The Many Entropies of One-Way Functions

One-way functions are the most basic, unstructured form of cryptographic hardness. Yet in a sequence of celebrated results (mostly in the eighties and early nineties), one-way functions were shown to imply a rich collection of cryptographic schemes and protocols (such as digital signatures and secret-key encryption). At the basis of this beautiful mathematical structure, are a few constructions of basic primitives: pseudorandom generators [Hastad-Impagliazzo-Levin-Luby ΓÇÿ91], universal one-way hash functions [Naor-Yung ΓÇÿ89, Rompel ΓÇÿ90], and more recently statistically hiding commitments and statistical zero-knowledge arguments [Haitner-Nguyen-Ong-Reingold-Vadhan ΓÇÿ06 & ΓÇÿ07]. In all three cases, turning raw hardness into a much more exploitable cryptographic object requires some very elaborate constructions and proofs. In this talk we will try to hint on how one-way functions naturally contain a basic form of each of these objects. The talk will be influenced by a recent line of results, simplifying and improving all of these constructions. The crux of each new construction is defining the ΓÇ£rightΓÇ¥ notion of computational entropy and recovering this form of entropy from one-way functions. Based on several works with (subsets of) Iftach Haitner, Thomas Holenstein, Salil Vadhan and Hoteck Wee.