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A primer on pseudorandom generators

Author: Oded Goldreich
Publisher: Providence, R.I. : American Mathematical Society, ©2010.
Series: University lecture series (Providence, R.I.), 55.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
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
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Details

Document Type: Book
All Authors / Contributors: Oded Goldreich
ISBN: 9780821851920 0821851926
OCLC Number: 615339073
Description: x, 114 p. : ill. ; 26 cm.
Contents: Third Theory of Randomness Organization of the Primer Standard Conventions General Paradigm Three fundamental aspects Notational conventions Some instatiations of the general paradigm General-Purpose Pseudorandom Generators Basic Definition Archetypical Application Computational Indistinguishability general formulation Relation to statistical closeness Indistinguishability by Multiple samples Amplifying the Stretch Function Background: one-way functions simple construction alternative presentation necessary and sufficient condition Non-uniformly Strong Pseudorandom Generators Stronger (Uniform-complexity) Notions Fooling stronger distinguishers Pseudorandom functions Conceptual Reflections Derandomization of Time-Complexity Classes Defining Canonical Derandomizers Constructing Canonical Derandomizers construction and its consequences Analyzing the construction Construction 3.4 as a general framework Reflections Regarding Derandomization Space-Bounded Distinguishers Definitional Issues Two Constructions Sketches of the proofs of Theorems 4.2 and 4.3 Derandomization of space-complexity classes Special Purpose Generators Pairwise Independence Generators taste of the applications Small-Bias Generators taste of the applications Random Walks on Expanders Background: expanders and random walks on them Hashing functions Leftover Hash Lemma On Randomness Extractors Generic Hard-Core Predicate Using Randomness in computation Simple Probabilistic Polynomial-Time Primality Test Testing Polynomial Identity Accidental Tourist Sees It All Cryptographic Applications of Pseudorandom functions Secret Communication Authenticated Communication Some Basic Complexity Classes
Series Title: University lecture series (Providence, R.I.), 55.
Responsibility: Oded Goldreich.

Abstract:

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 serveral 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. --Book Jacket.

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