield code="g">2.6.2.</subfield><subfield code="t">Analysis</subfield><subfield code="g">81 --</subfield><subfield code="g">2.7.1.</subfield><subfield code="t">Historical Notes</subfield><subfield code="g">89 --</subfield><subfield code="g">3</subfield><subfield code="t">Pseudorandom Generators</subfield><subfield code="g">101 --</subfield><subfield code="g">3.1.</subfield><subfield code="t">Motivating Discussion</subfield><subfield code="g">102 --</subfield><subfield code="g">3.1.1.</subfield><subfield code="t">Computational Approaches to Randomness</subfield><subfield code="g">102 --</subfield><subfield code="g">3.1.2.</subfield><subfield code="t">A Rigorous Approach to Pseudorandom Generators</subfield><subfield code="g">103 --</subfield><subfield code="g">3.2.</subfield><subfield code="t">Computational Indistinguishability</subfield><subfield code="g">103 --</subfield><subfield code="g">3.2.2.</subfield><subfield code="t">Relation to Statistical Closeness</subfield><subfield code="g">106 --</subfield><subfield code="g">3.2.3.</subfield><subfield code="t">Indistinguishability by Repeated Experiments</subfield><subfield code="g">107 --</subfield><subfield code="g">3.2.4.</subfield><subfield code="t">Indistinguishability by Circuits</subfield><subfield code="g">111 --</subfield><subfield code="g">3.2.5.</subfield><subfield code="t">Pseudorandom Ensembles</subfield><subfield code="g">112 --</subfield><subfield code="g">3.3.</subfield><subfield code="t">Definitions of Pseudorandom Generators</subfield><subfield code="g">112 --</subfield><subfield code="g">3.3.1.</subfield><subfield code="t">Standard Definition of Pseudorandom Generators</subfield><subfield code="g">113 --</subfield><subfield code="g">3.3.2.</subfield><subfield code="t">Increasing the Expansion Factor</subfield><subfield code="g">114 --</subfield><subfield code="g">3.3.3.</subfield><subfield code="t">Variable-Output Pseudorandom Generators</subfield><subfield code="g">118 --</subfield><subfield code="g">3.3.4.</subfield><subfield code="t">Applicability of Pseudorandom Generators</subfield><subfield code="g">119 --</subfield><subfield code="g">3.3.5.</subfield><subfield code="t">Pseudorandomness and Unpredictability</subfield><subfield code="g">119 --</subfield><subfield code="g">3.3.6.</subfield><subfield code="t">Pseudorandom Generators Imply One-Way Functions</subfield><subfield code="g">123 --</subfield><subfield code="g">3.4.</subfield><subfield code="t">Constructions Based on One-Way Permutations</subfield><subfield code="g">124 --</subfield><subfield code="g">3.4.1.</subfield><subfield code="t">Construction Based on a Single Permutation</subfield><subfield code="g">124 --</subfield><subfield code="g">3.4.2.</subfield><subfield code="t">Construction Based on Collections of Permutations</subfield><subfield code="g">131 --</subfield><subfield code="g">3.4.3.</subfield><subfield code="t">Using Hard-Core Functions Rather than Predicates</subfield><subfield code="g">134 --</subfield><subfield code="g">3.5.</subfield><subfield code="t">Constructions Based on One-Way Functions</subfield><subfield code="g">135 --</subfield><subfield code="g">3.5.1.</subfield><subfield code="t">Using 1-1 One-Way Functions</subfield><subfield code="g">135 --</subfield><subfield code="g">3.5.2.</subfield><subfield code="t">Using Regular One-Way Functions</subfield><subfield code="g">141 --</subfield><subfield code="g">3.5.3.</subfield><subfield code="t">Going Beyond Regular One-Way Functions</subfield><subfield code="g">147 --</subfield><subfield code="g">3.6.</subfield><subfield code="t">Pseudorandom Functions</subfield><subfield code="g">148 --</subfield><subfield code="g">3.6.3.</subfield><subfield code="t">Applications: A General Methodology</subfield><subfield code="g">157 --</subfield><subfield code="g">3.7.