. In this paper, we study the security of randomized CBC{MACs and propose a new construction that resists birthday paradox attacks and provably reaches full security. The proof is done in a new security model that may be of independent interest to study the security of randomized functions. The size of the MAC tags in this construction is optimal, i.e., exactly twice the size of the block cipher. Up to a constant, the security of the proposed randomized CBC{MAC using an n{bit block cipher is the same as the security of the usual encrypted CBC{MAC using a 2n{bit block cipher. Moreover, this construction adds a negligible computational overhead compared to the cost of a plain, non-randomized CBC{MAC. 1