Catalog Code: CPT
Print ISBN: 978-0-88385-719-9
220 pp., Paperbound, 2001
List Price: $50.95
MAA Member: $40.95
Series: MAA Textbooks
The book can be used at several different levels. Those interested in learning how to encipher messages using a variety of symmetric and asymmetric schemes will learn those techniques in this volume. Those interested in learning the mathematical foundations of these techniques will learn how and why the enciphering schemes actually work. And those who are looking for some challenging computer programming exercises will also find exercises in this book to keep them busy.
1. Monoalphabetic Substitution Ciphers
2. Polyalphabetic Substitution Ciphers
3. Polygraphic Substitutio Systems
4. Public Key Cryptography
Appendix A: ASCII Code
Appendix B: Taxonomy of Cryptography
Appendix C: Answers to Even-Numbered Problems
A common characteristic of all the cryptographic schemes so far considered is their symmetric nature—each scheme required the sender and the receiver of the message to share a bit of knowledge, namely the key used to encipher and decipher the text. In recent years, asymmetric cryptographic systems have been proposed. In such systems, rather than the sender and receiver sharing a common key, each participant has a public key E (for enciphering) and a private key D (for deciphering). The public and private keys of the sender are in no way related to the public and private keys of the receiver of the message. In fact, the public keys of the participants may well be published in a telephone directory format! For this reason, a scheme such as this is known as a public key scheme.
Suppose Beth wants to send Stephanie a message m using a public key system. Here's how this might work:
Should Molly intercept the encrypted message Es(m), she would need to discover Stephanie's private key Ds in order to decipher the message. Molly wouldn't be able to persuade Beth to reveal this key—Beth herself is clueless as to its identity!
Of all the implementations of public key cryptographic systems, one of the more popular is the so-called RSA algorithm, named for its inventors Ronald Rivest, Adi Shamir and Leonard Adelman. In this chapter we will examine the workings of this system and answer questions including:
Robert Edward Lewand received his PhD in mathematics from the University of Virginia. He is the co-author of two books: Expert System Development and Intelligent Systems Design. He has delivered numerous talks and published extensively in professional journals largely in the areas of expert systems and artificial intelligence. He has been the recipient of several awards: Outstanding Teacher in the Faculty of Science (Goucher College, 1980), Fulbright Faculty Exchange Award (1987), Outstanding Scholarship Award (Goucher College, 1989), Caroline Doebler Bruckerl Award for Outstanding Faculty Member (Goucher College, 1999), and the John Smith Award for Distinguished College or University Teaching (Maryland-Virginia-District of Columbia Section of the Mathematical Association of America, 2002).