</subfield><subfield code="t">Pseudorandom Permutations</subfield><subfield code="g">164 --</subfield><subfield code="g">3.8.1.</subfield><subfield code="t">Historical Notes</subfield><subfield code="g">169 --</subfield><subfield code="g">4</subfield><subfield code="t">Zero-Knowledge Proof Systems</subfield><subfield code="g">184 --</subfield><subfield code="g">4.1.</subfield><subfield code="t">Zero-Knowledge Proofs: Motivation</subfield><subfield code="g">185 --</subfield><subfield code="g">4.1.1.</subfield><subfield code="t">Notion of a Proof</subfield><subfield code="g">187 --</subfield><subfield code="g">4.1.2.</subfield><subfield code="t">Gaining Knowledge</subfield><subfield code="g">189 --</subfield><subfield code="g">4.2.</subfield><subfield code="t">Interactive Proof Systems</subfield><subfield code="g">190 --</subfield><subfield code="g">4.2.2.</subfield><subfield code="t">An Example (Graph Non-Isomorphism in IP)</subfield><subfield code="g">195 --</subfield><subfield code="g">4.2.3.</subfield><subfield code="t">Structure of the Class IP</subfield><subfield code="g">198 --</subfield><subfield code="g">4.2.4.</subfield><subfield code="t">Augmentation of the Model</subfield><subfield code="g">199 --</subfield><subfield code="g">4.3.</subfield><subfield code="t">Zero-Knowledge Proofs: Definitions</subfield><subfield code="g">200 --</subfield><subfield code="g">4.3.1.</subfield><subfield code="t">Perfect and Computational Zero-Knowledge</subfield><subfield code="g">200 --</subfield><subfield code="g">4.3.2.</subfield><subfield code="t">An Example (Graph Isomorphism in PZK)</subfield><subfield code="g">207 --</subfield><subfield code="g">4.3.3.</subfield><subfield code="t">Zero-Knowledge with Respect to Auxiliary Inputs</subfield><subfield code="g">213 --</subfield><subfield code="g">4.3.4.</subfield><subfield code="t">Sequential Composition ofh Zero-Knowledge Proofs</subfield><subfield code="g">216 --</subfield><subfield code="g">4.4.</subfield><subfield code="t">Zero-Knowledge Proofs for NP</subfield><subfield code="g">223 --</subfield><subfield code="g">4.4.1.</subfield><subfield code="t">Commitment Schemes</subfield><subfield code="g">223 --</subfield><subfield code="g">4.4.2.</subfield><subfield code="t">Zero-Knowledge Proof of Graph Coloring</subfield><subfield code="g">228 --</subfield><subfield code="g">4.4.3.</subfield><subfield code="t">General Result and Some Applications</subfield><subfield code="g">240 --</subfield><subfield code="g">4.4.4.</subfield><subfield code="t">Second-Level Considerations</subfield><subfield code="g">243 --</subfield><subfield code="g">4.5.</subfield><subfield code="t">Negative Results</subfield><subfield code="g">246 --</subfield><subfield code="g">4.5.1.</subfield><subfield code="t">On the Importance of Interaction and Randomness</subfield><subfield code="g">247 --</subfield><subfield code="g">4.5.2.</subfield><subfield code="t">Limitations of Unconditional Results</subfield><subfield code="g">248 --</subfield><subfield code="g">4.5.3.</subfield><subfield code="t">Limitations of Statistical ZK Proofs</subfield><subfield code="g">250 --</subfield><subfield code="g">4.5.4.</subfield><subfield code="t">Zero-Knowledge and Parallel Composition</subfield><subfield code="g">251 --</subfield><subfield code="g">4.6.</subfield><subfield code="t">Witness Indistinguishability and Hiding</subfield><subfield code="g">254 --</subfield><subfield code="g">4.6.2.</subfield><subfield code="t">Parallel Composition</subfield><subfield code="g">258 --</subfield><subfield code="g">4.7.</subfield><subfield code="t">Proofs of Knowledge</subfield><subfield code="g">262 --</subfield><subfield code="g">4.7.2.</subfield><subfield code="t">Reducing the Knowledge Error</subfield><subfield code="g">267 --</subfield><subfield code="g">4.7.3.