Bibliographic Details
| Title: |
Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions. |
| Authors: |
Zhang, Feng-rong1 zhfl203@163.com, Carlet, Claude2 claude.carlet@univ-paris8.fr, Hu, Yu-pu3 yphu@mail.xidian.edu.cn, Cao, Tian-jie1 tjcao@cumt.edu.cn |
| Source: |
Information Sciences. Nov2014, Vol. 283, p94-106. 13p. |
| Subjects: |
Nonlinear analysis, Boolean functions, Bent functions, Algebraic immunity, Iterative methods (Mathematics) |
| Abstract: |
In this paper, we modify a generalized indirect sum construction to construct functions with high nonlinearity. By utilizing the modified construction, highly nonlinear functions in (n + m) variables can be obtained from known bent functions in n variables and highly nonlinear functions in m variables. It is possible to obtain new (n + 15) -variable functions with nonlinearity 2 n + 15 - 1 - 2 (n + 15 - 1) / 2 + 20 × 2 n / 2 and new 12-variable 2-resilient functions with nonlinearity 2000 and algebraic degree 8, which achieve optimal algebraic immunity. Moreover, the modified construction can also be used as an iterative construction of a quadruple of disjoint spectra plateaued functions. In addition, we present sufficient conditions for a quadruple of disjoint spectra plateaued functions to have no nonzero linear structure. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
