Description

Book Synopsis
In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works.

Trade Review
The authors can be congratulated on making an important recent result accessible to a very wide audience." - Ch. Baxa, Monatsh Math

Table of Contents
  • Preface
  • Introduction
  • Part I. Foundations
  • Natural numbers and primes
  • Algorithms and complexity
  • Foundations of number theory
  • Prime numbers and cryptography
  • Part II. The AKS algorithm
  • The starting point: Fermat for polynomials
  • The theorem for Agrawal, Kayal, and Saxena
  • The algorithm
  • Open questions
  • Solutions and comments to important exercises
  • Bibliography
  • List of symbols
  • Index

Primality Testing for Beginners

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    A Paperback by Lasse Rempe–gillen, Rebecca Waldecker

    £47.70

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      Book details

      Publisher American Mathematical Society
      Published 1/30/2014 12:00:00 AM
      ISBN-13 9780821898833
      978-0821898833
      ISBN-10 0821898833
      Also in:
      Applied mathematics

      Description

      Book Synopsis
      In 2002, Agrawal, Kayal, and Saxena answered a long-standing open question by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. Rempe-Gillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works.

      Trade Review
      The authors can be congratulated on making an important recent result accessible to a very wide audience." - Ch. Baxa, Monatsh Math

      Table of Contents
      • Preface
      • Introduction
      • Part I. Foundations
      • Natural numbers and primes
      • Algorithms and complexity
      • Foundations of number theory
      • Prime numbers and cryptography
      • Part II. The AKS algorithm
      • The starting point: Fermat for polynomials
      • The theorem for Agrawal, Kayal, and Saxena
      • The algorithm
      • Open questions
      • Solutions and comments to important exercises
      • Bibliography
      • List of symbols
      • Index

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