Let's assume that Bob and Alice share a secret key in a symmetric key system. To begin a communication session, Bob generates two random numbers, R and S and encrypts then with the secret key, K. Bob sends the encrypted information to Alice. (Notice that all Alice knows is that she got a message that purports to be from Bob.) Alice uses the secret key (that matches Bob's) to decrypt the message and recovers R and S. Alice encrypts R using S as the encryption key and sends this ciphertext to Bob. Bob decrypts the ciphertext using S as the key and finds that the "R" he received from Alice matches the "R" he sent to her.

1. Alice has authenticated herself to Bob
2. Bob has authenticated himself to Alice
3. Alice and Bob have authenticated each other to the other
4. no authentication has been performed
5. all of the above
6. none of the above