Strongly secure privacy amplification cannot be obtained by encoder of Slepian-Wolf code

Authors:
Shun Watanabe;Tsuki Saitou;Ryutaroh Matsumoto;Tomohiko Uyematsu
Affiliations:
Department of Information Science and Intelligent Systems, Tokushima University, Tokushima, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, Japan
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Year:
2009

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Abstract

The privacy amplification is a technique to distill a secret key from a random variable by a hash function so that the distilled key and an eavesdropper's random variable is statistically independent. There are two kinds of security criteria for the key distilled by the privacy amplification: the weak security criterion and the strong security criterion. As a technique to distill a secret key, it is known that the encoder of a Slepian-Wolf (the source coding with full side-information at the decoder) code can be used as a hash function for the privacy am plification if we employ the weak security criterion. In this paper, we show that the encoder of a Slepian-Wolf code cannot be used as a hash function for the privacy amplification if we employ the strong security criterion.