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Douglas R. Stinson's
Cryptography: Theory and Practice is a mathematically intensive examination of cryptography, including ciphers, the Data Encryption Standard (DES), public key cryptography, one-way hash functions, and digital signatures. Stinson's explication of "zero-sum proofs"--a process by which one person lets another person know that he or she has a password without actually revealing any information--is especially good.
If you are new to the math behind cryptography but want to tackle it, the author covers all of the required background to understand the real mathematics here. Cryptography includes extensive exercises with each chapter and makes an ideal introduction for any math-literate person willing to get acquainted with this material.
--This text refers to an out of print or unavailable edition of this title.
Review
My favorite of the current crop of undergraduate books is the second edition of Cryptography: Theory and Practice by Douglas Stinson.
If I were learning/teaching cryptography for the first time to a class of undergraduate math majors, this is the book I would use.
- Bulletin of the AMS
About the First Edition:
If you want an in-depth mathematical treatise
[Cryptography] is probably the most professional resource. It has an excellent introduction to the early systems, including a description of Claude Shannon's work
The material on hash functions is very detailed.
-PC Update
This is
a book that will give the professional the data needed to implement cryptographic software, and the mathematician hints on both code breaking and creating.
- Books-on-Line
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