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A replay attack (also known as playback attack) is a form of network attack in which a valid data transmission is maliciously or fraudulently repeated or delayed. This is carried out either by the originator or by an adversary who intercepts the data and re-transmits it, possibly as part of a masquerade attack by IP packet substitution.
Suppose Alice wants to prove her identity to Bob. Bob requests her password as proof of identity, which Alice dutifully provides (possibly after some transformation like a hash function); meanwhile, Eve is eavesdropping on the conversation and keeps the password (or the hash). After the interchange is over, Eve (posing as Alice) connects to Bob; when asked for a proof of identity, Eve sends Alice's password (or hash) read from the last session, which Bob accepts thus granting access to Eve.
A way to avoid replay attacks is by using session tokens: Bob sends a one-time token to Alice, which Alice uses to transform the password and send the result to Bob (e.g. computing a hash function of the session token appended to the password). On his side Bob performs the same computation; if and only if both values match, the login is successful. Now suppose Eve has captured this value and tries to use it on another session; Bob sends a different session token, and when Eve replies with the captured value it will be different from Bob's computation.
Session tokens should be chosen by a random process (usually, pseudorandom processes are used). Otherwise Eve may be able to pose as Bob, presenting some predicted future token, and convince Alice to use that token in her transformation. Eve can then replay her reply at a later time (when the previously predicted token is actually presented by Bob), and Bob will accept the authentication.
One-time passwords are similar to session tokens in that the password expires after it has been used or after a very short amount of time. They can be used to authenticate individual transactions in addition to sessions. The technique has been widely implemented in personal online banking systems.
Timestamping is another way of preventing a replay attack. Synchronization should be achieved using a secure protocol. For example Bob periodically broadcasts the time on his clock together with a MAC. When Alice wants to send Bob a message, she includes her best estimate of the time on his clock in her message, which is also authenticated. Bob only accepts messages for which the timestamp is within a reasonable tolerance. The advantage of this scheme is that Bob does not need to generate (pseudo-) random numbers, with the trade-off being that replay attacks, if they are performed quickly enough i.e. within that 'reasonable' limit, could succeed.