Ask HN: Resources on how to safely make use of cryptographic primitives?

We all know we shouldn't roll our own crypto and that it's best to use well tested, audited libraries where possible.

However, for those times when existing libraries aren't suitable (or don't exist), it's important to get it right.

Where can I find some resources on safely and securely making use of cryptographic primitives?

I'm thinking about signing data, authenticating signatures, encrypting data (both symmetric and asymmetric ciphers) at rest, encrypting streaming data, creating keys, managing public/private keys, generating secure random data.

A lot of existing resources I've found are geared towards understanding and implementing cryptographic algorithms. Virtually every platform provides these in some form or another. I want to learn how to safely use them.