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Decorrelation theory has recently been proposed in order to address the security of block ciphers and other cryptographic primitives over a finite domain. We show here how to extend it to infinite domains, which can be used in the Message Authentication Code (MAC) case. In 1994, Bellare, Kilian and Rogaway proved that CBC-MAC is secure when the input length is fixed. This has been extended by Petrank and Rackoff in 1997 with a variable length. In this paper, we prove a result similar to Petrank and Rackoff's one by using decorrelation theory. This leads to a slightly improved result and a more compact proof. This result means to be a general proving technique for security, which can be compared to the approach which was announced by Maurer at CRYPTO'99.