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Erschienen in:
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2014 | OriginalPaper | Buchkapitel

Information Theoretic Security for Encryption Based on Conditional Rényi Entropies

verfasst von : Mitsugu Iwamoto, Junji Shikata

Erschienen in: Information Theoretic Security

Verlag: Springer International Publishing

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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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Vorheriges Kapitel On the Transmit Beamforming for MIMO Wiretap Channels: Large-System Analysis
Nächstes Kapitel Insider-Proof Encryption with Applications for Quantum Key Distribution
Fußnoten
1
Throughout of the paper, the base of logarithm is \(e\). Note that the base of logarithm is not essential since the same arguments hold for arbitrary base of logarithm. We also define \(0^0:=0\) for \(\alpha =0\).
 
2
This form of the chain rule is inductively obtained by using the postulate (d) in [8, p. 547].
 
3
In the case of \(\alpha = 1\), conditional Rényi entropies coincide with conditional Shannon entropy, and hence, chain rule is of course satisfied. In addition, it is obvious that \(R_\alpha ^\mathsf{JA}(X|Y)\) also satisfies the chain rule since it is defined to satisfy the chain rule.
 
4
We can show that CRE is satisfied by \(R_\alpha ^\mathsf{RW}(X|Y)\) in the case of \(\alpha > 1\).
 
5
Strictly speaking, our bounds are slightly more general than Shannon’s bounds and Alimomeni and Safavi-Naini’s one, since we have removed the assumption that \(\pi _{enc}\) and \(\pi _{dec}\) are deterministic
 
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Metadaten
Titel
Information Theoretic Security for Encryption Based on Conditional Rényi Entropies
verfasst von
Mitsugu Iwamoto
Junji Shikata
Copyright-Jahr
2014
Buch
Information Theoretic Security

Print ISBN: 978-3-319-04267-1

Electronic ISBN: 978-3-319-04268-8

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-319-04268-8_7