.net Client Side Web app?

Never done any .net stuff before and am wondering if it is possible to run a .Net web application client side through a browser? Or does it only work by processing on the server then spit out an HTML page? I would like to leverage the System.Security.Cryptography.X509Certificates namespace to开发者_StackOverflow access a user's Windows-MY keystore and pull out a X509 cert and its associated private key, which must be done client side, not server side for obvious reasons.

Ended up making a C# dll and registered it as a COM object, then interacted with it via JavaScript through the browser.