I would like to embed some C# .Net code that does some simple Encryption/Decryption functions into a web page. This will be an internal web page so users will be implicitly trusted. Is there any way to do this? I will need to hit user's Windows-MY key store (via CAPI) to pull out the keys for decryption and hit an LDAP server to grab public keys for encryption.


Question: How to use ARM software in Raspberry?
Answer: Short answer: Without the source code, you can't (unless you convince the developers to support the ARM architecture).

Long answer: Think of the apps on a phone.  If there wasn't a similar application for your computer, you could not run the phone application on your computer natively. This is also the same reason Raspberry Pi users can't run Ubuntu.  

So how can you get the software you want on the Raspberry Pi?
To start, you need the source code.  Unfortunately for you, it does not look like it is publicly available.  If you were able to get your hands on the source code, you would have to build it; depending on the size of the source code base, you might need a build farm for that.