Is it possible to encrypt with private key using .net RSACryptoServiceProvider?

Question

I know that RSACryptoServiceProvider can encrypt with the public key, then it can be decrypted with the private key.

Is it possible to encrypt with the private key a

Answer 1

This is what I understand RSA signature.

pseudo code:

First Alice made a signature:

alice_signature = encrypt(alice_message, alice_private_key)

Then Bob Eve... (anyone who having alice_public_key) verify the signature:

decrypted_message = decrypt(alice_signature, alice_public_key)

To confirm:

if(received_message_from_alice == decrypted_message)
  the signature proved the message is from alice