Invitation to Cryptology, 1st edition

Published by Pearson (August 31, 2001) © 2002

  • Thomas H. Barr
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For a one-semester undergraduate-level course in Cryptology, Mathematics, or Computer Science.

Designed for either the intelligent freshman (good at math) or for a low-level junior year first course, Cryptology introduces a wide range of up-to-date cryptological concepts along with the mathematical ideas that are behind them. The new and old are organized around a historical framework. A variety of mathematical topics that are germane to cryptology (e.g., modular arithmetic, Boolean functions, complexity theory, etc.) are developed, but they do not overshadow the main focus of the text. Unlike other texts in this field, Cryptology brings students directly to concepts of classical substitutions and transpositions and issues in modern cryptographic methods.



1. Origins, Examples, and Ideas in Cryptology.

A Crypto-Chronology. Cryptology and Mathematics: Functions. Crypto: Models, Maxims, and Mystique.



2. Classical Cryptographic Techniques.

Shift Ciphers and Modular Arithmetic. Affine Ciphers; More Modular Arithmetic. Substitution Ciphers. Transposition Ciphers. Polyalphabetic Substitutions. Probability and Expectation. The Friedman and Kasiski Tests. Cryptanalysis of the Vingenere Cipher. The Hill Cipher; Matrices.



3. Symmetric Computer-Based Cryptology.

Number Representation. Boolean and Numerical Functions. Computational Complexity. Stream Ciphers and Feedback Shift Registers. Block Ciphers. Hash Functions.



4. Public-Key Cryptography.

Primes, Factorization, and the Euclidean Algorithm. The Merkle-Hellman Knapsack. Fermat's Little Theorem. The RSA Public-Key Cryptosystem. Key Agreement. Digital Signatures. Zero-Knowledge Identification Protocols.



5. Case Studies and Issues.

Case Study I: DES. Case Study II: PGP. Public-Key Infrastructure. Law and Issues Regarding Cryptography.



Glossary.


Bibliography.


Table of Primes.


Answers to Selected Exercises.


Index.

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