Yet Another Introductory Number Theory Textbook - Cryptology Emphasis

by Jonathan A. Poritz

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This introductory number theory textbook has a particular emphasis on connections to cryptology. The cryptologic material arising naturally out of the ambient number theory. The main cryptologic applications — being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem — come out so naturally from considerations of Euler's Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy's assertion of the purity and eternal inapplicability of number theory.

Description from LibreTexts.

Publisher
Colorado State University – Pueblo
Subjects
Mathematics, Combinatorics and Discrete Mathematics
Licence
CC BY-SA, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. Preface
  7. 1: Well-Ordering and Division
  8. 1.1: The Well-Ordering Principle and Mathematical Induction
  9. 1.2: Algebraic Operations with Integers
  10. 1.3: Divisibility and the Division Algorithm
  11. 1.4: Representations of Integers in Different Bases
  12. 1.5: The Greatest Common Divisor
  13. 1.6: The Euclidean Algorithm
  14. 2: Congruences
  15. 2.1: Introduction to Congruences
  16. 2.2: Linear Congruences
  17. 2.3: The Chinese Remainder Theorem
  18. 2.4: Another Way to Work with Congruences - Equivalence Classes
  19. 2.5: Euler's ϕ Function
  20. 3: Primes Numbers
  21. 3.1: Basics and the FTA
  22. 3.2: Wilson's Theorem
  23. 3.3: Multiplicative Order and Applications
  24. 3.4: Another Approach to Fermat's Little and Euler's Theorems
  25. 4: Cryptology
  26. 4.1: Some Speculative History
  27. 4.2: The Caesar Cipher and Its Variants
  28. 4.3: Frequency Analysis
  29. 4.4: Public-Key Crypto - the RSA Cryptosystem
  30. 4.5: Digital Signatures
  31. 4.6: Man-in-the-Middle Attacks, Certificates, and Trust
  32. 5: Indices and Discrete Logarithms
  33. 5.0: Prelude to Indices and Discrete Logarithms
  34. 5.1: More Properties of Multiplicative Order
  35. 5.2: A Necessary Digression - Gauss’s Theorem on Sums of Euler’s Function
  36. 5.3: Primitive Roots
  37. 5.4: Indices
  38. 5.5: Diffie-Helman Key Exchange
  39. 5.6: The ElGamal Cryptosystem
  40. Back Matter
  41. Bibliography
  42. Index
  43. Glossary
  44. Detailed Licensing