An Efficient Characterization of a Family of Hyperbent Functions

Lisonek P.

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An Efficient Characterization of a Family of Hyperbent Functions

机译：一族双曲函数的有效刻画

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摘要

Charpin and Gong recently characterized a large class of hyperbent functions defined on fields of order $2^n$, which include the well-known monomial functions with the Dillon exponent as a special case. We give a reformulation of the Charpin-Gong criterion in terms of the number of rational points on certain hyperelliptic curves. We present two applications of our result: The time needed to check the hyperbentness of a specific function is now polynomial in $n$ , and hyperbent functions with subfield coefficients can be constructed.

机译：Charpin和Gong最近在$ 2 ^ n $阶域上定义了一大类双曲函数，其中包括众所周知的单项函数，其中Dillon指数作为特例。根据某些超椭圆曲线上有理点的数量，我们重新给出了Charpin-Gong准则。我们给出了结果的两个应用：现在，检查特定函数的双曲性所需的时间是$ n $的多项式，并且可以构造具有子字段系数的双曲函数。

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《Information Theory, IEEE Transactions on》 |2011年第9期|p.6010-6014|共5页
作者
Lisonek P.;
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作者单位

Department of Mathematics, Simon Fraser University, Burnaby, Canada;

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正文语种 eng
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关键词
Bent function; Hadamard spectrum; hyperbent function; hyperelliptic curve; time complexity; zeta function;

机译：Bent函数;Hadamard谱;超弯函数;超椭圆曲线;时间复杂度;zeta函数;

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An Efficient Characterization of a Family of Hyperbent Functions

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