2009

Number Theory in Science and Communication

With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

Authors:

ISBN: 978-3-540-85297-1 (Print) 978-3-540-85298-8 (Online)

Table of contents (32 chapters)

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  1. Front Matter

    Pages I-XXIV

  2. A Few Fundamentals

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-20

      Introduction

    3. No Access

      Book Chapter

      Pages 21-29

      The Natural Numbers

    4. No Access

      Book Chapter

      Pages 31-43

      Primes

    5. No Access

      Book Chapter

      Pages 45-69

      The Prime Distribution

  3. Some Simple Applications

    1. Front Matter

      Pages 71-71

    2. No Access

      Book Chapter

      Pages 73-107

      Fractions: Continued, Egyptian and Farey

  4. Congruences and the Like

    1. Front Matter

      Pages 109-109

    2. No Access

      Book Chapter

      Pages 111-117

      Linear Congruences

    3. No Access

      Book Chapter

      Pages 119-137

      Diophantine Equations

    4. No Access

      Book Chapter

      Pages 139-145

      The Theorems of Fermat Wilson and Euler

    5. No Access

      Book Chapter

      Pages 147-158

      Permutations Cycles and Derangements

  5. Cryptography and Divisors

    1. Front Matter

      Pages 159-159

    2. No Access

      Book Chapter

      Pages 161-170

      Euler Trap Doors and Public-Key Encryption

    3. No Access

      Book Chapter

      Pages 171-177

      The Divisor Functions

    4. No Access

      Book Chapter

      Pages 179-191

      The Prime Divisor Functions

    5. No Access

      Book Chapter

      Pages 193-194

      Certified Signatures

    6. No Access

      Book Chapter

      Pages 195-211

      Primitive Roots

    7. No Access

      Book Chapter

      Pages 213-216

      Knapsack Encryption

  6. Residues and Diffraction

    1. Front Matter

      Pages 217-217

    2. No Access

      Book Chapter

      Pages 219-232

      Quadratic Residues

  7. Chinese and Other Fast Algorithms

    1. Front Matter

      Pages 233-233

    2. No Access

      Book Chapter

      Pages 235-243

      The Chinese Remainder Theorem and Simultaneous Congruences

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      Book Chapter

      Pages 245-249

      Fast Transformation and Kronecker Products

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      Book Chapter

      Pages 251-252

      Quadratic Congruences

  8. Pseudoprimes, Möbius Transform, and Partitions

    1. Front Matter

      Pages 253-253

    2. No Access

      Book Chapter

      Pages 255-266

      Pseudoprimes Poker and Remote Coin Tossing

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