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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. |

More information: |

### Abstract:

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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