International Association
for Cryptologic Research

We revisit the randomized approach followed in the design of the RMAC message authentication code in order to construct a MAC with similar properties, but based on Wegman-Carter's $\varepsilon$-universal hash families instead of a classical CBC chain. This yields a new message authentication code called FRMAC whose security bounds are, as in RMAC, beyond the birthday paradox limit. With efficient hash functions in software, the performance of FRMAC for large messages is similar to those of the fastest previously known schemes. FRMAC can also be more efficient for small messages. Furthermore, due to relaxed requirements about the nonces in the security proof, the implementation of FRMAC in real applications tends to be easier.

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 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. We give a full standard proof of our construction using one pass of a block cipher with 2n-bit keys but there also is a proof for n-bit keys block ciphers in the ideal cipher model.