</subfield><subfield code="t">Zero-Knowledge Proofs of Knowledge for NP</subfield><subfield code="g">268 --</subfield><subfield code="g">4.7.5.</subfield><subfield code="t">Proofs of Identity (Identification Schemes)</subfield><subfield code="g">270 --</subfield><subfield code="g">4.7.6.</subfield><subfield code="t">Strong Proofs of Knowledge</subfield><subfield code="g">274 --</subfield><subfield code="g">4.8.</subfield><subfield code="t">Computationally Sound Proofs (Arguments)</subfield><subfield code="g">277 --</subfield><subfield code="g">4.8.2.</subfield><subfield code="t">Perfectly Hiding Commitment Schemes</subfield><subfield code="g">278 --</subfield><subfield code="g">4.8.3.</subfield><subfield code="t">Perfect Zero-Knowledge Arguments for NP</subfield><subfield code="g">284 --</subfield><subfield code="g">4.8.4.</subfield><subfield code="t">Arguments of Poly-Logarithmic Efficiency</subfield><subfield code="g">286 --</subfield><subfield code="g">4.9.</subfield><subfield code="t">Constant-Round Zero-Knowledge Proofs</subfield><subfield code="g">288 --</subfield><subfield code="g">4.9.1.</subfield><subfield code="t">Using Commitment Schemes with Perfect Secrecy</subfield><subfield code="g">289 --</subfield><subfield code="g">4.9.2.</subfield><subfield code="t">Bounding the Power of Cheating Provers</subfield><subfield code="g">294 --</subfield><subfield code="g">4.10.</subfield><subfield code="t">Non-Interactive Zero-Knowledge Proofs</subfield><subfield code="g">298 --</subfield><subfield code="g">4.10.3.</subfield><subfield code="t">Extensions</subfield><subfield code="g">306 --</subfield><subfield code="g">4.11.</subfield><subfield code="t">Multi-Prover Zero-Knowledge Proofs</subfield><subfield code="g">311 --</subfield><subfield code="g">4.11.2.</subfield><subfield code="t">Two-Sender Commitment Schemes</subfield><subfield code="g">313 --</subfield><subfield code="g">4.11.3.</subfield><subfield code="t">Perfect Zero-Knowledge for NP</subfield><subfield code="g">317 --</subfield><subfield code="g">4.12.1.</subfield><subfield code="t">Historical Notes</subfield><subfield code="g">320 --</subfield><subfield code="g">Appendix</subfield><subfield code="t">A Background in Computational Number Theory</subfield><subfield code="g">331 --</subfield><subfield code="g">A.1.</subfield><subfield code="t">Prime Numbers</subfield><subfield code="g">331 --</subfield><subfield code="g">A.1.1.</subfield><subfield code="t">Quadratic Residues Modulo a Prime</subfield><subfield code="g">331 --</subfield><subfield code="g">A.1.2.</subfield><subfield code="t">Extracting Square Roots Modulo a Prime</subfield><subfield code="g">332 --</subfield><subfield code="g">A.1.3.</subfield><subfield code="t">Primality Testers</subfield><subfield code="g">332 --</subfield><subfield code="g">A.1.4.</subfield><subfield code="t">On Uniform Selection of Primes</subfield><subfield code="g">333 --</subfield><subfield code="g">A.2.</subfield><subfield code="t">Composite Numbers</subfield><subfield code="g">334 --</subfield><subfield code="g">A.2.1.</subfield><subfield code="t">Quadratic Residues Modulo a Composite</subfield><subfield code="g">335 --</subfield><subfield code="g">A.2.2.</subfield><subfield code="t">Extracting Square Roots Modulo a Composite</subfield><subfield code="g">335 --</subfield><subfield code="g">A.2.3.</subfield><subfield code="t">Legendre and Jacobi Symbols</subfield><subfield code="g">336 --</subfield><subfield code="g">A.2.4.</subfield><subfield code="t">Blum Integers and Their Quadratic-Residue Structure</subfield><subfield code="g">337 --</subfield><subfield code="g">Appendix B</subfield><subfield code="t">Brief Outline of Volume</subfield><subfield code="g">338 --</subfield><subfield code="g">B.1.</subfield><subfield code="t">Encryption: Brief Summary</subfield><subfield code="g">338 --</subfield><subfield code="g">B.1.3.