Martin Dietzfelbinger

Primality Testing in Polynomial Time (eBook, PDF)

From Randomized Algorithms to "PRIMES Is in P"

• Format: PDF

Produktbeschreibung

A self-contained treatment of theoretically and practically important efficient algorithms for the primality problem. The text covers 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 volume is written for students of computer science, in particular 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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 150
• Erscheinungstermin: 17. August 2004
• Englisch
• ISBN-13: 9783540259336
• Artikelnr.: 53092372

Autorenporträt

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 Universität Paderborn with a thesis on randomized algorithms; in the same year he became a professor of computer science at the Universität Dortmund. Since 1998, he holds the chair for Complexity Theory and Efficient Algorithms at the Faculty of Computer Science and Automation of the Technische Universität Ilmenau, Germany. His main research interests are in complexity theory and data structures.

Inhaltsangabe

1. Introduction: Efficient Primality Testing.- 2. Algorithms for Numbers and Their Complexity.- 3. Fundamentals from Number Theory.- 4. Basics from Algebra: Groups, Rings, and Fields.- 5. The Miller-Rabin Test.- 6. The Solovay-Strassen Test.- 7. More Algebra: Polynomials and Fields.- 8. Deterministic Primality Testing in Polynomial Time.- A. Appendix.

Rezensionen

From the reviews:

"This book gives an account of the recent proof by M. Agrawal, N. Kayal and N. Saxena ... that one can decide in polynomial time whether a given natural number is prime or composite. ... It presents the background needed from number theory and algebra to make the proof accessible to undergraduates. ... This concise book is written for students of computer science and of mathematics." (Samuel S. Wagstaff, Mathematical Reviews, Issue 2005 m)

"The book can logically be separated into two parts: the first covering introductory material and the second covering the AKS result itself. ... Chapters ... are a joy to read, and I found the proofs and explanations clear and concise. Amazingly, the material is presented in full, with complete proofs given for all results necessary for proving the main results of the book. ... I would enthusiastically and wholeheartedly recommend this book ... ." (Jonathan Katz, SIGACT News, Vol. 37 (1), 2006)