Primality Testing in Polynomial Time

From Randomized Algorithms to "PRIMES is in P"

Prof. Dr. Martin Dietzfelbinger                                                        

                        Technische Universität lmenau

Fakultät Informatik und Automatisierung

Institut für Theoretische Informatik

FG Komplexitätstheorie und Effiziente Algorithmen


About this book

This book treats 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 decimal 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 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.


  • Computational Number Theory
  • Deterministic Primality Testing
  • Efficient Algorithms
  • Efficient Primality Testing
  • Factorization
  • Number Theoretical Algorithms
  • Polynomial Time Algorithms
  • Primality Testing
  • Randomized Algorithms

Bibliographic data:

Springer-Verlag Heidelberg Berlin New York
Lecture Notes in Computer Science, Vol.3000
Published 2004
147 p. Also available online
ISBN 3-540-40344-2

Errata (sorted by date; last update: 2008-08-14)

Errata (sorted by page number; last update: 2008-08-14)

Publisher's website