A mathematical problem for security analysis of hash functions and pseudorandom generators

Authors:
Koji Nuida;Takuro Abe;Shizuo Kaji;Toshiaki Maeno;Yasuhide Numata
Affiliations:
Research Center for Information Security, National Institute of Advanced Industrial Science and Technology, Ibaraki, Japan;Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan;Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yamaguchi, Japan;Department of Electrical Engineering, Kyoto University, Kyoto, Japan;Department of Mathematical Informatics, The University of Tokyo, Tokyo, Japan and Japan Science and Technology Agency, CREST, Japan
Venue:
IWSEC'11 Proceedings of the 6th International conference on Advances in information and computer security
Year:
2011

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Abstract

The aim of this paper is to emphasize the significance of a certain mathematical problem in research on information security. We point out that the mathematical problem, which we refer to as "Function Density Problem," has connections to the following two major cryptographic topics; security analysis of hash functions in the real world (like SHA-1), and construction of pseudorandom generators with some enhanced security property. We also provide a first example to show how a study of Function Density Problem can contribute to the progress of the above-mentioned two topics. Other potential applications of Function Density Problem to information security are also discussed.