Primality testing in polynomial time : from randomized algorithms to "primes" is in P / Martin Dietzfelbinger.Material type: TextSeries: SerienbezeichnungLecture notes in computer science: ; Lecture notes in computer science: 3000.Publisher: Berlin ; New York : Springer, ©2004Edition: 1st edDescription: 1 online resource (x, 147 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 3540259333; 9783540259336; 1280307951; 9781280307959; 9786610307951; 6610307954Subject(s): Polynomials | Numbers, Prime | Algorithms | MATHEMATICS -- Algebra -- Elementary | Algorithms | Numbers, Prime | PolynomialsGenre/Form: Electronic books. Additional physical formats: Print version:: Primality testing in polynomial time.DDC classification: 512.9/42 LOC classification: QA246 | .D54 2004Other classification: 54.10 | 54.62 | 54.00 | 54.52 | SS 4800 | 004 | 510 | DAT 532f Online resources: Click here to access online
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Includes bibliographical references (pages 143-144) and index.
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.
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.