Limits on the Efficiency of One-Way Permutation-Based Hash Functions

Naor and Yung show that a one-bit-compressing universal one-way hash function (UOWHF) can be constructed based on a one-way permutation. This construction can be iterated to build a UOWHF which compresses by n bits, at the cost of n invocations of the one-way permutation. We show that this construction is not far from optimal, in the following sense: there exists an oracle relative to which there exists a oneway permutation with inversion probability 2-p(n) (for any p(n) (log n)), but any construction of an n-bit-compressing UOWHF requires ( n/p(n)) invocations of the one-way permutation, on average. (For example, there exists in this relativized world a one-way permutation with inversion probability n-(1) , but no UOWHF that invokes it fewer than ( n/ log n) times.) Thus any proof that a more efficient UOWHF can be derived from a one-way permutation is necessarily non-relativizing; in particular, no provable construction of a more efficient UOWHF can exist based solely on a "b...

• Type: Conference
• Year: 1999
• Where: FOCS
• Authors: Jeong Han Kim, Daniel R. Simon, Prasad Tetali
• Keywords: FOCS 1999, Inversion Probability, One-way Permutations, Theoretical Computer Science, Universal One-way Hash Function