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The security of randomized message authentication code, MAC for short, is typically depending on the uniqueness of random initial vectors (IVs). Thus its security bound usually contains O(q2/2n), when random IV is n bits and q is the number of MACed messages. In this paper, we present how to break this birthday barrier without increasing the randomness. Our proposal is almost as efficient as the well-known Carter-Wegman MAC, uses n-bit random IVs, and provides the security bound roughly O(q3/22n). We also provide blockcipher-based instantiations of our proposal. They are almost as efficient as CBC-MAC and the security is solely based on the pseudorandomness of the blockcipher.

How to Thwart Birthday Attacks against MACs via Small Randomness