Encryption keys: RSA vs. ElGamal

[Robert J. Hansen]

> So it would be great if someone could tell me how they differ when 
> it comes to security and efficiency.

Answering this in detail will require at least a solid undergraduate
degree in either CS or mathematics.  I am coming close to a Ph.D. in
computer science, and I still screw up some of the finer points of the
relationship between the integer factorization problem and the discrete
logarithm problem.

Beware of any straightforward answers you get to this problem.  They are
almost undoubtedly simplified to the point of gross inaccuracy.

> know. Please don't give me "they're both secure enough" or "just 
> use the defaults" type of answers, I want detailed information.

Unless you know what you're doing and why, use the defaults.  That is
the absolute best advice I can give, the absolute best advice I think
almost anyone can give.

> Are there any patent issues with ElGamal?

Not in the opinion of the IETF.