On Constructing Universal One-Way Hash Functions from Arbitrary One-Way Functions

A fundamental result in cryptography is that a digital signature scheme can be constructed from an arbitrary one-way function. A proof of this somewhat surprising statement follows from two results: first, Naor and Yung defined the notion of universal one-way hash functions and showed that the existence of such hash functions implies the existence of secure digital signature schemes. Subsequently, Rompel showed that universal one-way hash functions could be constructed from arbitrary one-way functions. Unfortunately, despite the importance of the result, a complete proof of the latter claim has never been published. In fact, a careful reading of Rompel’s original conference publication reveals a number of errors in many of his arguments which have (seemingly) never been addressed. We provide here what is — as far as we know — the first complete write-up of Rompel’s proof that universal one-way hash functions can be constructed from arbitrary one-way functions. ∗Dept. of Computer Science, University of Maryland. {jkatz,cykoo}@cs.umd.edu †This research was supported in part by NSF CAREER award #0447075.