New construction of highly nonlinear resilient S-boxes via linear codes
New construction of highly nonlinear resilient S-boxes via linear codes
复制标题
通过线性代码构建高度非线性弹性 S 盒
DOI：
10.1007/s11704-020-0182-y
复制
发表时间：
2021-09
影响因子：
4.2
通讯作者：
Yongzhuang Wei
中科院分区：
文献类型：
--
作者：
Haixia Zhao;Yongzhuang Wei
在通常的面向硬件的流密码的非线性组合器中，高度非线性弹性函数起着至关重要的作用。在过去的三十年里，构造高度非线性弹性函数的主要思想得益于级联大量的仿射子函数。然而，这些作为密码核心部件的弹性函数往往会受到猜测和确定攻击或代数攻击，因为变元的非线性布尔函数通过将其固定在n/2个变量上很容易产生部分线性关系。如何在不串联大量n/2元仿射子函数的情况下设计出高度非线性的弹性函数(S盒)是一个重要的课题。本文提出了一种新的高非线性弹性函数的构造方法。这些函数由两类子函数组成。更具体地说，第一类(非线性部分)既包含2k个变量的Bent函数，也包含利用[n/2-k，m，d]不相交的线性码得到的n/2k个变量的仿射子函数。第二类(线性部分)包括一些n/2个变量的线性子函数，这些子函数是由[n/2，m，d]不相交的线性码得到的。结果表明，这些弹性函数具有高度的非线性度和高代数度。特别是，与以往著名的弹性S盒不同的是，这些新的S盒不能通过固定在n/2个变量上直接分解成n/2个变量的仿射子函数。这意味着使用这些弹性函数作为分量函数的S盒(向量布尔函数)对猜想和确定攻击或代数攻击具有更好的密码学性质。
Highly nonlinear resilient functions play a crucial role in nonlinear combiners which are usual hardware oriented stream ciphers. During the past three decades, the main idea of construction of highly nonlinear resilient functions are benefited from concatenating a large number of affine subfunctions. However, these resilient functions as core component of ciphers usually suffered from the guess and determine attack or algebraic attack since then-variable nonlinear Boolean functions can be easily given rise to partial linear relations by fixing at mostn/2 variables of them. How to design highly nonlinear resilient functions (S-boxes) without concatenating a large number ofn/2 variables affine subfunctions appears to be an important task. In this article, a new construction of highly nonlinear resilient functions is proposed. These functions consist of two classes subfunctions. More specially, the first class (nonlinear part) contains both the bent functions with 2kvariables and some affine subfunctions withn/2 —kvariables which are attained by using [n/2 —k,m,d] disjoint linear codes. The second class (linear part) includes some linear subfunctions withn/2 variables which are attained by using [n/2,m,d] disjoint linear codes. It is illustrated that these resilient functions have high nonlinearity and high algebraic degree. In particular, It is different from previous well-known resilient S-boxes, these new S-boxes cannot be directly decomposed into some affine subfunctions withn/2 variables by fixing at mostn/2 variables. It means that the S-boxes (vectorial Boolean functions) which use these resilient functions as component functions have more favourable cryptography properties against the guess and determine attack or algebraic attacks.
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通过不相交线性代码构建具有严格几乎最优非线性的弹性 S 盒
影响因子：
2.5
作者：
Zhang WeiGuo;Pasalic Enes
通讯作者：
Pasalic Enes
DOI：
10.1109/tir.2002.800492
发表时间：
2002-08
期刊：
IEEE Trans. Inf. Theory
影响因子：
--
作者：
E. Pasalic;S. Maitra
通讯作者：
E. Pasalic;S. Maitra
DOI：
10.1007/3-540-45708-9_35
发表时间：
2002-08
期刊：
--
影响因子：
--
作者：
C. Carlet
通讯作者：
C. Carlet
DOI：
10.1109/18.6037
发表时间：
1988-05
期刊：
IEEE Trans. Inf. Theory
影响因子：
--
作者：
Guo-Zhen Xiao;J. Massey
通讯作者：
Guo-Zhen Xiao;J. Massey
DOI：
10.1007/978-3-662-43933-3_30
发表时间：
2013-03
期刊：
IACR Cryptol. ePrint Arch.
影响因子：
--
作者：
Christina Boura;A. Canteaut
通讯作者：
Christina Boura;A. Canteaut