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Number Theory for Computing

  • Song Y. Yan

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Song Y. Yan
    Pages 1-137
  3. Song Y. Yan
    Pages 139-258
  4. Song Y. Yan
    Pages 259-361
  5. Back Matter
    Pages 363-381

About this book

Introduction

Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART [219] The theory of numbers, in mathematics, is primarily the theory of the prop­ erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How­ ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica­ tions in other areas, particularly in computing and information technology.

Keywords

Notation algorithmic number theory arithmetic functions computational number theory cryptography cryptology discrete logarithms elementary number theory elliptic curves hash function information information security information theory number

Authors and affiliations

  • Song Y. Yan
    • 1
  1. 1.Computer ScienceAston UniversityBirminghamUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04053-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-04055-3
  • Online ISBN 978-3-662-04053-9
  • Buy this book on publisher's site
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