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The Kerberos Network Authentication Service (V5
, 1993
"... draftietfkrbwgkerberosclarifications00.txt ..."
Limits on the Efficiency of OneWay PermutationBased Hash Functions
 In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science
, 1999
"... Naor and Yung ([NY89]) show that a onebit compressing universal oneway hash function (UOWHF) can be constructed based on a oneway permutation. This construction can be iterated to build a UOWHF which compresses by "n bits, at the cost of "n invocations of the oneway permutation. We sho ..."
Abstract

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Naor and Yung ([NY89]) show that a onebit compressing universal oneway hash function (UOWHF) can be constructed based on a oneway permutation. This construction can be iterated to build a UOWHF which compresses by "n bits, at the cost of "n invocations of the oneway 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 \Gammap(n) (for any p(n) 2 !(log n)), but any construction of an "nbitcompressing UOWHF requires \Omega\Gamma p n=p(n)) invocations of the oneway permutation, on average. (For example, there exists in this relativized world a oneway permutation with inversion probability n \Gamma!(1) , but no UOWHF that invokes it fewer than \Omega\Gamma p n= log n) times.) Thus any proof that a more efficient UOWHF can be derived from a oneway permutation is necessarily nonrelativizing; in particular, no provable construction...