Security of Iterated Hash Functions Based on Block Ciphers

Cryptographic hash functions obtained by iterating a round function constructed from a block cipher and for which the hash-code length is twice the block length m of the underlying block cipher are considered. The computational security of such hash functions against two particular attacks, namely, the free-start target and free-start collision attacks, is investigated; these two attacks differentiate themselves from the "usual" target and colliiion attacks by not specifying the initial value of the iterations. The motivation is that computationally secure iterated hash functions against these two particular attacks implies computationally secure iterated hash functions against the "usual" target and collision attacks. For a general class of such 2m-bit iterated hash functions, tighter upper bounds than the one yet published in the literature on the complexity of free-start target and free-start collision attacks are derived. A proposal for a am-bit iterated hash function achieving these upper bounds is made; this new proposal is shown to be computationally more secure against free-start target and free-start collision attacks than some of the already proposed schemes falling into this general class. I t is also shown that our proposal is better than the present proposal for an IS0 standard in the sense that both schemes achieve these upper bounds but one encryption is required in our proposal for hashing one m-bit message block as opposed to two encryptions in the I S 0 proposal. Finally, two new attacks on the LOKI Double-Block-Hash function are pIesented with lower complexities than the known ones.