Using Hard Problems to Create Pseudorandom Generators - Softcover

Nisan, Noam

Softcover

ISBN 10: 026264052X ISBN 13: 9780262640527

Publisher: MIT Press, 2003

Synopsis

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.

Contents
Introduction - Hardness vs. Randomness - Pseudorandom Generators for Logspace and Multiparty Protocols

About this title

About the Author

Noam Nisan is Professor at the Institute of Computer Science and Engineering, Hebrew University of Jerusalem.

Edition details

• Publisher: MIT Press
• Publication date: 2003
• Language: English
• ISBN 10: 026264052X
• ISBN 13: 9780262640527
• Binding: Paperback
• Number of pages: 56