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  • © 1994

A Course in Number Theory and Cryptography

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 114)

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  • ISBN: 978-1-4419-8592-7
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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
  2. Some Topics in Elementary Number Theory

    • Neal Koblitz
    Pages 1-30
  3. Finite Fields and Quadratic Residues

    • Neal Koblitz
    Pages 31-53
  4. Cryptography

    • Neal Koblitz
    Pages 54-82
  5. Public Key

    • Neal Koblitz
    Pages 83-124
  6. Primality and Factoring

    • Neal Koblitz
    Pages 125-166
  7. Elliptic Curves

    • Neal Koblitz
    Pages 167-199
  8. Back Matter

    Pages 200-235

About this book

. . . both Gauss and lesser mathematicians may be justified in rejoic­ ing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A Mathematician's Apology, 1940 G. H. Hardy would have been surprised and probably displeased with the increasing interest in number theory for application to "ordinary human activities" such as information transmission (error-correcting codes) and cryptography (secret codes). Less than a half-century after Hardy wrote the words quoted above, it is no longer inconceivable (though it hasn't happened yet) that the N. S. A. (the agency for U. S. government work on cryptography) will demand prior review and clearance before publication of theoretical research papers on certain types of number theory. In part it is the dramatic increase in computer power and sophistica­ tion that has influenced some of the questions being studied by number theorists, giving rise to a new branch of the subject, called "computational number theory. " This book presumes almost no background in algebra or number the­ ory. Its purpose is to introduce the reader to arithmetic topics, both ancient and very modern, which have been at the center of interest in applications, especially in cryptography. For this reason we take an algorithmic approach, emphasizing estimates of the efficiency of the techniques that arise from the theory.

Keywords

  • Prime
  • adopted textbook
  • continued fraction
  • cryptography
  • finite field
  • number theory

Authors and Affiliations

  • Department of Mathematics, University of Washington, Seattle, USA

    Neal Koblitz

Bibliographic Information

  • Book Title: A Course in Number Theory and Cryptography

  • Authors: Neal Koblitz

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-8592-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94293-3

  • Softcover ISBN: 978-1-4612-6442-2

  • eBook ISBN: 978-1-4419-8592-7

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: X, 235

  • Topics: Number Theory

Buying options

eBook
USD 49.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-8592-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 64.95
Price excludes VAT (USA)
Hardcover Book
USD 64.95
Price excludes VAT (USA)