A sufficient condition for constructing some XOR-based iterative target collision resistant hash functions

Most modern hash functions are constructed by iterating a compression function. 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 a variant of second preimage resistant property, called CV-SPR. Second, we prove that the CV-SPR property of compress functions suffice to ensure some XOR-based hash functions target resistant to collision. Moreover, we analyze the role of the XOR operation played and why this condition is not suitable for Enveloped Shoup and XTH iterations.