Citation:
ArXiv 2020.pdf | 626 KB |
Abstract:
Version History: Full version of part of an STOC 2009 paper.
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the \(i\)'th output block of a generator \(\mathsf{G}\) has accessible entropy at most \(k\) if the following holds: when conditioning on its prior coin tosses, no polynomial-time strategy \(\mathsf{\widetilde{G}}\) can generate valid output for \(\mathsf{G}\)'s \(i \)'th output block with entropy greater than \(k\). A generator has inaccessible entropy if the total accessible entropy (summed over the blocks) is noticeably smaller than the real entropy of \(\mathsf{G}\)'s output.
As an application of the above notion, we improve upon the result of Haitner, Nguyen, Ong, Reingold, and Vadhan [Sicomp '09], presenting a much simpler and more efficient construction of statistically hiding commitment schemes from arbitrary one-way functions.