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Security notions for information theoretically secure encryptions

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2 Author(s)
Mitsugu Iwamoto ; Center for Frontier Science, the University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585 Japan ; Kazuo Ohta

This paper is concerned with several security notions for information theoretically secure encryptions defined by the variational (statistical) distance. To ensure the perfect secrecy (PS), the mutual information is often used to evaluate the statistical independence between a message and a cryptogram. On the other hand, in order to recognize the information theoretically secure encryptions and computationally secure ones comprehensively, it is necessary to reconsider the notion of PS in terms of the variational distance. However, based on the variational distance, three kinds of definitions for PS are naturally introduced, but their relations are not known. In this paper, we clarify that one of three definitions for PS with the variational distance, which is a straightforward extension of Shannon's perfect secrecy, is stronger than the others, and the weaker two definitions of PS are essentially equivalent to the statistical versions of indistinguishability and semantic security.

Published in:

Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on

Date of Conference:

July 31 2011-Aug. 5 2011