Information Theoretic Security for Encryption Based on Conditional Rényi Entropies

Abstract

Abstract. 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 of key sizes is 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. Finally, a new optimal symmetric key encryption is proposed which achieve our lower bounds.

Quantum Information Processing with Finite Resources

“…It has been found in the study of the classical special case (see, e.g. [55,93]) that generalizations based on (5.9) have severe limitations, for example they generally do not satisfy a data-processing inequality. On the other hand, definitions based on the underlying divergence, as in (5.12) …”

Non-asymptotic and asymptotic analyses on Markov chains in several problems

“…There are several definitions of conditional Rényi entropies (see [22], [23] for extensive review), and we use the one defined in [24] and the one defined by Arimoto [25]. We shall call the former one the lower conditional Rényi entropy (cf.…”

“…For more detailed review of conditional Rényi entropies, see [23]. For a correlated random variable (X, Y ) on X × Y with probability distribution P XY and a marginal distribution Q Y on Y, we introduce the conditional Rényi entropy of order 1 + θ relative to Q Y as…”

On a General Definition of Conditional Rényi Entropies

“…By usage of the properties of α-β-γ CRE, it is easy to conclude that the basic properties are satisfied for all α, β, γ: Table 2 we list the properties and their fulfilments for the cases when the mutual information is defined using C, JA, RW, A and H conditional Rényi entropies [9]. Thus, if the MI is defined using any of the previously considered CRE definitions, it fails down to satisfy some of the properties properties D4-D6.…”