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

*Jonathan Katz and Chiu-Yuen Koo*

**Abstract: **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.

**Category / Keywords: **foundations /

**Date: **received 16 Sep 2005, last revised 24 Sep 2005

**Contact author: **jkatz at cs umd edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20050925:010052 (All versions of this report)

**Short URL: **ia.cr/2005/328

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