A Quick Introduction to Cryptography

As a mathematician, I’ve always enjoyed encryption, and have followed it since my days at Digital where, of necessity, many corporate consulting engineers became experts in security. (The Morris worm didn’t hit Digital’s Ultrix but was shocking none-the-less. Mitnick’s theft of the source code for Digital’s flagship operating system VMS was, to say the least, embarrassing.)

My Ph.D. thesis generalized a classification of singular elliptic curves, and thus using the group structure on an elliptic curve for encryption deeply fascinated me.

There are quite a few very nice online courses, books, and papers on encryption. Search YouTube and Google for them. There are two issues to watch out for with older material. One is that someone may have recently cracked an encryption scheme, and the other issue is that more and more powerful computers enable brute force attacks that can break older encryption schemes.

Out of my private notes and many past talks I’ve put together and updated a few of my slides for an easy one hour introduction to cryptography for the working engineer. These slides are Quick Cryptography Introduction, and they list some of my favorite cryptography references.

Of course, to keep the presentation even close to an hour, many interesting and important topics were either given a cursory mention, or omitted entirely. In fact, I culled out more slides than I left in. There are, however, a couple “P.T. Barnum” slides that list such omitted topics and hint at future talks.

The very last slide of the presentation points out something both obvious and deep: Encryption is only a tiny part of security. While all working engineers should know the basics of cryptography (the contents of the presentation is a start), we should also realize, for example, that the people aspects of security dominate almost all security breaches. Weak passwords, poor software maintenance, lack of employee education on social engineering, etc. are still rampant. On the technology side, much software is simply poorly designed from a security perspective. We’ve a long ways to go in security, but learning a little cryptography is a good prerequisite.


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