Converting Meet-In-The-Middle Preimage Attack into Pseudo Collision Attack: Application to SHA-2

In this paper, we present a new technique to construct a collision attack from a particular preimage attack which is called a partial target preimage attack. Since most of the recent meet-in-the-middle preimage attacks can be regarded as the partial target preimage attack, a collision attack is derived from the meet-in-the-middle preimage attack. By using our technique, pseudo collisions of the 43-step reduced SHA-256 and the 46-step reduced SHA-512 can be obtained with complexities of 2 and 2, respectively. As far as we know, our results are the best pseudo collision attacks on both SHA-256 and SHA-512 in literature. Moreover, we show that our pseudo collision attacks can be extended to 52 and 57 steps of SHA-256 and SHA-512, respectively, by combined with the recent preimage attacks on SHA-2 by bicliques. Furthermore, since the proposed technique is quite simple, it can be directly applied to other hash functions. We apply our algorithm to several hash functions including Skein and BLAKE, which are the SHA-3 finalists. We present not only the best pseudo collision attacks on SHA-2 family, but also a new insight of relation between a meet-in-the-middle preimage attack and a pseudo collision attack.