مقدمه‌ای بر تولیدکننده‌های شبه‌تصادفی (سری سخنرانی‌های دانشگاهی، ۵۵)

A fresh look at the question of randomness was taken in the theory of computing: A distribution is pseudorandom if it cannot be distinguished from the uniform distribution by any efficient procedure. This paradigm, originally associating efficient procedures with polynomial-time algorithms, has been applied with respect to a variety of natural classes of distinguishing procedures. The resulting theory of pseudorandomness is relevant to science at large and is closely related to central areas of computer science, such as algorithmic design, complexity theory, and cryptography. This primer surveys the theory of pseudorandomness, starting with the general paradigm, and discussing various incarnations while emphasizing the case of general-purpose pseudorandom generators (withstanding any polynomial-time distinguisher). Additional topics include the “derandomization” of arbitrary probabilistic polynomial-time algorithms, pseudorandom generators withstanding space-bounded distinguishers, and several natural notions of special-purpose pseudorandom generators. The primer assumes basic familiarity with the notion of efficient algorithms and with elementary probability theory, but provides a basic introduction to all notions that are actually used. As a result, the primer is essentially self-contained, although the interested reader is at times referred to other sources for more detail. Cover 1 Title page 4 Contents 6 Preface 10 Introduction 12 General-purpose pseudorandom generators 22 Derandomization of time-complexity classes 46 Space-bounded distinguishers 58 Special purpose generators 70 Concluding remarks 88 Hashing functions 90 On randomness extractors 94 A generic hard-core predicate 100 Using randomness in computation 104 Cryptographic applications of pseudorandom functions 110 Some basic complexity classes 114 Bibliography 118 Index 124 Back Cover 130