BKALASCR.RVW   20011122

"Algebraic Aspects of Cryptography", Neal Koblitz, 2001,
3-540-63446-0, U$64.99
%A   Neal Koblitz koblitz@math.washington.edu
%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