</subfield><subfield code="t">Beyond Eavesdropping Security</subfield><subfield code="g">343 --</subfield><subfield code="g">B.2.</subfield><subfield code="t">Signatures: Brief Summary</subfield><subfield code="g">345 --</subfield><subfield code="g">B.3.</subfield><subfield code="t">Cryptographic Protocols: Brief Summary</subfield><subfield code="g">350.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Coding theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85027654</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Cryptography</subfield><subfield code="x">Mathematics.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Cryptographie</subfield><subfield code="x">Mathématiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">BUSINESS & ECONOMICS</subfield><subfield code="x">Business Writing.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Coding theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Cryptography</subfield><subfield code="x">Mathematics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Kryptologie</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4033329-2</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Basic tools Tomo 1 Foundations of cryptography (Text)</subfield><subfield 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| id | ZDB-4-EBA-ocm55234763 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:15:32Z |
| institution | BVB |
| isbn | 1280430060 9781280430060 0511546890 9780511546891 9781461949176 1461949173 |
| language | English |
| oclc_num | 55234763 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press, |
| record_format | marc |
| spelling | Goldreich, Oded. Foundations of cryptography : basic tools / Oded Goldreich. Cambridge, U.K. ; New York : Cambridge University Press, 2001. 1 online resource text txt rdacontent computer c rdamedia online resource cr rdacarrier Title from title screen. Includes bibliographical references and indexes. Cryptography is concerned with the conceptualization, definition and construction of computing systems that address security concerns. The design of cryptographic systems must be based on firm foundations. This book presents a rigorous and systematic treatment of the foundational issues: defining cryptographic tasks and solving new cryptographic problems using existing tools. It focuses on the basic mathematical tools: computational difficulty (one-way functions), pseudorandomness and zero-knowledge proofs. The emphasis is on the clarification of fundamental concepts and on demonstrating the feasibility of solving cryptographic problems, rather than on describing ad-hoc approaches. The book is suitable for use in a graduate course on cryptography and as a reference book for experts. The author assumes basic familiarity with the design and analysis of algorithms; some knowledge of complexity theory and probability is also useful. 1.1.1. Encryption Schemes 2 -- 1.1.2. Pseudorandom Generators 3 -- 1.1.3. Digital Signatures 4 -- 1.1.4. Fault-Tolerant Protocols and Zero-Knowledge Proofs 6 -- 1.2. Some Background from Probability Theory 8 -- 1.2.1. Notational Conventions 8 -- 1.2.2. Three Inequalities 9 -- 1.3. Computational Model 12 -- 1.3.1. P, NP, and NP-Completeness 12 -- 1.3.2. Probabilistic Polynomial Time 13 -- 1.3.3. Non-Uniform Polynomial Time 16 -- 1.3.4. Intractability Assumptions 19 -- 1.3.5. Oracle Machines 20 -- 1.4. Motivation to the Rigorous Treatment 21 -- 1.4.1. Need for a Rigorous Treatment 21 -- 1.4.2. Practical Consequences of the Rigorous Treatment 23 -- 1.4.3. Tendency to Be Conservative 24 -- 1.5.1. Historical Notes 25 -- 1.5.3. Open Problems 27 -- 2 Computational Difficulty 30 -- 2.1. One-Way Functions: Motivation 31 -- 2.2. One-Way Functions: Definitions 32 -- 2.2.1. Strong One-Way Functions 32 -- 2.2.2. Weak One-Way