A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity |
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Authors: | Ziran Tu Yingpu Deng |
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Institution: | (1) State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, 710071, China;(2) State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China |
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Abstract: | In this paper, a combinatorial conjecture about binary strings is proposed. Under the assumption that the proposed conjecture
is correct, two classes of Boolean functions with optimal algebraic immunity can be obtained. The functions in first class
are bent, and then it can be concluded that the algebraic immunity of bent functions can take all possible values except one.
The functions in the second class are balanced, and they have optimal algebraic degree and the best nonlinearity up to now. |
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Keywords: | |
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