### DIMACS Theoretical Computer Science Seminar

Title: Universal One-Way Hash Functions via Inaccessible Entropy

Speaker: **Hoeteck Wee**, Queens College, CUNY

Date: Wednesday, November 3, 2010 11:00-12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

This paper revisits the construction of Universally One-Way Hash Functions (UOWHFs) from any one-way function due to Rompel (STOC 1990).
We give a simpler construction of UOWHFs which also obtains better efficiency and security.
The construction exploits a strong connection to the recently introduced notion of *inaccessible entropy* (Haitner et al. STOC 2009).
With this perspective, we observe that a small tweak of any one-way function f is already a weak form of a UOWHF:
Consider F(x, i) that outputs the i-bit long prefix of f(x).
If F were a UOWHF then given a random x and i it would be hard to come up with x' \neq x such that F(x, i) = F(x', i).
While this may not be the case, we show (rather easily) that it is hard to sample x' with almost full entropy among all the possible such values of x'.
The rest of our construction simply amplifies and exploits this basic property.