Title: Shannon Entropy Versus Renyi Entropy from a Cryptographic Viewpoint
Abstract: We provide a new inequality that links two important entropy notions: Shannon Entropy $$H_1$$ and collision entropy $$H_2$$ . Our formula gives the worst possible amount of collision entropy in a probability distribution, when its Shannon Entropy is fixed. While in practice it is easier to evaluate Shannon entropy than other entropy notions, it is well known in folklore that it does not provide a good estimate of randomness quality from a cryptographic viewpoint, except very special settings. Our results and techniques put this in a quantitative form, allowing us to precisely answer the following questions: Our approach involves convex optimization techniques, which yield the shape of the "worst" distribution, and the use of the Lambert W function, by which we resolve equations coming from Shannon Entropy constraints. We believe that it may be useful and of independent interests elsewhere, particularly for studying Shannon Entropy with constraints.
Publication Year: 2015
Publication Date: 2015-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 11
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