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Paper 2013/440

Information Theoretic Security for Encryption Based on Conditional Renyi Entropies

Mitsugu Iwamoto and Junji Shikata

Abstract

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.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Information Theoretic Cryptography(Conditional) Rényi entropyImpossibilitySymmetric-key EncryptionSecret Sharing Schemes
Contact author(s)
mitsugu @ uec ac jp
History
2014-09-04: last of 2 revisions
2013-07-18: received
See all versions
Short URL
https://ia.cr/2013/440
License
Creative Commons Attribution
CC BY
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