Revisiting Conditional Renyi Entropies and Generalizing Shannon's Bounds in Information Theoretically Secure Encryption?


Abstract. Information theoretic cryptography is discussed based on conditional Renyi en-tropies. Our discussion focuses not only on cryptography but also on the denitions of con-ditional 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 sev-eral guessing strategies. Based on these results, unied 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, a new optimal symmetric key encryption is proposed which achieve our lower bounds

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