Finite set theory and its application to cryptology |
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| Institution: | 1. State Key Lab of Software Engineering, Computer School, Wuhan University, Wuhan, China;2. Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Gulin, China;3. College of Communication and Information, University of Kentucky, USA;4. School of Computer Science and Technology, Nanjing University of Posts and Telecommunications, Nanjing, China;1. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China;2. University of Aizu, Aizu-Wakamatsu City, Fukushima 9658580, Japan;3. Cyberspace Security Research Center, Peng Cheng Laboratory, Shenzhen 518055, China;4. Department of Information Management, National Dong Hwa University, Hualien 97401, Taiwan R.O.C.;5. Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan R.O.C.;1. School of Cyberspace Security, Xi’an University of Posts and Telecommunications, Xi’an 710121, China;2. State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China;3. Fujian Provincial Key Laboratory of Network Security and Cryptology, College of Mathematics and Informatics, Fujian Normal University, China |
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| Abstract: | The concept of the (k, n, L)-set (or threshold set) of a finite set A is presented in this paper, based on the requirement of solving cryptology problems. It is proved that for a (k′, n′)-threshold scheme of any special or given k′, n′, the general (k, n)-threshold scheme is constructed by the (k, n, L)-set (or threshold set) of set A. A k, n, L)-set (or threshold set) of set A is constructed from an uniform (k, n)-set for L = |A| or a nonuniform (k, n)-set for L = |A| - 1. |
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