# blockcipher-based MACs with variable length that are UF-CMA secure?

There are may papers and notes explain why CBC-MAC is only UF-CMA secure for fix length messages. Are there any other blockcipher-based (blockcipher and hash combined included) MACs that is UF-CMA secure with variable length messages?

Alternatively there is a general theorem that $$F_k(H_\kappa(m))$$ is a PRF (and thus a secure MAC) as long as $$F$$ is a secure fixed-length PRF and $$H$$ is a collision-resistant (potentially-keyed) hash function. You can find a proof of this e.g. in the Boneh-Shoup book (section 7). This e.g. brings the (parts of) the security proofs for HMAC and PMAC. Additionally you can somewhat easily define MACs based on this, e.g. $$\operatorname{AES}_{k_1}(\operatorname{GHASH}_{k_2}(m\|\operatorname{len}(m)))$$.