BKIMPECC.RVW   990115

"Implementing Elliptic Curve Cryptography", Michael Rosing, 1999,
1-884777-69-4, U$47.95/C$67.95
%A   Michael Rosing cryptech@mcs.com
%C   32 Lafayette Place, Greenwich, CT   06830
%D   1999
%G   1-884777-69-4
%I   Manning Publications Co.
%O   U$47.95/C$67.95 hetr@manning.com 516-887-9747
%P   313 p.
%T   "Implementing Elliptic Curve Cryptography"

Modern asymmetric (or "public") key cryptography uses mathematical
operations that are fairly easy to do in one direction, but extremely
hard to do in reverse.  The standard example used (indeed, the one
that is almost synonymous with public key encryption) is that of
factoring.  Given two large prime numbers, it is a straightforward
task to multiply them together and find the resulting multiplicand. 
However, given a large number that is a product of two large prime
factors, it is extremely difficult to find those two primes.

Elliptic curves have a similar property.  A characteristic of an
elliptic curve is that any two points on the curve can be "added," and
the resulting point will also be on the curve.  However, it is
difficult, given only the final point, to find the original two that
were added.  Thus, this attribute can be used as the basis of an
asymmetric encryption system.

Rosing doesn't get around to explaining what an elliptic curve is
until chapter five, so you have to take a fair amount on faith.  In
spite of the comments in the first few pages of the book promoting the
advantages of understanding the fundamentals, it is quite easy to
believe that the text was written to explain some sample code, since
there is far more emphasis on dealing with carry bits than there is in
the background explanations.  He starts in chapter one by talking
about exponential curves (as in, a good crypto system is one where the
work done to encrypt a message grows more slowly than the work
required to crack it) and the enormous magnitude of address spaces. 
Chapter two doesn't really deal with number theory until halfway
through, concentrating on coding for arithmetic with large integers,
and rushing through conceptual explanations in order to get into yet
more programming.  Polynomials are introduced in chapter three, but,
again, I couldn't say that the subject is really covered.  At one
point a new term, undefined, is introduced.  The comment, "If you
don't know what that means, just remember that it works!" is not
terribly helpful when we have no idea what it works for.  Normal basis
is given a mathematical definition, but almost no explanation, in
chapter four.  The explanation of elliptic curves, in chapter five, is
much better, but, relying as it does on some understanding of
polynomial and normal basis, still leaves a lot to be desired.

It is interesting to note, in chapter six, that the basics of
cryptology is treated every bit as cavalierly as the math.  The
explanation of public key cryptography is extremely terse, and, in
fact, contains several minor errors.  Chapter seven looks at some
practical building blocks like random number generation and
"handshaking" protocols.  The elliptic curve encryption scheme and
IEEE P1363 standard mask and hash functions are reviewed in chapter
eight.  Chapters nine and ten discuss advanced topics in key exchange
and digital signatures respectively.  Fine details for performance
enhancement in specific sections of code are covered in chapter
eleven.  A sample analysis and design is given in chapter twelve.

Now, granted, Rosing's purpose is engineering and implementation and
not math tutorials.  And, to be fair, he does provide information on a
number of points of programming not often dealt with in the more
academic texts.  However, as he points out, you cannot simply use the
sample code in the book and expect it to work in all cases and for all
purposes.  Therefore, if the programmer does not understand, to some
extent, how the system works, the eventual system may have flaws and
weaknesses.  However helpful the programming pointers handed out in
every chapter, design must be based on concepts, and these are very
poorly provided.  If, on the other hand, you learned UNIX by studying
the source code, you might do reasonably well with this book.

copyright Robert M. Slade, 1999   BKIMPECC.RVW   990115