Primality Testing in Polynomial Time: From Randomized Algorithms to "Primes Is in P"

by Dietzfelbinger, Martin

• ISBN13: 9783540403449
• ISBN10: 3540403442
• Format: Paperback
• Copyright: 2004-08-30
• Publisher: Springer Verlag

Summary

This book is devoted to algorithms for the venerable primality problem: Given a natural number n, decide whether it is prime or composite. The problem is basic in number theory, efficient algorithms that solve it, i.e., algorithms that run in a number of computational steps which is polynomial in the number of digits needed to write n, are important for theoretical computer science and for applications in algorithmics and cryptology. This book gives a self-contained account of theoretically and practically important efficient algorithms for the primality problem, covering the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal, and Saxena. The textbook is written for students of computer science, in particular for those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.

Author Biography

Univ.-Prof. Dr.(USA) Martin Dietzfelbinger (b. 1956) studied Mathematics in Munich and earned his Ph.D. from the University of Illinois at Chicago. In 1992, he obtained his Habilitation at the Universit+ñt Paderborn with a thesis on randomized algorithms; in the same year he became a professor of computer science at the Universit+ñt Dortmund. Since 1998, he holds the chair for Complexity Theory and Efficient Algorithms at the Faculty of Computer Science and Automation of the Technische Universit+ñt Ilmenau, Germany. His main research interests are in complexity theory and data structures.

Table of Contents

Introduction : efficient primality testing	p. 1
Algorithms for numbers and their complexity	p. 13
Fundamentals from number theory	p. 23
Basics from algebra : groups, rings, and fields	p. 55
The Miller-Rabin test	p. 73
The Solovay-Strassen test	p. 85
More algebra : polynomials and fields	p. 95
Deterministic primality testing in polynomial time	p. 115
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