FileMaker 13's whole-file encryption uses AES-256, I believe. There isn't a built-in feature implementing SHA hashes, but these can be implemented natively in FileMaker with calculations or scripting or (more easily) using a plug-in. For TLS transport, you can handle that in the setup around FileMaker by using TLS for a VPN used to connect to FileMaker, or encrypt a remote desktop session using TLS.
or (more easily) using a plug-in
Thanks Jeremy, is there a specific cryptography plug-in you'd recommend? Ideally it'd be open source, or at least the implementation would be verified by an independent entity.
There are not many open-source FileMaker plug-ins, and probably fewer with outside verification. If you can find a Java/Groovy package that meets your standards, you could execute it in FileMaker with the ScriptMaster plug-in.
I've read about the ScripMaster plug-in. Has your experience with it been good?
I bet I can find an appropriate Java cryptography package, thanks!