The eight variable homogeneous degree three bent functions
نویسندگان
چکیده
منابع مشابه
On the degree of homogeneous bent functions
It is well known that the degree of a 2m-variable bent function is at most m. However, the case in homogeneous bent functions is not clear. In this paper, it is proved that there is no homogeneous bent functions of degree m in 2m variables when m > 3; there is no homogenous bent function of degree m− 1 in 2m variables when m > 4; Generally, for any nonnegative integer k, there exists a positive...
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Bent functions are important cryptographic Boolean functions. In order to enumerate eight-variable bent functions, we solve the following three key problems. Firstly, under the action of AGL(7, 2), we almost completely classify R(4, 7)/R(2, 7). Secondly, we construct all seven-variable plateaued functions from the orbits of R(4, 7)/R(2, 7). Thirdly, we present a fast algorithm to expand plateau...
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This paper discusses homogeneous bent functions. The space of homogeneous functions of degree three in six boolean variables was exhaustively searched and thirty bent functions were found. These are found to occur in a single orbit under the action of relabeling of the variables. The homogeneous bent functions identiied exhibit interesting combinatorial structures and are, to the best of our kn...
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In this paper we present a result towards the conjectured nonexistence of homogeneous rotation symmetric bent functions having degree > 2.
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ژورنال
عنوان ژورنال: Journal of Discrete Algorithms
سال: 2008
ISSN: 1570-8667
DOI: 10.1016/j.jda.2006.08.004