Collision Resistance of Double-Block-Length Hash Function against Free-Start Attack

In this article, we discuss the security of double-blocklength (DBL) hash functions against the free-start collision attack. We focus on the DBL hash functions composed of compression functions of the form F(x) = ( f (x), f (p(x))), where f is a smaller compression function and p is a permutation. We first show, in the random oracle model, that a significantly good upper bound can be obtained on the success probability of the free-start collision attack with sufficient conditions on p and the set of initial values. We also show that a similar upper bound can be obtained in the ideal cipher model if f is composed of a block cipher. key words: double-block-length hash function, random oracle model, ideal cipher model, collision resistance, free-start collision attack