Primality Testing in Polynomial Time

From Randomized Algorithms to "PRIMES Is in P"
2004
ISBN: 978-3-540-40344-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 3000, 150 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 260 g

Reihe: Lecture Notes in Computer Science

A self-contained treatment 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 volume is written for students of computer science, in particular those with a special interest in cryptology, and students of mathematics. The text may be used as a supplement for courses or for self-study.

Zielgruppe

Research

Autoren/Hrsg.

Dietzfelbinger, Martin

Fachgebiete

• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Programmierung: Methoden und Allgemeines
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.