Abstract
We revisit the problem of black-box constructions of universal one-way hash functions (UOWHFs) from several typical classes of one-way functions (OWFs), and give respective constructions that either improve or generalize the best previously known. Along the way, we use several techniques that might be of independent interest. We show that almost 1-to-1 (except for a negligible fraction) one-way functions and known (almost-)regular one-way functions are equivalent in the known-hardness (or non-uniform) setting, by giving an optimal construction of the former from the latter. In addition, we show how to transform any one-way function that is far from regular (but only weakly regular on a noticeable fraction of domain) into an almost-regular one-way function.
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