Studies in Complexity and Cryptography. Miscellanea on the Interplay between Randomness and Computation : In Collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron,

This book presents a collection of 36 pieces of scientific work in the areas of complexity theory and foundations of cryptography: 20 research contributions, 13 survey articles, and 3 programmatic and reflective viewpoint statements. These so far formally unpublished pieces were written by Oded Goldreich, some in collaboration with other scientists. The articles included in this book essentially reflect the topical scope of the scientific career of Oded Goldreich now spanning three decades. In particular the topics dealt with include average-case complexity, complexity of approximation, derandomization, expander graphs, hashing functions, locally testable codes, machines that take advice, NP-completeness, one-way functions, probabilistically checkable proofs, proofs of knowledge, property testing, pseudorandomness, randomness extractors, sampling, trapdoor permutations, zero-knowledge, and non-iterative zero-knowledge. All in all, this potpourri of studies in complexity and cryptography constitutes a most valuable contribution to the field of theoretical computer science centered around the personal achievements and views of one of its outstanding representatives. Front Matter....Pages - Finding the Shortest Move-Sequence in the Graph-Generalized 15-Puzzle Is NP-Hard....Pages 1-5 Proving Computational Ability....Pages 6-12 On Constructing 1-1 One-Way Functions....Pages 13-25 On the Circuit Complexity of Perfect Hashing....Pages 26-29 Collision-Free Hashing from Lattice Problems....Pages 30-39 Another Proof That $\mathcal{BPP}\subseteq \mathcal{PH}$ (and More)....Pages 40-53 Strong Proofs of Knowledge....Pages 54-58 Simplified Derandomization of BPP Using a Hitting Set Generator....Pages 59-67 On Testing Expansion in Bounded-Degree Graphs....Pages 68-75 Candidate One-Way Functions Based on Expander Graphs....Pages 76-87 Using the FGLSS-Reduction to Prove Inapproximability Results for Minimum Vertex Cover in Hypergraphs....Pages 88-97 The GGM Construction Does NOT Yield Correlation Intractable Function Ensembles....Pages 98-108 From Logarithmic Advice to Single-Bit Advice....Pages 109-113 On Probabilistic versus Deterministic Provers in the Definition of Proofs of Knowledge....Pages 114-123 On the Average-Case Complexity of Property Testing....Pages 124-135 A Candidate Counterexample to the Easy Cylinders Conjecture....Pages 136-140 From Absolute Distinguishability to Positive Distinguishability....Pages 141-155 Testing Graph Blow-Up....Pages 156-172 Proximity Oblivious Testing and the Role of Invariances....Pages 173-190 In a World of P=BPP....Pages 191-232 Notes on Levin’s Theory of Average-Case Complexity....Pages 233-247 Three XOR-Lemmas — An Exposition....Pages 248-272 On Yao’s XOR-Lemma....Pages 273-301 A Sample of Samplers: A Computational Perspective on Sampling....Pages 302-332 Short Locally Testable Codes and Proofs....Pages 333-372 Bravely, Moderately: A Common Theme in Four Recent Works....Pages 373-389 On the Complexity of Computational Problems Regarding Distributions....Pages 390-405 Basing Non-Interactive Zero-Knowledge on (Enhanced) Trapdoor Permutations: The State of the Art....Pages 406-421 Average Case Complexity, Revisited....Pages 422-450 Basic Facts about Expander Graphs....Pages 451-464 A Brief Introduction to Property Testing....Pages 465-469 Introduction to Testing Graph Properties....Pages 470-506 Randomness and Computation....Pages 507-539 On Security Preserving Reductions – Revised Terminology....Pages 540-546 Contemplations on Testing Graph Properties....Pages 547-554 Another Motivation for Reducing the Randomness Complexity of Algorithms....Pages 555-560 Back Matter....Pages - Paying witness to the author's thirty-year career in science, these high-quality papers, some co-written with colleagues, reflect his professional range, covering material from average-case complexity to derandomization and probabilistically checkable proofs.