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Construction of resilient functions

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Construction of Resilient Functions

Constructions of highly nonlinear resilient plateaud functions

The 1st Chinese Conference on Trusted Computing and Information Security

作者： ZHANG Jie, WEN Qiao-yan School of Science, Beijing University of Posts and Telecommunications , Beijing 100876, China State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing 100039, China

＜正＞ Based on the relationship between nonlinearity and resiliency of a multi-output function, we present a methodfor constructing nonintersecting linear codes from packing design. Through these linear codes, we obtain n-variable, m-output, t-resilient functions with very high nonlinearity. Their nonlinearities are currently the best results for most of

关键词： resilient functions packing design correlation-immune functions linear codes

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High Technology Letters 2011年第2期17卷 220-222页

作者：张卫国 Chen Yuan ISN Laboratory Xidian University Xi＇ an 710071 China

The main results in this paper are to construct two classes of plateaued functions with desirable cryptographic properties. By using the Maiorana-McFarland construction, a class of highly nonlinear resilient plateaued functions satisfying the propagation criterion has been obtained. Johansson,s et al＇ s construction is modified slightly to obtain highly nonlinear multi-output resilient plateaued functions.

关键词： cryptography boolean functions correcting codes plateaued functions resilient functions error

Construction and Count of 1-resilient Rotation Symmetric Boolean functions on 4p Variables

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Chinese Journal of Electronics 2017年第6期26卷 1276-1283页

作者： PANG Shanqi XU Wenju DU Jiao WANG Ying College of Mathematics and Information Science Henan Normal University

This paper studies the properties of orbit matrix and gives a formula to compute the number of these orbit matrices on 4p variables, where p is an odd prime. It has been demonstrated that the construction of 1-resilient Rotation symmetric Boolean functions(RSBFs) on 4p variables is equivalent to solving an equation system. By the proposed method, all 1-resilient RSBFs on 12 variables can be constructed. We present a counting formula for the total number of all 1-resilient RSBFs on 4p variables. As application of our method, some 1-resilient RSBFs on 12 variables are presented.

关键词： Cryptography Rotation symmetric Boolean functions Orbit matrix resilient functions

Construction and Count of 1-resilient Rotation Symmetric Boolean functions on pr Variables

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Chinese Journal of Electronics 2014年第4期23卷 816-820页

作者： DU Jiao PANG Shanqi WEN Qiaoyan LIAO Xin College of Mathematics and Information Science Henan Normal University State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications College of Information Science and Engineering Hunan University

Construction and count of 1-resilient Rotation symmetric Boolean functions(RSBFs) on p r variables are demonstrated. It is proved that constructions of1-resilient RSBFs on p r variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on p r variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.

关键词： Cryptography Rotation symmetric Support table Correlation-immune resilient functions

The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean functions

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Chinese Journal of Electronics 2018年第5期27卷 995-1001页

作者： DU Jiao FU Shaojing QU Longjiang LI Chao PANG Shanqi College of Mathematics and Information Science Henan Normal University Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control Henan Normal University College of Computer Science National University of Defense Technology College of Liberal Arts and Science National University of Defense Technology

A new characterization of balanced rotation symmetric（n, m）-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric（p;, m）-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric（2;, m）-functions for 2 ≤ m ≤ 2;-r. With the help of these results, we also prove that there exist rotation symmetric resilient（2;, m）-functions for 2 ≤ m ≤ 2;-r-1.

关键词： Cryptography Rotation symmetric Orbit matrix Correlation immune resilient functions

Application of Orthogonal Array and Walsh Transform in resilient Function

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Chinese Journal of Electronics 2018年第2期27卷 281-286页

作者： PANG Shanqi WANG Jing WANG Xunan WANG Xiaoli College of Mathematics and Information Science Henan Normal University Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control Henan Normal University

The relationship between Walsh transform of a Boolean function and the orthogonality of some columns of its support table is investigated. This result improves the characterization of the orthogonality of Orthogonal array(OA). Stinson and Massey gave two construction methods of linear resilient functions, one is to use linear code, the other is to utilize the large set of orthogonal arrays and right cosets. And another major contribution is to show the equivalence of two methods.

关键词： resilient functions Orthogonal array(OA) Linear code Walsh transform