Upper bounds on the numbers of resilient functions and of bent functions
Upper bounds on the numbers of resilient functions and of bent functions
复制标题
弹性函数和弯曲函数数量的上限
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
A. Klapper
中科院分区：
文献类型：
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作者：
C. Carlet;A. Klapper
弯曲函数和弹性函数在密码学、编码理论和组合学中起着重要的作用。然而，在给定数量的变量上的弯曲和弹性函数的数量是未知的。甚至连弯曲函数数目的合理界都不知道，而最著名的弹性函数数目的界对于高阶函数来说似乎很弱。在本文中，我们提出了新的界，它大大改进了由这些函数的度数限制直接推导出的界。对于弯曲函数，它是这种类型的第一个。在m弹性函数的情况下，它改进了已知的m大的边界。
Bent and resilient functions play significant roles in cryptography, coding theory, and combinatorics. However, the numbers of bent and resilient functions on a given number of variables are not known. Even a reasonable bound on the number of bent functions is not known and the best known bound on the number of resilient functions seems weak for functions of high orders. In this paper we present new bounds which significantly improve upon those which can be directly deduced from the restrictions on the degrees of these functions. In the case of bent functions, it is the first one of this type. In the case of m-resilient functions, it improves upon the known bounds for m large.