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Studies in Complexity and Cryptography: Miscellanea on the Interplay between Randomness and Computation

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This volume contains a collection of studies in the areas of complexity theory and foundations of cryptography. These studies were conducted at different times during the last couple of decades. Although many of these studies have been referred to by other works, none of them was formally published before.

Indeed, this volume is quite unusual, and it raises two opposite questions regarding the publication of the foregoing studies: (1) why were these studies not published (formally) before, and (2) why are they being published now?

Let me start with the second question. In the years that have elapsed since the completion of many of these individual studies, I have occasionally looked at them for some reason. On these occasions, I felt that it is somewhat inappropriate that these works were never published formally (although many of them were posted on forums such as ECCC). The current volume is aimed at amending this situation somewhat.

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 These so far formally unpublished pieces were written by Oded Goldreich, some in collaboration with other scientists.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.

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