September 09, 2008

Cryptology as a capstone

I'm starting in on the last class needed to complete my master's program.  As luck would have it, I've been able to substitute grad-level cryptology for what ought to have been a graduate course in analysis or statistics.  Analysis in this case means proving things like calculus and trigonometry actually work, and statistics means proving things like central limit theorem.  Analysis was interesting but not especially relevant to my professional life when I took it at the 400 level, and I've had statistics a dozen ways from Sunday as part of discrete math, physics, and data mining courses.  Neither was terribly enticing.

Cryptology, on the other hand, is everything I've ever wanted from mathematics.  Crypto is where pure math becomes something physical, tangible, and powerful.  Many great mathematicians of the past lived and died, spending their entire careers studying and proving what would one day be the theoretical underpinnings of modern cryptology, many of whom never saw any of their work have a single practical application.  Now it's at the base of nearly every electronic communication in one form or another, and without it much of our modern world of e-commerce, email, chat, and ATMs would be impossible.

There are three primary things that an intercepting party can do to interfere with a secure communication:
1) Decrypt and read the message, gaining the information contained therein
2) Corrupt the message before it reaches the intended recipient (change the ciphertext)
3) Subvert the message (change the plaintext)

Conversely, there are four main goals for any modern cryptosystem:
1) Encrypt and decrypt data securely (this is where the algorithms come in)
2) Maintain/monitor data integrity in transit (typically a hash function)
3) Conduct authentication and identification (protocol)
4) Provide non-repudiation in communication (sender cannot deny, digital signature)

I've got an inkling on most of these, but learning the actualities will be very cool.  Aside from my AI courses, this is one of the few to which I've really looked forward.

Posted by: leoncaruthers at 08:14 PM | No Comments | Add Comment
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