Functions 35 -- 2.2.3. Two Useful Length Conventions 35 -- 2.2.4. Candidates for One-Way Functions 40 -- 2.2.5. Non-Uniformly One-Way Functions 41 -- 2.3. Weak One-Way Functions Imply Strong Ones 43 -- 2.3.1. Construction and Its Analysis (Proof of Theorem 2.3.2) 44 -- 2.3.2. Illustration by a Toy Example 48 -- 2.4. One-Way Functions: Variations 51 -- 2.4.1. Universal One-Way Function 52 -- 2.4.2. One-Way Functions as Collections 53 -- 2.4.3. Examples of One-Way Collections 55 -- 2.4.4. Trapdoor One-Way Permutations 58 -- 2.4.5. Claw-Free Functions 60 -- 2.4.6. On Proposing Candidates 63 -- 2.5. Hard-Core Predicates 64 -- 2.5.2. Hard-Core Predicates for Any One-Way Function 65 -- 2.5.3. Hard-Core Functions 74 -- 2.6. Efficient Amplification of One-Way Functions 78 -- 2.6.1. Construction 80 -- 2.6.2. Analysis 81 -- 2.7.1. Historical Notes 89 -- 3 Pseudorandom Generators 101 -- 3.1. Motivating Discussion 102 -- 3.1.1. Computational Approaches to Randomness 102 -- 3.1.2. A Rigorous Approach to Pseudorandom Generators 103 -- 3.2. Computational Indistinguishability 103 -- 3.2.2. Relation to Statistical Closeness 106 -- 3.2.3. Indistinguishability by Repeated Experiments 107 -- 3.2.4. Indistinguishability by Circuits 111 -- 3.2.5. Pseudorandom Ensembles 112 -- 3.3. Definitions of Pseudorandom Generators 112 -- 3.3.1. Standard Definition of Pseudorandom Generators 113 -- 3.3.2. Increasing the Expansion Factor 114 -- 3.3.3. Variable-Output Pseudorandom Generators 118 -- 3.3.4. Applicability of Pseudorandom Generators 119 -- 3.3.5. Pseudorandomness and Unpredictability 119 -- 3.3.6. Pseudorandom Generators Imply One-Way Functions 123 -- 3.4. Constructions Based on One-Way Permutations 124 -- 3.4.1. Construction Based on a Single Permutation 124 -- 3.4.2. Construction Based on Collections of Permutations 131 -- 3.4.3. Using Hard-Core Functions Rather than Predicates 134 -- 3.5. Constructions Based on One-Way Functions 135 -- 3.5.1. Using 1-1 One-Way Functions 135 -- 3.5.2. Using Regular One-Way Functions 141 -- 3.5.3. Going Beyond Regular One-Way Functions 147 -- 3.6. Pseudorandom Functions 148 -- 3.6.3. Applications: A General Methodology 157 -- 3.7. Pseudorandom Permutations 164 -- 3.8.1. Historical Notes 169 -- 4 Zero-Knowledge Proof Systems 184 -- 4.1. Zero-Knowledge Proofs: Motivation 185 -- 4.1.1. Notion of a Proof 187 -- 4.1.2. Gaining Knowledge 189 -- 4.2. Interactive Proof Systems 190 -- 4.2.2. An Example (Graph Non-Isomorphism in IP) 195 -- 4.2.3. Structure of the Class IP 198 -- 4.2.4. Augmentation of the Model 199 -- 4.3. Zero-Knowledge Proofs: Definitions 200 -- 4.3.1. Perfect and Computational Zero-Knowledge 200 -- 4.3.2. An Example (Graph Isomorphism in PZK) 207 -- 4.3.3. Zero-Knowledge with Respect to Auxiliary Inputs 213 -- 4.3.4. Sequential Composition ofh Zero-Knowledge Proofs 216 -- 4.4. Zero-Knowledge Proofs for NP 223 -- 4.4.1. Commitment Schemes 223 -- 4.4.2. Zero-Knowledge Proof of Graph Coloring 228 -- 4.4.3. General Result and Some Applications 240 -- 4.4.4. Second-Level Considerations 243 -- 4.5. Negative Results 246 -- 4.5.1. On the Importance of Interaction and Randomness 247 -- 4.5.2. Limitations of Unconditional Results 248 -- 4.5.3. Limitations of Statistical ZK Proofs 250 -- 4.5.4. Zero-Knowledge and Parallel Composition 251 -- 4.6. Witness Indistinguishability and Hiding 254 -- 4.6.2. Parallel Composition 258 -- 4.7. Proofs of Knowledge 262 -- 4.7.2. Reducing the Knowledge Error 267 -- 4.7.3. Zero-Knowledge Proofs of Knowledge for NP 268 -- 4.7.5. Proofs of Identity (Identification Schemes) 270 -- 4.7.6. Strong Proofs of Knowledge 274 -- 4.8. Computationally Sound Proofs (Arguments) 277 -- 4.8.2. Perfectly Hiding Commitment Schemes 278 -- 4.8.3. Perfect Zero-Knowledge Arguments for NP 284 -- 4.8.4. Arguments of Poly-Logarithmic Efficiency 286 -- 