An observant reader will have noticed something peculiar and useful about our RSA encryption and decryption algorithms. Remember these equations?

		    C = M^e mod n
		    M = C^d mod n
		    

M is what we have thought of as plain text, and C is what we have thought of as cipher text. But mathematically, both M and C are just numbers between 0 and n. Therefore, we could equally well write the equations:

		    M = C^e mod n
		    C = M^d mod n
		    

Here we get a whole new concept just by switching around C and M. Suppose Alice holds the private key d and wishes to assure Bob that the message M was really from her, rather than from some imposter (Mallory). All Alice needs to do is calculate C = M^d mod n and send C to Bob.