Studies in Complexity and Cryptography

Research Contributions.- Finding the Shortest Move-Sequence in the Graph-Generalized 15-Puzzle Is NP-Hard.- Proving Computational Ability.- On Constructing 1-1 One-Way Functions.- On the Circuit Complexity of Perfect Hashing.- Collision-Free Hashing from Lattice Problems.- Another Proof That BPP ae PH (and More).- Strong Proofs of Knowledge.- Simplified Derandomization of BPP Using a Hitting Set Generator.- On Testing Expansion in Bounded-Degree Graphs.- Candidate One-Way Functions Based on Expander Graphs.- Using the FGLSS-Reduction to Prove Inapproximability Results for Minimum Vertex Cover in Hypergraphs.- The GGM Construction Does NOT Yield Correlation Intractable Function Ensembles.- From Logarithmic Advice to Single-Bit Advice.- On Probabilistic versus Deterministic Provers in the Definition of Proofs of Knowledge.- On the Average-Case Complexity of Property Testing.- A Candidate Counterexample to the Easy Cylinders Conjecture.- From Absolute Distinguishability to Positive Distinguishability.- Testing Graph Blow-Up.- Proximity Oblivious Testing and the Role of Invariances.- In a World of P=BPP.- Surveys.- Notes on Levin's Theory of Average-Case Complexity.- Three XOR-Lemmas -- An Exposition.- On Yao's XOR-Lemma.- A Sample of Samplers: A Computational Perspective on Sampling.- Short Locally Testable Codes and Proofs.- Bravely, Moderately: A Common Theme in Four Recent Works.- On the Complexity of Computational Problems Regarding Distributions.- Basing Non-Interactive Zero-Knowledge on (Enhanced) Trapdoor Permutations: The State of the Art.- Average Case Complexity, Revisited.- Basic Facts about Expander Graphs.- A Brief Introduction to Property Testing.- Introduction to Testing Graph Properties.- Randomness and Computation.- Programmatic and Reflective Articles.- On Security Preserving Reductions -- Revised Terminology.- Contemplations on Testing Graph Properties.- Another Motivation for Reducing the Randomness Complexity of Algorithms.- About the Authors.