Foundations of Cryptography, Volume 1: Basic Techniques

By Oded Goldreich

Cryptography is anxious with the conceptualization, definition and building of computing structures that handle safety matters. This ebook offers a rigorous and systematic remedy of the foundational concerns: defining cryptographic initiatives and fixing new cryptographic difficulties utilizing current instruments. It specializes in the elemental mathematical instruments: computational hassle (one-way functions), pseudorandomness and zero-knowledge proofs. instead of describing ad-hoc techniques, this e-book emphasizes the explanation of basic strategies and the demonstration of the feasibility of fixing cryptographic difficulties. it truly is appropriate to be used in a graduate path on cryptography and as a reference e-book for specialists.

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2. 2. 2. three 2. four. 2. five. 2. 6. ∗ 2. 7. 30 One-Way capabilities: Motivation One-Way services: Definitions 2. 2. 1. robust One-Way services 2. 2. 2. susceptible One-Way features 2. 2. three. helpful size Conventions 2. 2. four. applicants for One-Way services 2. 2. five. Non-Uniformly One-Way capabilities susceptible One-Way features suggest robust Ones 2. three. 1. the development and Its research (Proof of Theorem 2. three. 2) 2. three. 2. representation by way of a Toy instance 2. three. three. dialogue One-Way capabilities: adaptations 2. four. 1. ∗ common One-Way functionality 2. four. 2. One-Way capabilities as Collections 2. four. three. Examples of One-Way Collections 2. four. four. Trapdoor One-Way variations 2. four. five. ∗ Claw-Free features 2. four. 6. ∗ On offering applicants Hard-Core Predicates 2. five. 1. Definition 2. five. 2. Hard-Core Predicates for Any One-Way functionality 2. five. three. ∗ Hard-Core features effective Amplification of One-Way features 2. 6. 1. the development 2. 6. 2. research Miscellaneous 2. 7. 1. old Notes 2. 7. 2. feedback for extra analyzing 2. 7. three. Open difficulties 2. 7. four. workouts three Pseudorandom turbines three. 1. a hundred and one Motivating dialogue three. 1. 1. Computational techniques to Randomness three. 1. 2. A Rigorous method of Pseudorandom turbines three. 2. three. three. 31 32 32 35 35 forty forty-one forty three forty four forty eight 50 fifty one fifty two fifty three fifty five fifty eight 60 sixty three sixty four sixty four sixty five seventy four seventy eight eighty eighty one 88 89 89 ninety one ninety two Computational Indistinguishability three. 2. 1. Definition three. 2. 2. Relation to Statistical Closeness three. 2. three. Indistinguishability by way of Repeated Experiments three. 2. four. ∗ Indistinguishability by means of Circuits three. 2. five. Pseudorandom Ensembles Definitions of Pseudorandom turbines three. three. 1. regular Definition of Pseudorandom turbines viii 102 102 103 103 104 106 107 111 112 112 113 CONTENTS three. three. 2. three. three. three. ∗ three. three. four. three. three. five. three. three. 6. three. four. expanding the growth issue Variable-Output Pseudorandom turbines The Applicability of Pseudorandom turbines Pseudorandomness and Unpredictability Pseudorandom turbines indicate One-Way capabilities structures according to One-Way diversifications three. four. 1. development in response to a unmarried Permutation three. four. 2. building in line with Collections of diversifications three. four. three. ∗ utilizing Hard-Core services instead of Predicates three. five. ∗ buildings in keeping with One-Way services three. five. 1. utilizing 1-1 One-Way capabilities three. five. 2. utilizing common One-Way capabilities three. five. three. Going past common One-Way services three. 6. Pseudorandom capabilities three. 6. 1. Definitions three. 6. 2. building three. 6. three. purposes: A common technique three. 6. four. ∗ Generalizations ∗ three. 7. Pseudorandom diversifications three. 7. 1. Definitions three. 7. 2. development three. eight. Miscellaneous three. eight. 1. old Notes three. eight. 2. feedback for extra interpreting three. eight. three. Open difficulties three. eight. four. workouts four Zero-Knowledge facts platforms four. 1. four. 2. four. three. four. four. 114 118 119 119 123 124 124 131 134 one hundred thirty five a hundred thirty five 141 147 148 148 one hundred fifty 157 158 164 164 166 169 169 one hundred seventy 172 172 184 Zero-Knowledge Proofs: Motivation four. 1. 1. The suggestion of an explanation four. 1. 2. Gaining wisdom Interactive evidence structures four. 2. 1. Definition four. 2. 2. An instance (Graph Non-Isomorphism in IP ) four. 2. three. ∗ The constitution of the category IP four. 2. four. Augmentation of the version Zero-Knowledge Proofs: Definitions four. three. 1. excellent and Computational Zero-Knowledge four.

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