Meet-in-the-middle preimage attacks revisited new results on MD5 and HAVAL

In this paper, we revisit previous meet-in-the-middle preimage attacks on hash functions. We firstly present a technical improvement for the existing local-collision and initial-structure techniques. With applying some equivalent transformation, we can significantly reduce the memory requirement from the original proposals. We then revisit the previous preimage attacks on MD5 and HAVAL with recent techniques. Consequently, we can improve the memory complexity of the previous preimage attack on full MD5 from 2
⁴⁵
to 2
¹³
and on full 4-pass HAVAL from 2
⁶⁴
to 2
³²
. Moreover, we extend the preimage attack on 5-pass HAVAL from 151 steps to 158 steps, and present the first preimage attack with a single block message for 3-pass HAVAL.