First, thanks very much for creating this, looks great!
One helpful improvement would be to package a sample site that could be run, similar to what is done with the PHP and Python examples from the Yubico repo. My experience so far has been that the round trip with the Javascript API and the Chrome permissions is the most difficult part of understanding the setup. This could be eased if the rest of the sample was "known good".
A DbContext constructor that requires a single string parameter is called in DataContext.cs and this causes Entity Framework to try to use a connection string with a name specified by the parameter ("DataContext"). The web.config does not have a connection string with this name, but it has a default one named "DefaultConnection". I found this MSDN article and decided to change the string parameter value to either "DefaultConnection" or "name=DefaultConnection".
Can we expect an update to support .NET Core? I would like to use this library but cannot until it supports .NET Standard. You would likely have to drop the Bouncy Castle dependency.