Cryptology ePrint Archive: Report 2013/440

Revisiting Conditional R\'enyi Entropies and Generalizing Shannon's Bounds in Information Theoretically Secure Encryption

Mitsugu Iwamoto and Junji Shikata

Abstract: Information theoretic cryptography is discussed based on conditional R\'enyi entropies. Our discussion focuses not only on cryptography but also on the definitions of conditional R\'enyi entropies and the related information theoretic inequalities. First, we revisit conditional R\'enyi entropies, and clarify what kind of properties are required and actually satisfied. Then, we propose security criteria based on R\'enyi entropies, which suggests us deep relations between (conditional) R\'enyi entropies and error probabilities by using several guessing strategies. Based on these results, unified proof of impossibility, namely, the lower bounds of key sizes is derived based on conditional R\'enyi 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, a new optimal symmetric key encryption is proposed which achieve our lower bounds.

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

Original Publication (with major differences): ICITS2013

Date: received 13 Jul 2013, last revised 4 Sep 2014

Contact author: mitsugu at uec ac jp

Available format(s): PDF | BibTeX Citation

Version: 20140904:134140 (All versions of this report)

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