The notion of HILL Entropy appeared in the breakthrough construction of a PRG from any one-way function (Håstad et al.), and has become the most important and most widely used variant of computational entropy. In turn, Metric Entropy defined as a relaxation of HILL Entropy, has been proven to be much easier to handle, in particular in the context of computational generalizations of the Green-Tao-Ziegler Dense Model Theorem which find applications in leakage-resilient cryptography, memory delegation or deterministic encryption.
Fortunately, Metric Entropy can be converted, with some loss in quality, to HILL Entropy as shown by Barak, Shaltiel and Wigderson.
In this paper we improve their result, reducing the loss in quality of entropy. Our bound is tight and, interestingly, independent of size of the probability space. As an interesting example of application we derive the computational dense model theorem with best possible parameters. Our approach is based on the theory of convex approximation in $L^p$-spaces.Category / Keywords: Pseudoentropy, Dense Model Theorem, Convex Approximation Original Publication (with minor differences): ICITS 2015 Date: received 14 Oct 2014, last revised 19 Mar 2015 Contact author: maciej skorski at gmail com Available format(s): PDF | BibTeX Citation Note: This work appears as a part of the paper ``Metric Pseudoentropy: Characterizations, Transformations and Applications '', to appear at ICITS 2015. Preliminary versions of this work appeared in the Proceedings of Student Research Forum Papers and Posters at SOFSEM 2015. Version: 20150319:094626 (All versions of this report) Short URL: ia.cr/2014/836 Discussion forum: Show discussion | Start new discussion