Bøger af Oded Goldreich

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 These so far formally unpublished pieces were written by Oded Goldreich, some in collaboration with other scientists.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

An interactive proof system is called doubly-efficient if the prescribed prover strategy can be implemented in polynomial-time and the verifier's strategy can be implemented in almost-linear time. This book surveys some of the known results regarding doubly-efficient interactive proof systems.

This primer concentrates on three types of probabilistic proof systems: interactive proofs, zero-knowledge proofs, and probabilistically checkable proofs. Surveying the basic results regarding these proof systems, the primer stresses the essential role of randomness in each of them.

Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness.