Cryptology ePrint Archive: Report 2013/440

Information Theoretic Security for Encryption Based on Conditional Renyi Entropies

Mitsugu Iwamoto and Junji Shikata

Abstract: In this paper, information theoretic cryptography is discussed based on conditional Renyi entropies. Our discussion focuses not only on cryptography but also on the de nitions of conditional Renyi entropies and the related information theoretic inequalities. First, we revisit conditional Renyi entropies, and clarify what kind of properties are required and actually satis ed. Then, we propose security criteria based on Renyi entropies, which suggests us deep relations between (conditional) Renyi entropies and error probabilities by using several guessing strategies. Based on these results, uni ed proof of impossibility, namely, the lower bounds of key sizes is derived based on conditional Renyi entropies. Our model and lower bounds include the Shannon's perfect secrecy, and the min-entropy based encryption presented by Dodis, and Alimomeni and Safavi-Naini. Finally, new optimal symmetric key cryptography and almost optimal secret sharing schemes are proposed which achieve our lower bounds.

Category / Keywords: foundations / Information Theoretic Cryptography, (Conditional) R\'enyi entropy, Impossibility, Symmetric-key Encryption, Secret Sharing Schemes

Date: received 13 Jul 2013

Contact author: mitsugu at uec ac jp

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Version: 20130718:185331 (All versions of this report)

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