"Algebraic Aspects of Cryptography", Neal Koblitz, 2001,

3-540-63446-0, U$64.99

%A Neal Koblitz koblitz@...

%C 175 Fifth Ave., New York, NY 10010

%D 1998

%G 3-540-63446-0

%I Springer-Verlag

%O U$64.95 212-460-1500 800-777-4643

%P 206 p.

%T "Algebraic Aspects of Cryptography"

When certain technical people find out that I am involved in data

security, they assert an interest in cryptography, and an intention to

write a cryptographic program sometime. While I not wish to disparage

this goal, questioning of the individual's background in mathematics

tends to point out that the task is harder than they might have

foreseen. The magic phrase "number theory" is usually the dividing

line. For those who make it past that limit, I am going to recommend

that they get Koblitz's work. Not that I am implying that this book

is more demanding than it needs to be: only that the topic itself is a

difficult one.

This is the heart of cryptology: the underlying foundations that make

it work. The material presented does not address specific programs,

standards, or even algorithms, but deals with the basic mathematical

theory that can be used to construct algorithms, or test their

strength.

Chapter one is something of an overview, touching on many fields of

cryptography and introducing an appropriate and exemplar equation for

each. Theories related to the strength of cryptographic algorithms

are given in chapter two. Basic algebra associated with primes are

discussed in chapter three, underlying the more common asymmetric

(public key) systems such as RSA. Chapter four outlines an

illustrative history of the development, cracking, and improvement of

one particular algorithm, demonstrating the mathematical work

necessary to each step. Knapsack type problems and theories are

explained in chapter five. Chapter six deals with the currently very

highly regarded elliptic curve algorithms, and is backed up with an

even more extensive appendix on hyperelliptic curves.

This is not an introduction. It is intended as a text for graduate

(or possibly advanced undergraduate) work, and requires a solid

background in mathematics or engineering. For those seriously

interested in cryptography, though, it is worth the work.

copyright Robert M. Slade, 2001 BKALASCR.RVW 20011122

====================== (quote inserted randomly by Pegasus Mailer)

rslade@... rslade@... slade@... p1@...

The great majority of mankind is satisfied with appearances, as

though they were realities, and is often even more influenced by

the things that seem than by those that are. - Niccolo Machiavelli

http://victoria.tc.ca/techrev or http://sun.soci.niu.edu/~rslade