The Security of Cipher Block Chaining

The Cipher Block Chaining { Message Authentication Code (CBC MAC) speciies that a message x = x 1 x m be authenticated among parties who share a secret key a by tagging x with a preex of f (m) a (x) def = f a (f a (f a (f a (x 1)x 2) x m?1)x m) ; where f is some underlying block cipher (eg. f = DES). This method is a pervasively used international and U.S. standard. We provide its rst formal justiication, showing the following general lemma: that cipher block chaining a pseudorandom function gives a pseudorandom function. Underlying our results is a technical lemma of independent interest, bounding the success probability of a computationally unbounded adversary in distinguishing between a random ml-bit to l-bit function and the CBC MAC of a random l-bit to l-bit function.