Uses of Randomness in Algorithms and Protocols - Couverture rigide

Kilian, Joe

 
9780262111539: Uses of Randomness in Algorithms and Protocols
Couverture rigide
ISBN 10 : 0262111535 ISBN 13 : 9780262111539
Editeur : The MIT Press, 1990

Synopsis

Uses of Randomness in Algorithms and Protocols makes fundamental contributions to two different fields of complexity theory: computational number theory and cryptography. The most famous result is Goldwasser and Kilian's invention of a new approach to distinguish prime numbers from composites, using methods from the theory of elliptic curves over finite fields. The Goldwasser-Kilian algorithm is the first to yield a polynomial size proof of its assertions, ensuring correctness while still provably running fast on most inputs. This new primality test implies for the first time and without any assumptions that large certified primes can be generated in expected polynomial time under a distribution that is close to uniform. It provides a provocative new link between algebraic geometry and primality testing, one of the most ancient algorithmic problems in number theory. Heuristic implementations of the algorithm are currently considered to be the fastest existing methods to certify primes. Kilian also provides two elegant and original contributions to theoretical cryptography. He shows how to base general two-party protocols on a simple protocol, known as "oblivious transfer," proving the first completeness result of this kind. He also introduces a generalization of interactive proof systems, known as "multi-prover interactive proof systems," and shows that anything provable in this model is provable in zero knowledge.

Contents
Introduction • New Techniques in Primality Testing • Committing Bits Using Oblivious Transfer • Circuit Evaluation Using Oblivious Transfer: The NC1 Circuit Base • Oblivious Evaluation of Arbitrary Circuits • Interactive Proof Systems with Multiple Provers

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Joe Kilian is a National Science Foundation Postdoctoral Fellow at MIT and Harvard.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
The MIT Press
Date d'édition
1990
Langue
anglais
ISBN 10 
0262111535
ISBN 13 
9780262111539
Reliure
Relié
Nombre de pages
260
Coordonnées du fabricant
non disponible
Personne responsable
non disponible