Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
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DOI：
10.1002/sec.356
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发表时间：
2012-06
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影响因子：
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通讯作者：
Fengrong Zhang;Yu-pu Hu;Min Xie;Yongzhuang Wei
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文献类型：
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作者：
Fengrong Zhang;Yu-pu Hu;Min Xie;Yongzhuang Wei
在本文中，我们专注于设计具有理想加密特性的 1-弹性布尔函数。首先，我们提出了一种新颖的二次构造来获得 1-弹性函数。接下来，我们展示这些构造的 1-弹性函数的属性与初始函数的属性之间的关系。基于n个变量上的弯曲函数的构造和一类，我们可以得到一类具有高代数免疫性的(n + 3)变量1-弹性不可分离密码函数，其非线性等于弯曲串联界限2n + 2 − 2(n + 2)/2。此外，我们提出了一组关于奇数个变量的 1-弹性不可分离函数，具有最佳代数度、高代数免疫性和高非线性。版权所有 © 2012 约翰·威利父子有限公司
In this paper, we concentrate on the design of 1-resilient Boolean functions with desirable cryptographic properties. Firstly, we put forward a novel secondary construction to obtain 1-resilient functions. Next, we present the relationships between the properties of these constructed 1-resilient functions and that of the initial functions. Based on the construction and a class of bent functions on n variables, we can obtain a class of (n + 3)-variable 1-resilient non-separable cryptographic functions with a high algebraic immunity, whose nonlinearity is equal to the bent concatenation bound 2n + 2 − 2(n + 2)/2. Furthermore, we propose a set of 1-resilient non-separable functions on odd number of variables with an optimal algebraic degree, a high algebraic immunity, and a high nonlinearity. Copyright © 2012 John Wiley & Sons, Ltd.