tl;dr:

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