Take a look at this tutorial of Dustin Horne on RSA Encryption and Silverlight.
Source: Dustin Horne's Blog
While Silverlight is a powerful tool for rich client applications, it lacks the ability to perform asymmetric encryption out of the box. In this article, I'm going to share a cryptography class library I've been working on and show you how to use it to perform standards compliant RSA Encryption in Silverlight that is cross compatible with .NET's built in RSACryptoServiceProvider, allowing you to encrypt from Silverlight using my library and decrypt on your website using the RSACryptoServiceProvider. For brevity, only examples using my class library will be shown except for a few examples that show equivelant functionality from the RSACryptoServiceProvider (RSACSP).