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Cryptological Mathematics
by Robert Lewand

This book introduces the reader to elementary yet rigorous mathematics from several different branches of the subject including number theory, abstract algebra, matrix algebra, probability, and statistics; all of which play a role in enciphering and deciphering secret messages. Those interested in learning how to encipher messages using a variety of symmetric and asymmetric schemes will learn those techniques in this volume. Those who want to learn the mathematical foundations of these techniques will learn how and why the enciphering schemes actually work. Those who are looking for some challenging computer programming exercises will find exercises in this book to keep them busy. The book may be used profitably by amateur cryptographers, motivated liberal arts students, and mathematics or computer science majors alike. The book begins by considering simple monoalphabetic substitution ciphers (additive, multiplicative, affine and keyword) and then moves through a polyalphabetic substitution cipher (the Vignere Square) and on to polygraphic substitution ciphers (including Hill's system). Finally the RSA Public Key Encryption System is introduced along with several of its variations. At each step the mathematics required to understand these systems is introduced in a thorough yet gentle manner. The book also invites interested readers to program the algorithms it describes. Some exercises can be done using a simple spreadsheet program; others are best handled by a symbolic algebra system. In addition, the book contains biographical sketches of some lesser-known yet fascinating personalities who had been involved with cryptography. Whether a reader is interested in cryptology, mathematics, or computer science, he or she will discover engaging and delightful material in this volume.

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  • Brand name: MAA
  • Author: Robert Lewand
  • ISBN: 978-0-88385-719-9
  • 220 pp.
  • Paperback
  • 2000
  • Series: Textbooks
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