RSA user authentication can be used to confidently and positively identify a user. Given users Alice and Bob, where Alice wishes to send a safe, signed message to Bob. A hashing function should be applied to the message m and the unique message digest m' can be used to confidently affirm user identity, since no two messages should yield the same result. This message digest may now be encrypted with her private key, to create a digital signature which can be sent along with the message. Bob can decrypt the digital signature using her public key to yield the message digest. This can now be compared with the result of the hash of the sent message. If these two are the same, the digital signature can be considered to be successfully verified. From this it can be seen that anyone can perform this authentication, since only Alice's private and public keys are used. If Alice wished to secure the message, she would have had to encrypt the message sent with Bob's public key. Bob would have to decrypt it using his private key before hashing it to compare to the message digest. Since the public RSA exponent e is usually much smaller than the private exponent d, digital signature verification is more often faster than signing. This is useful because it is more likely for message signing to be performed once while verification may take place multiple times.