> Can people provide recomendations and other comments on > which books to buy on PKI and IPsec
Some books I thought cost-effective, from easiest to hardest:
"Applied Cryptography: Protocols, Algorithms, and Souce Code in C" by Bruce Schneier 2nd ed (Wiley 1996)
758 pages of extremely readable reference material on all kinds of symmetric and asymmetric cryptography. A bit dated at this point, for example, there are only a few paragraphs on Elliptic Curve. Look for 3rd edition.
"Network Security with OpenSSL", John Viega, Matt Messier, and Pravir Chandra (O'Reilly 2002)
The "Seal" book (pictures of seals on the cover). Practical info on OpenSSL plus other topics. I've almost always been impressed with O'Reilly books. I've said "there may be a non-O'Reilly book that better addresses your particular concerns, but if you own TWO books on a subject, one should probably be the O'Reilly one". Especially the Nutshell books.
"Implementing Elliptic Curve Cryptography" by Michael Rosing (Manning 1999)
There were a bunch of >$100 books on Elliptic Curve. This one was about $80 IIRC and is very practical. The author answers his email and was very helpful. I'm still working on understanding "optimal normal basis" :-)
"Topics in Algebra", I. N. Herstein 2nd ed (Wiley 1964)
This is a college Math 400 level textbook on group theory and other mathematical topics. You can understand RSA at the number-theoretic level but you have to take Euler's theorem as a given. At the group-theoretic level you can prove it as a property of any group*. This book is not an easy read. I have spend more than ten years trying to understand Chapter 2... But I did find in Chapter 7 the existance and uniqueness properties of Gallois fields, which really helped me understand the Elliptic Curve stuff, especially extension fields.
* Euler's Theorem: If n is a positive integer and a is relatively prime to n, then a ^ phi(n) = 1 mod n
this is a simple number-theory corollary of
Lagrange's theorem: if G is a finite group and H is a subgroup of G then o(H) is a divisor of o(G)
that is, the size of any subgroup of a group is a submultiple of the size of the original group, and you can then show the desired corollary:
if G is a finite group and a belongs-to G then a ^ o(G) = e
by considering the subgroup of G generated by a.
We pass from group theory to number theory by considering the reduced group Z*[n] which has phi(n) members and the identity (e in this notation) as 1 (one). This is the core of the RSA system where n = pq and phi(n) = (p-1)(q-1) and the decryption recovers the plain text by ending up multiplying it by one...
-- Charles B (Ben) Cranston mailto: [EMAIL PROTECTED] http://www.wam.umd.edu/~zben
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