Free dll for Asymmetric encryption

I don't think so as the mathematics of asymmetric key encryption, where the decrypting key can't be deduced from the encrypting key, would be against it.

Of course, you can always encrypt a large file in small pieces using RSA but performance would be terrible and it would probably be insecure to boot.

You can also 'fake' asymmetric encryption by first applying a transformation (which can be as complicated as you like) to the encrypting key before applying a symmetric algorithm. You then give the transformed key to the recipient. Even if the recipient had possession of both keys it might be difficult to tell that one had been derived from another and performance would be almost as good as symmetric encryption!

If you've been given this to do as an exercise, they might be waiting to see whether you're devious enough to come up with the latter option :)

To the best of my knowledge, asymmetric key cryptography is only suitable for encrypting small amounts of data, typically smaller than the key itself.

I'd be very surprised if there were an asymmetric algorithm available for encrypting large files and, even if there was, it would be too slow to be of any practical use.

However, you could use the .NET RSA implementation to encrypt the key for subsequent symmetric encryption of the file using AES etc.