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Cryptology by Discovery:
An Introduction to Conjecture and Proof
Tamara Veenstra
Contents
Index
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Contents
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Front Matter
Colophon
Preface
1
Introduction
Basic Ideas
Cryptograms
Investigations: Introduction
2
Monoalphabetic Ciphers
Shift Ciphers
Modular Arithmetic
Exercises Set 1
Decimation Ciphers
Exercises Set 2
Mathematical Statements
Affine Ciphers
Exercises Set 3
Keyword Columnar Ciphers
Frequency Analysis
Exercises Set 4
Investigations: Monoalphabetic
3
Vigenère Cipher
Vigenère Encryption
Probability, Permutations and Combinations
Exercises Set 5
Vigenére Cryptanalysis
Exercises Set 6
Investigations: Vigenère
4
The Enigma Machine
Cipher Machines
Enigma Mechanics
Exercises Set 7
Permutations and Letter Chains
Cribs and Bombes
Exercises Set 8
Investigations: Enigma
5
Public Key Cryptography
Introduction
Diffie-Hellman Key Exchange
Exercises Set 9
A Number Trick
Fermat and Induction
Exercises Set 10
RSA cryptosystem
Exercises Set 11
Digital Signatures
Exercises Set 12
Investigations: Public Key
6
Block Ciphers
Playfair Cipher
Exercises Set 13
Hill Cipher
Data Encryption Standard
Exercises Set 14
Investigations: Block Ciphers
Review Exercises
Reference
A
Computation in other Bases
Base 26 conversions
Binary Conversions
B
Intro to Sage and Python
C
Sage Cells Index
Index
Authored in PreTeXt
Cryptology by Discovery:
An Introduction to Conjecture and Proof
Tamara Veenstra
Department of Mathematics
University of Redlands
tamara_veenstra@redlands.edu
September 19, 2020
Colophon
Preface
