• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文会议>Cryptography and coding >A New Family of Hyper-Bent Boolean Functions in Polynomial Form
【24h】

A New Family of Hyper-Bent Boolean Functions in Polynomial Form

机译：多项式形式的超弯曲布尔函数的新族

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Bent functions are maximally nonlinear Boolean functions and exist only for functions with even number of inputs. These combinatorial objects, with fascinating properties, are rare. The class of bent functions contains a subclass of functions the so-called hyper-bent functions whose properties are still stronger and whose elements are still rarer. (Hyper)-bent functions are not classified. A complete classification of these functions is elusive and looks hopeless. So, it is important to design constructions in order to know as many of (hyper)-bent functions as possible. Few constructions of hyper-bent functions defined over the Galois field F_(2~n) (n = 2m) are proposed in the literature. The known ones are mostly monomial functions.rnThis paper is devoted to the construction of hyper-bent functions. We exhibit an infinite class over F_(2~n) (n = 2m, m odd) having the form f(x) = Tr_1~(o(s_1)) (ax~(s_1)) +Tr_1~(0(s_2)) (bx~(s_2)) where o(s_i) denotes the cardinality of the cyclotomic class of 2 modulo 2~n - 1 which contains s_i and whose coefficients a and b are, respectively in F_(2~(o(s_1))) and F_(2~(o(s_2))). We prove that the exponents s_1 = 3(2~m - 1) and s_2 = (2~n-1/)/3, where a ∈ F_(2~n)(a ≠ 0) and b ∈ F_4 provide a construction of hyper-bent functions over F_(2~n) with optimum algebraic degree. We give an explicit characterization of the bentness of these functions, in terms of the Kloosterman sums and the cubic sums involving only the coefficient a.
机译：Bent函数是最大程度的非线性布尔函数，仅对于输入数为偶数的函数存在。这些具有引人入胜的属性的组合对象很少见。弯曲函数类包含函数的子类，即所谓的超弯曲函数，它们的属性仍然更强，而元素仍然更罕见。 （超级）弯曲功能未分类。这些功能的完整分类是难以捉摸的，而且看起来毫无希望。因此，设计构造很重要，以便尽可能多地了解（超）弯曲功能。文献中很少提出在Galois场F_（2〜n）（n = 2m）上定义的超弯曲函数的构造。已知的函数主要是单项函数。本文致力于超弯曲函数的构造。我们在F_（2〜n）（n = 2m，m奇数）上表现出无限类，形式为f（x）= Tr_1〜（o（s_1））（ax〜（s_1））+ Tr_1〜（0（s_2） ））（bx〜（s_2））其中o（s_i）表示2模2〜n-1的环原子类的基数，该基数包含s_i，其系数a和b分别位于F_（2〜（o（s_1） ）））和F_（2〜（o（s_2）））。我们证明了指数s_1 = 3（2〜m-1）和s_2 =（2〜n-1 /）/ 3，其中a∈F_（2〜n）（a≠0）和b∈F_4提供了一个构造具有最佳代数度的F_（2〜n）上的超弯曲函数我们用仅涉及系数a的Kloosterman和和三次和给出了这些函数的弯曲度的明确表征。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号