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| Title Details: | |
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Primality |
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| Authors: |
Poulakis, Dimitrios |
| Reviewer: |
Tzanakis, Nikolaos |
| Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY > COMPUTATIONAL NUMBER THEORY MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE > ALGORITHMS AND COMPLEXITY MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE > INFORMATION ASSURANCE AND SECURITY > CRYPTOGRAPHY |
| Keywords: |
Computational Number Theory
Primality Cryptography |
| Description: | |
| Abstract: |
In this chapter we describe some claasical primality tests based on the theorems of Lucas, Pocklington, Fermat, Solovay-Strassen
and Miller-Rabin. Finally, we shall study the AKS algorithm which has been invented by The Indian Mathematiciens M. Agrawal, N. Kayal and N. Saxena, and is the first determinist polynomial time algorithm for testing whether or not a positive integer is prime. |
| Table of Contents: |
Chapter 6 contains the following sectionsι:
6.1 Lucas και Pocklington tests 6.2 Carmichael Numbers 6.3 The Solovay − Strassen test 6.4 The Miller − Rabin test 6.5 The AKS Algorithm 6.5.1 A generalization of Fermat's theorem 6.5.2 Some Lemmas 6.5.3 Description of the AKS Algorithm 6.6 Exercises Bibliography |
| Technical Editors: |
Karakostas, Anastasios |
| Type: |
Chapter |
| Creation Date: | 2015 |
| Item Details: | |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| Handle | http://hdl.handle.net/11419/1049 |
| Bibliographic Reference: | Poulakis, D. (2015). Primality [Chapter]. In Poulakis, D. 2015. Computational Number Theory [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1049 |
| Language: |
Greek |
| Is Part of: |
Computational Number Theory |
| Number of pages |
31 |
| Publication Origin: |
Kallipos, Open Academic Editions |