Computational Number Theory

Abhijit Das

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March 18, 2013 by Chapman and Hall/CRC
Textbook - 614 Pages - 13 B/W Illustrations
ISBN 9781439866153 - CAT# K12950
Series: Discrete Mathematics and Its Applications

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Features

  • Explores many important computational issues and recent developments in number theory
  • Presents an elementary treatment of the material, eliminating the need for an extensive background in mathematics
  • Uses the GP/PARI number-theory calculator to illustrate complicated algorithms
  • Describes the application of number theory in public-key cryptography
  • Contains numerous examples and exercises, with some solutions in an appendix

Solutions manual available upon qualifying course adoption

Summary

Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and practitioners of cryptography in industry.

Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications. It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. It then discusses elliptic curves, primality testing, algorithms for integer factorization, computing discrete logarithms, and methods for sparse linear systems. The text also shows how number-theoretic tools are used in cryptography and cryptanalysis. A dedicated chapter on the application of number theory in public-key cryptography incorporates recent developments in pairing-based cryptography.

With an emphasis on implementation issues, the book uses the freely available number-theory calculator GP/PARI to demonstrate complex arithmetic computations. The text includes numerous examples and exercises throughout and omits lengthy proofs, making the material accessible to students and practitioners.

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