Extending second-preimage-resistant-like compress functions to XOR-based target collision resistant hash functions

The XOR-based method put forth by Bellare and Rogaway, and later improved by Shoup, is wildly used to construct target collision resistant hash functions. We consider the relationship between XOR-based target collision resistant hash functions and second preimage resistant compress functions. The contributions of this paper are twofold. First, we present the variants of evaluated second preimage resistant property, called e´-SPR. Second, we prove that the e´-SPR property of compress functions suffice to ensure the XOR-based hash functions target resistant to collision. More generic, we prove that other second preimage resistant properties, such as the r-SPR and c-SPR can achieve this goal as well.