4.9. Constant-Round Zero-Knowledge Proofs 288 -- 4.9.1. Using Commitment Schemes with Perfect Secrecy 289 -- 4.9.2. Bounding the Power of Cheating Provers 294 -- 4.10. Non-Interactive Zero-Knowledge Proofs 298 -- 4.10.3. Extensions 306 -- 4.11. Multi-Prover Zero-Knowledge Proofs 311 -- 4.11.2. Two-Sender Commitment Schemes 313 -- 4.11.3. Perfect Zero-Knowledge for NP 317 -- 4.12.1. Historical Notes 320 -- Appendix A Background in Computational Number Theory 331 -- A.1. Prime Numbers 331 -- A.1.1. Quadratic Residues Modulo a Prime 331 -- A.1.2. Extracting Square Roots Modulo a Prime 332 -- A.1.3. Primality Testers 332 -- A.1.4. On Uniform Selection of Primes 333 -- A.2. Composite Numbers 334 -- A.2.1. Quadratic Residues Modulo a Composite 335 -- A.2.2. Extracting Square Roots Modulo a Composite 335 -- A.2.3. Legendre and Jacobi Symbols 336 -- A.2.4. Blum Integers and Their Quadratic-Residue Structure 337 -- Appendix B Brief Outline of Volume 338 -- B.1. Encryption: Brief Summary 338 -- B.1.3. Beyond Eavesdropping Security 343 -- B.2. Signatures: Brief Summary 345 -- B.3. Cryptographic Protocols: Brief Summary 350. Coding theory. http://id.loc.gov/authorities/subjects/sh85027654 Cryptography Mathematics. Cryptographie Mathématiques. BUSINESS & ECONOMICS Business Writing. bisacsh Coding theory fast Cryptography Mathematics fast Kryptologie gnd http://d-nb.info/gnd/4033329-2 has work: Basic tools Tomo 1 Foundations of cryptography (Text) https://id.oclc.org/worldcat/entity/E39PCXpfVMpCd4vmy6bWJvHYKd https://id.oclc.org/worldcat/ontology/hasWork 9780521791724 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616989 Volltext |
| spellingShingle | Goldreich, Oded Foundations of cryptography : basic tools / Encryption Schemes Pseudorandom Generators Digital Signatures Fault-Tolerant Protocols and Zero-Knowledge Proofs Some Background from Probability Theory Notational Conventions Three Inequalities Computational Model P, NP, and NP-Completeness Probabilistic Polynomial Time Non-Uniform Polynomial Time Intractability Assumptions Oracle Machines Motivation to the Rigorous Treatment Need for a Rigorous Treatment Practical Consequences of the Rigorous Treatment Tendency to Be Conservative Historical Notes Open Problems 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 Construction and Its Analysis (Proof of Theorem 2.3.2) Illustration by a Toy Example 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 Hard-Core Predicates for Any One-Way Function Hard-Core Functions Efficient Amplification of One-Way Functions Construction Analysis Motivating Discussion Computational Approaches to Randomness A Rigorous Approach to Pseudorandom Generators Computational Indistinguishability 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 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 Applications: A General Methodology Pseudorandom Permutations Zero-Knowledge Proof Systems Zero-Knowledge Proofs: Motivation Notion of a Proof Gaining Knowledge Interactive Proof Systems An Example (Graph Non-Isomorphism in IP) 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 ofh Zero-Knowledge Proofs Zero-Knowledge Proofs for NP Commitment Schemes Zero-Knowledge Proof of Graph Coloring 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 Parallel Composition Proofs of Knowledge Reducing the Knowledge Error Zero-Knowledge Proofs of Knowledge for NP Proofs of Identity (Identification Schemes) Strong Proofs of Knowledge Computationally Sound Proofs (Arguments) 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 Extensions Multi-Prover Zero-Knowledge Proofs Two-Sender Commitment Schemes Perfect Zero-Knowledge for NP A 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 Legendre and Jacobi Symbols Blum Integers and Their Quadratic-Residue Structure Brief Outline of Volume Encryption: Brief Summary Beyond Eavesdropping Security Signatures: Brief Summary Cryptographic Protocols: Brief Summary Coding theory. http://id.loc.gov/authorities/subjects/sh85027654 Cryptography Mathematics. Cryptographie Mathématiques. BUSINESS & ECONOMICS Business Writing. bisacsh Coding theory fast Cryptography Mathematics fast Kryptologie gnd http://d-nb.info/gnd/4033329-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85027654 http://d-nb.info/gnd/4033329-2 |
