Provably Hard Zero-Way Functions

Intuitively, a function ƒ(fnof) is zero-way if, without a trapdoor, both computing ƒ and computing ƒ-1 are hard. We first point out that there exists a counterexample for the generic method to construct zero-way functions shown by Niemi-Renvall in Asiacrypt’94. We then give some examples of zero-way functions that are provably hard to compute, that is computing ƒ and ƒ-1 is proven to be as hard as breaking the Diffie-Hellman key exchange scheme or breaking the RSA cryptosystem.