Customer Reviews

The Mathematics of Ciphers: Number Theory and RSA Cryptography

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4 star:		(2)
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This book is a very readable introduction to the theory of numbers. The author manages to concentrate in a relatively short book and with a very clear and pleasant style the material necessary to understand the mathematics underneath the RSA cryptosystem. No previous knowledge of advanced mathematics is assumed. Perhaps not enough for mathematicians, but more than rewarding for the rest of us. It reminds me a bit of the style of M. Gardner. Books on mathematics can be very dull without the style of exposition of Mr. Coutinho. Highly recommended !

The book revolves around RSA. The motivation for the book is that the reader wants to understand public/private key cryptography, where this is represented by the seminal RSA algorithm.

The author assumes little previous acquaintance with number theory on your part. He develops his arguments from this minimal background. So modular arithmetic is introduced, and thence such key ideas as groups, primality tests, Chinese Remainder Theorem and, finally, the RSA cryptosystem. Each chapter has a problem set of moderate difficulty.

A maths undergraduate at the sophomore level or higher should be able to benefit from the book.

I've used this book for teaching the basic theory of RSA cryptography. However, some knowledge of number theory is required in order to get full benefit of the text and exercises. I found "Number Theory and Its History," by Oystein Ore, to be an excellent complement to this text.

(Note that there are a few typographical errors in the exercises, but these are easily spotted.)

This is an excellent introductory text to the subject matter. Understanding RSA requires a sound foundation in Number Theory and the book provides just that.
There are other texts out there which either approach the subject as a recreational endeavour in which to appeal to a layman audience, the proofs are usually just sketched over and then there are others which expect decent grounding in number theory.
This book is more of a self contained text where anyone with a high school math skills would not find the need to consult an external resource.

This book was required for a Theory of Numbers class I took in college. I didn't want to pay college bookstore prices so I found it here on Amazon. The book took about a week to arrive, so I suggest ordering ASAP. The condition was brand new, and I was completely satisfied.

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