Preimages for Reduced SHA-0 and SHA-1

In this paper, we examine the resistance of the popular hash function SHA-1 and its predecessor SHA-0 against dedicated preimage attacks. In order to assess the security margin of these hash functions against these attacks, two new cryptanalytic techniques are developed: – Reversing the inversion problem: the idea is to start with an impossible expanded message that would lead to the required digest, and then to correct this message until it becomes valid without destroying the preimage property. – Pgraphs: an algorithm based on the theory of random graphs that allows the conversion of preimage attacks on the compression function to attacks on the hash function with less effort than traditional meet-in-the-middle approaches. Combining these techniques, we obtain preimage-style shortcuts attacks for up to 45 steps of SHA-1, and up to 50 steps of SHA-0 (out of 80).