Information theoretic security for encryption based on conditional Rényi entropies

M Iwamoto, J Shikata - … Security: 7th International Conference, ICITS 2013 …, 2014 - Springer
M Iwamoto, J Shikata
Information Theoretic Security: 7th International Conference, ICITS 2013 …, 2014Springer
In this paper, information theoretic cryptography is discussed based on conditional Rényi
entropies. Our discussion focuses not only on cryptography but also on the definitions of
conditional Rényi entropies and the related information theoretic inequalities. First, we revisit
conditional Rényi entropies, and clarify what kind of properties are required and actually
satisfied. Then, we propose security criteria based on Rényi entropies, which suggests us
deep relations between (conditional) Rényi entropies and error probabilities by using …
Abstract
In this paper, information theoretic cryptography is discussed based on conditional Rényi entropies. Our discussion focuses not only on cryptography but also on the definitions of conditional Rényi entropies and the related information theoretic inequalities. First, we revisit conditional Rényi entropies, and clarify what kind of properties are required and actually satisfied. Then, we propose security criteria based on Rényi entropies, which suggests us deep relations between (conditional) Rényi entropies and error probabilities by using several guessing strategies. Based on these results, unified proof of impossibility, namely, the lower bounds on key sizes are derived based on conditional Rényi 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 at ICITS2012. Finally, a new optimal symmetric key encryption protocol achieving the lower bounds is proposed.
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