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Yet Another Introductory Number Theory Textbook - Cryptology Emphasis
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.
- Author
- Jonathan A. Poritz
- Publisher
- Colorado State University – Pueblo
- Source
- LibreTexts
- License
- CC BY-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 33 sections
- 01: Well-Ordering and Division
- 1.01: The Well-Ordering Principle and Mathematical Induction
- 1.02: Algebraic Operations with Integers
- 1.03: Divisibility and the Division Algorithm
- 1.04: Representations of Integers in Different Bases
- 1.05: The Greatest Common Divisor
- 1.06: The Euclidean Algorithm
- 02: Congruences
- 2.01: Introduction to Congruences
- 2.02: Linear Congruences
- 2.03: The Chinese Remainder Theorem
- 2.04: Equivalence Classes
- 2.05: Euler's ϕ Function
- 03: Primes Numbers
- 3.01: Basics and the FTA
- 3.02: Wilson's Theorem
- 3.03: Multiplicative Order and Applications
- 3.04: Another Approach to Fermat's Little and Euler's Theorems
- 04: Cryptology
- 4.01: Some Speculative History
- 4.02: The Caesar Cipher and Its Variants
- 4.03: Frequency Analysis
- 4.04: Public-Key Crypto - the RSA Cryptosystem
- 4.05: Digital Signatures
- 4.06: Man-in-the-Middle Attacks Certificates and Trust
- 05: Indices Discrete Logarithms
- 5.00: Introduction to Indices and Discrete Logarithms
- 5.01: More Properties of Multiplicative Order
- 5.02: Gauss's Theorem on Sums of Euler's Function
- 5.03: Primitive Roots
- 5.04: Indices
- 5.05: Diffie-Helman Key Exchange
- 5.06: The ElGamal Cryptosystem