International Association
for Cryptologic Research

In this paper, information theoretic cryptography is discussed based on conditional Renyi entropies. Our discussion focuses not only on cryptography but also on the denitions 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 satised. 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, 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, new optimal symmetric key cryptography and almost optimal secret sharing schemes are proposed which achieve our lower bounds.