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Designed for students with no background in college-level mathematics, the book assumes minimal mathematical prerequisites and incorporates student-friendly Maplets throughout that provide practical examples of the techniques used. Technology Resource By using the Maplets, students can complete complicated tasks with relative ease.

They can encrypt, decrypt, and cryptanalyze messages without the burden of understanding programming or computer syntax. The authors explain topics in detail first before introducing one or more Maplets. All Maplet material and exercises are given in separate, clearly labeled sections. Instructors can omit the Maplet sections without any loss of continuity and non-Maplet examples and exercises can be completed with, at most, a simple hand-held calculator.

The Maplets are available for download at www.

The Math Needed for Computer Science (Part 2) - Number Theory and Cryptography

A Gentle, Hands-On Introduction to Cryptology After introducing elementary methods and techniques, the text fully develops the Enigma cipher machine and Navajo code used during World War II, both of which are rarely found in cryptology textbooks. The authors then demonstrate mathematics in cryptology through monoalphabetic, polyalphabetic, and block ciphers.

It also explores current U.

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Richard E. The prerequisites are modest no college-level mathematics is assumed , but a fair amount of interesting material is covered. The necessary mathematical background for these topics — chiefly elementary number theory particularly modular arithmetic , matrices, basic combinatorics and probability — is developed from scratch as needed.

All told, the authors have done an admirable job of balancing the competing goals of producing a text that can be read by people with limited mathematics background, but at the same time is maintained at a college level.

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First, there is the selection of topics. Also, the exercises in this book, though plentiful, do not call for the production of proofs.


Instead, they involve computation or, on occasion, the production of a brief essay based on some outside reading. Solutions to some, but not all, of the exercises, appear in an Appendix of about 35 pages. Likewise, there are very few theorems that are formally stated as such in the text, and those that are, are accompanied not by formal proofs but by illustrative examples.

Several other distinctive features of the book should be explicitly mentioned. These are essentially applets for Maple, and their use allows a student to make use of Maple without having to learn Maple syntax.

These Maplets appear frequently throughout the book, but when they do, they appear in separate sections that are entirely independent of the rest of the book and, thus, can be skipped if an instructor does not want to use this technology. There are plenty of other worked out examples in the book that do not require anything more sophisticated than a calculator to follow. Another noteworthy feature is a chapter discussing some historically interesting examples of ciphers from World War II: the Enigma machine and Navajo code.

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Following an unusually detailed multi-page description of how an Enigma machine worked actually, two specific examples of Enigma machines are discussed and the introduction of some background combinatorial principles, there is a section discussing the cryptanalysis of the Enigma; references are also given to both non-fictional and fictional works involving the machine, including the book Enigma by Robert Harris and the subsequent movie of the same name based on it.

This is followed by a section on the Navajo code talkers used by the Americans in the Pacific during the war. Because of these added phrases, as well as the fact that some uncommon words had to be translated a letter at a time using an encoded phonetic alphabet, the Navajo code consisted of approximately words by the end of the war, and the code talkers had to know all these words by memory. The Nicolas Cage movie Windtalkers is about the use of this code, and is mentioned briefly in an exercise in the text.

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  7. The idea of writing a cryptography book for a non-major audience is not a new one; about ten years ago, for example, Thomas Barr wrote An Invitation to Cryptology , also intended for a general college audience. The use of Maplets is certainly another distinguishing feature, as is the detailed description of the Enigma machine which is mentioned briefly, as part of a more general historical discussion, in the Barr text and Navajo code talkers.