| title | Foundations of cryptography : basic tools / |
| title_alt | Encryption Schemes Pseudorandom Generators Digital Signatures Fault-Tolerant Protocols and Zero-Knowledge Proofs Some Background from Probability Theory Notational Conventions Three Inequalities Computational Model P, NP, and NP-Completeness Probabilistic Polynomial Time Non-Uniform Polynomial Time Intractability Assumptions Oracle Machines Motivation to the Rigorous Treatment Need for a Rigorous Treatment Practical Consequences of the Rigorous Treatment Tendency to Be Conservative Historical Notes Open Problems 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 Construction and Its Analysis (Proof of Theorem 2.3.2) Illustration by a Toy Example 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 Hard-Core Predicates for Any One-Way Function Hard-Core Functions Efficient Amplification of One-Way Functions Construction Analysis Motivating Discussion Computational Approaches to Randomness A Rigorous Approach to Pseudorandom Generators Computational Indistinguishability 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 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 Applications: A General Methodology Pseudorandom Permutations Zero-Knowledge Proof Systems Zero-Knowledge Proofs: Motivation Notion of a Proof Gaining Knowledge Interactive Proof Systems An Example (Graph Non-Isomorphism in IP) 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 ofh Zero-Knowledge Proofs Zero-Knowledge Proofs for NP Commitment Schemes Zero-Knowledge Proof of Graph Coloring 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 Parallel Composition Proofs of Knowledge Reducing the Knowledge Error Zero-Knowledge Proofs of Knowledge for NP Proofs of Identity (Identification Schemes) Strong Proofs of Knowledge Computationally Sound Proofs (Arguments) 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 Extensions Multi-Prover Zero-Knowledge Proofs Two-Sender Commitment Schemes Perfect Zero-Knowledge for NP A 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 Legendre and Jacobi Symbols Blum Integers and Their Quadratic-Residue Structure Brief Outline of Volume Encryption: Brief Summary Beyond Eavesdropping Security Signatures: Brief Summary Cryptographic Protocols: Brief Summary |
| title_auth | Foundations of cryptography : basic tools / |
| title_exact_search | Foundations of cryptography : basic tools / |
| title_full | Foundations of cryptography : basic tools / Oded Goldreich. |
| title_fullStr | Foundations of cryptography : basic tools / Oded Goldreich. |
| title_full_unstemmed | Foundations of cryptography : basic tools / Oded Goldreich. |
| title_short | Foundations of cryptography : |
| title_sort | foundations of cryptography basic tools |
| title_sub | basic tools / |
| topic | Coding theory. http://id.loc.gov/authorities/subjects/sh85027654 Cryptography Mathematics. Cryptographie Mathématiques. BUSINESS & ECONOMICS Business Writing. bisacsh Coding theory fast Cryptography Mathematics fast Kryptologie gnd http://d-nb.info/gnd/4033329-2 |
| topic_facet | Coding theory. Cryptography Mathematics. Cryptographie Mathématiques. BUSINESS & ECONOMICS Business Writing. Coding theory Cryptography Mathematics Kryptologie |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616989 |
| work_keys_str_mv | AT goldreichoded foundationsofcryptographybasictools |