An Introduction to Cryptography is a textbook intended for a one-semester introductory undergraduate course in cryptography. It is a substantial revision of the first edition, published in 2000: changes include restructuring the presentation of background material and inclusion of new material regarding the internet, viruses, network security and similar issues. In this edition, most basic background material is contained in the first two chapters rather than being spread through the chapters: mathematical concepts are covered in chapter 1, and cryptographic basics in chapter 2.
Concepts are presented very clearly and systematically, beginning with formal definitions of divisibility and parity and chapter 1, and substitution and transposition ciphers in chapter 2. Over 300 exercises are included, and solutions are provided for odd-numbered exercises. A particularly nice feature is the keying of specific exercises to concepts: for instance after defining the floor function, Mollin advises the student to check his/her understanding by solving specific exercises.
An Introduction to Cryptography is a textbook, not a popular book on cryptography, although sections of it may be understood by anyone with an interest in the subject. Chapters 7 and 8, which discuss topics including email, network and internet security, and computer viruses, will also be of interest to people working in computer science. The presentation is leavened by inclusion of over 60 short essays and biographies of individuals important in the history of mathematics and cryptography, from Euclid to Heisenberg.
Richard Mollin is a Professor of Mathematics and Statistics at the University of Calgary and the founder of the Canadian Number Theory Association. He has over 180 publications in the fields of algebra, number theory and computational mathematics, including 8 previous books.
Sarah Boslaugh is a Performance Analyst for BJC HealthCare and an adjunct professor at the Washington University School of Medicine in St. Louis, Missouri. She has written two books, An Intermediate Guide to SPSS Programming: Using Syntax for Data Management (SAGE, 2005) and Secondary Data Sources for Public Health: A Practical Guide (Cambridge University Press, forthcoming May 2007) and is editor-in-chief of The Encyclopedia of Epidemiology (forthcoming from Sage, November 2007).
Primes, Primality Testing, and Induction
An Introduction to Congruences
Euler, Fermat, and Wilson
The Index Calculus and Power Residues
Legendre, Jacobi, & Quadratic Reciprocity
Definitions and Illustrations
Modes of Operation
DES AND AES
S-DES and DES
The Ideas behind PKC
Digital Envelopes and PKCs
DSA - The DSS
True Primality Tests
Probabilistic Primality Tests
Classical Factorization Methods
The Continued Fraction Algorithm
The Quadratic Sieve
The Elliptic Curve Method (ECM)
ELECTRONIC MAIL AND INTERNET SECURITY
History of the Internet and the WWW
Pretty Good Privacy (PGP)
Protocol Layers and SSL
Internetworking and Security - Firewalls
Client-Server Model and Cookies
Login and Network Security
Viruses and Other Infections