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This paper uses a variant of the notion of \emph{inaccessible entropy}(Haitner, Reingold, Vadhan and Wee, STOC 2009), to give an alternativeconstruction and proof for the fundamental result, first proved by Rompel (STOC1990), that \emph{Universal One-Way Hash Functions (UOWHFs)} can be based onany one-way functions. We observe that a small tweak of any one-way function$f$ is already a weak form of a UOWHF: consider the function $F(x,i)$ thatreturns the $i$-bit-long prefix of $f(x)$. If $F$ were a UOWHF then given arandom $x$ 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) thatit is hard to sample $x'$ with almost full entropy among all the possible suchvalues of $x'$. The rest of our construction simply amplifies and exploits thisbasic property.Combined with other recent work, the construction of threefundamental cryptographic primitives (Pseudorandom Generators, StatisticallyHiding Commitments and UOWHFs) out of one-way functions is now to a largeextent unified. In particular, all three constructions rely on and manipulatecomputational notions of entropy in similar ways. Pseudorandom Generators relyon the well-established notion of pseudoentropy, whereas Statistically HidingCommitments and UOWHFs rely on the newer notion of inaccessible entropy.

Inaccessible Entropy II: IE Functions and Universal One-Way Hashing