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Using hard problems to create pseudorandom generators

Author: Noam Nisan
Publisher: Cambridge, Mass. : MIT Press, ©1992.
Dissertation: Revision of the author's thesis (Ph. D.)--University of California, Berkeley, 1988.
Series: ACM distinguished dissertations.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : EnglishView all editions and formats
Summary:
"Randomization is an important tool in the design of algorithms, and the ability of randomization to provide enhanced power is a major research topic in complexity theory. Noam Nisan continues the investigation into the power of randomization and the relationships between randomized and deterministic complexity classes by pursuing the idea of emulating randomness, or pseudorandom generation. Pseudorandom generators  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Nisan, Noam.
Using hard problems to create pseudorandom generators.
Cambridge, Mass. : MIT Press, ©1992
(DLC) 91040779
(OCoLC)24848488
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Noam Nisan
ISBN: 9780262256728 026225672X
OCLC Number: 827307440
Notes: "Noam Nisan is Lecturer in the Department of Computer Science at Hebrew University in Jerusalem. He received his doctoral degree from the University of California, Berkeley."
Description: 1 online resource (vi, 43 pages).
Contents: 1. Introduction --
2. Hardness vs. randomness --
3. Multiparty protocols and pseudorandom generators for logspace --
4. Recent results.
Series Title: ACM distinguished dissertations.
Responsibility: Noam Nisan.

Abstract:

"Randomization is an important tool in the design of algorithms, and the ability of randomization to provide enhanced power is a major research topic in complexity theory. Noam Nisan continues the investigation into the power of randomization and the relationships between randomized and deterministic complexity classes by pursuing the idea of emulating randomness, or pseudorandom generation. Pseudorandom generators reduce the number of random bits required by randomized algorithms, enable the construction of certain cryptographic protocols, and shed light on the difficulty of simulating randomized algorithms by deterministic ones. The research described here deals with two methods of constructing pseudorandom generators from hard problems and demonstrates some surprising connections between pseudorandom generators and seemingly unrelated topics such as multiparty communication complexity and random oracles. Nisan first establishes a precise connection between computational complexity and pseudorandom number generation, revealing that efficient deterministic simulation of randomized algorithms is possible under much weaker assumptions than was previously known, and bringing to light new consequences concerning the power of random oracles. Using a remarkable argument based on multiparty communication complexity, Nisan then constructs a generator that is good against all tests computable in logarithmic space. A consequence of this result is a new construction of universal traversal sequences."

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