My suggestion is: work your way through the Matasano Crypto Challenges. They're free, just sitting there on a static web page, with no signup required.
Actually implement cryptographic attacks before trying to design crypto.
That's not just my recommendation; it's also what Bruce Schneier has been writing for decades.
The problem with my suggestion is that most people who work their way from block cipher attacks through RSA error oracles are "scared straight", and lose the desire to plunk fancy crypto into their applications. Once you see how subtle some of the most devastating attacks are, you start to see why so few crypto engineers write chat apps.