Results on Constructions of Rotation Symmetric Bent and Semi-bent Functions
Results on Constructions of Rotation Symmetric Bent and Semi-bent Functions
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DOI：
10.1007/978-3-319-12325-7_2
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
C. Carlet;Guang-pu Gao;Wenfen Liu
中科院分区：
文献类型：
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作者：
C. Carlet;Guang-pu Gao;Wenfen Liu
本文引入了一类三次旋转对称（RotS）函数，并证明了它可以产生Bent和Semi-Bent函数.据我们所知，这是第二个主要建设的无限类的非二次RotS bent功能，可以找到和第一类的非二次RotS半bent功能。我们还研究了一类幂等元（通过选择一个正规基来给出RotS函数）。我们推导出这些幂等元之间的弯曲函数的表征，我们与他们的精确测定APN功能的框架中研究的问题。顺便说一句，这里给出的幂等性的证明对于研究从RotS函数构造幂等元的论文是有用的，该论文题为“A secondary construction and a transformation on rotation symmetric functions，and their action on bent and semi-bent functions”，由同一作者发表在JCT series A期刊上。
In this paper, we introduce a class of cubic rotation symmetric (RotS) functions and prove that it can yield bent and semi-bent functions. To the best of our knowledge, this is the second primary construction of an infinite class of nonquadratic RotS bent functions which could be found and the first class of nonquadratic RotS semi-bent functions. We also study a class of idempotents (giving RotS functions through the choice of a normal basis ofover). We derive a characterization of the bent functions among these idempotents and we relate their precise determination to a problem studied in the framework of APN functions. Incidentally, the proofs of bentness given here are useful for a paper studying a construction of idempotents from RotS functions, entitled “A secondary construction and a transformation on rotation symmetric functions, and their action on bent and semi-bent functions” by the same authors, to appear in the journal JCT series A.