The complexity of estimating min-entropy

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The complexity of estimating min-entropy
Goldreich, Sahai, and Vadhan (CRYPTO 1999) proved that the promise problem for estimating the Shannon entropy of a distribution sampled by a given circuit is NISZK-complete. We consider the analogous problem for estimating the min-entropy and prove that it is SBPcomplete, where SBP is the class of promise problems that correspond to approximate counting of NP witnesses. The result holds even when the sampling circuits are restricted to be 3-local. For logarithmic-space samplers, we observe that this problem is NP-complete by a result of Lyngsø and Pedersen on hidden Markov models (JCSS 2002).
Thomas Watson
Added 31 Mar 2016
Updated 31 Mar 2016
Type Journal
Year 2016
Where CC
Authors Thomas Watson
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