"Applied Cryptography" is the best-written book on this topic that I know of. Author is a brilliant communicator. Esp. the section on cryptographic protocols should be required reading for any computer scientist. It's not overly rigorous or mathematical, and has a lot of informality and humor, so it's a fairly light read. You don't need a lot of mathematical maturity to read it (and reading things like this helps develop mathematical maturity).
Unfortunately, the 2nd edition adds "50% more words, 7 more chapters, and over 1600 new references." I thought the first edition was better in length. It was novel-length, and reads as well as a novel. Going from long-ish novel to short-ish trilogy makes this somewhat less readable. But c'est la vie.
To learn about some cryptography fundamentals:
* Read Katz & Lindell's Introduction to Modern Cryptography
* If you're missing math background, read Timothy Gowers' blog
* Supplement: Take Jonathan Katz' and Dan Boneh's MOOCS (links in post)
To get to the point where you can "design/analyze crypto protocols" (and maybe know what you're doing):
* Read Oded Goldreich's Foundations of Cryptography (Volumes 1&2)
* Try to have quasi-intelligent conversations with real cryptographers (advice for this in blog post)
* Get a PhD somewhere with a good crypto program
edit: formatting