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On designated-weight Boolean functions with highest algebraic immunity

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Science china Mathematics 2010年第11期53卷 2847-2854页

作者： liu MeiCheng1,3, DU YuSong2, PEI DingYi2 & lin dongdai1 1The state key laboratory of information security, institute of software of chinese academy of sciences, beijing 100190, china 2College of Mathematics and information sciences, Guangzhou University, Guangzhou 510006, china 3Graduate University of chinese academy of sciences, beijing 100049, china 1. The state key laboratory of information security Institute of Software of Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100049 China2. College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China

Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions. In this paper, we study ∑d-1 i=0 (ni)-weight Boolean functions with algebraic immunity achiev-ing the minimum of d and n - d + 1, which is highest for the functions. We present a simpler sufficient and necessary condition for these functions to achieve highest algebraic immunity. In addition, we prove that their algebraic degrees are not less than the maximum of d and n - d + 1, and for d = n1 +2 their nonlinearities equalthe minimum of ∑d-1 i=0 (ni) and ∑ d-1 i=0 (ni). Lastly, we identify two classes of such functions, one having algebraic degree of n or n-1.

关键词： cryptography Boolean function algebraic immunity algebraic degree nonlinearity

A New Upper Bound on the Order of Affine Sub-families of NFSRs

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Journal of Systems Science & Complexity 2020年第1期33卷 196-214页

作者： liu Junying ZHENG Qunxiong lin dongdai state key laboratory of information security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China School of Cyber security University of Chinese Academy of SciencesBeijing 100049China state key laboratory of Cryptology Beijing 100878China PLA Strategic Support Force information Engineering University Zhengzhou 450002China

Nonlinear feedback shift registers(NFSRs)are widely used as building blocks in the design of stream *** NFSR(f)be an NFSR with the characteristic function f and let G(f)be the set of output sequences of NFSR(f).For a given NFSR(f),if there exists an affine Boolean function l such that G(l)?G(f),then G(l)is called an affine sub-family of NFSR(f).In this paper,by skillfully combining previous ideas,the authors give a new upper bound on the order of affine sub-families of NFSR(f).Compared with the four known bounds,the bound is better than three of them,and in some cases is also better than the rest one.

关键词： Affine sub-families families of NFSR sequences nonlinear feedback shift registers stream ciphers

A Note on Rotation Symmetric S-boxes

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Journal of Systems Science & Complexity 2019年第5期32卷 1460-1472页

作者： GAO Guangpu lin dongdai liu Wenfen state key laboratory of Mathematical Engineering and Advanced Computing Zhengzhou 450002China state key laboratory of information security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China state key laboratory of information security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China Guangxi key laboratory of Cryptogpraphy and information security Guilin University of Electronic TechnologyGuilin 541004China

This paper is twofold. The first is devoted to study a class of quadratic rotation symmetric S-boxes(RSSBs) which was presented by Gao G, et al., Constructions of quadratic and cubic rotation symmetric bent functions, IEEE Transactions on information Theory, vol. 58, no. 7, pp. 4908 –4913, 2012, by decomposing a class of cubic rotation symmetric bent functions. The authors obtain its nonlinearity and differential uniformity of such class of S-boxes. In particular, the compositional inversion of the class of rotation symmetric S-boxes is also presented. Then the authors introduce a steepest-descent-like search algorithm for the generation of RSSBs. The algorithm finds 5,6,7,8-bit RSSBs with very good cryptographic properties which can be applied in designing cryptographical algorithms.

关键词： Dual Keccak permutation rotation symmetry S-box

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理想格上格基的快速三角化算法研究

电子与信息学报 2020年第1期42卷 98-104页

作者：张洋刘仁章林东岱中国科学院信息工程研究所信息安全国家重点实验室北京100093 中国科学院大学网络空间安全学院北京100049 卫士通摩石实验室北京100166

为了提高理想格上格基的三角化算法的效率,该文通过研究理想格上的多项式结构提出了一个理想格上格基的快速三角化算法,其时间复杂度为O(n3log2B),其中n是格基的维数,B是格基的无穷范数。基于该算法,可以得到一个计算理想格上格基Smith... 详细信息

为了提高理想格上格基的三角化算法的效率,该文通过研究理想格上的多项式结构提出了一个理想格上格基的快速三角化算法,其时间复杂度为O(n3log2B),其中n是格基的维数,B是格基的无穷范数。基于该算法,可以得到一个计算理想格上格基Smith标准型的确定算法,且其时间复杂度也比现有的算法要快。更进一步,对于密码学中经常所使用的一类特殊的理想格,可以用更快的算法将三角化矩阵转化为格基的Hermite标准型。

关键词：理想格 Hermite标准型 Smith标准型三角化

基于Nonce重用的ACORN v3状态恢复攻击

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通信学报 2020年第8期41卷 11-21页

作者：张国双陈晓林东岱刘凤梅中国科学院信息工程研究所北京100093 中国科学院大学网络空间安全学院北京100049 信息保障技术重点实验室北京100072

基于差分代数方法,利用猜测确定技术给出了Nonce重用两次情况下ACORN v3的状态恢复攻击,攻击所需的计算复杂度为2122.5c,数据复杂度和存储复杂度可忽略不计,其中c是求解线性方程组的复杂度。针对Nonce多次重用时的情形进行了分析,发现AC... 详细信息

基于差分代数方法,利用猜测确定技术给出了Nonce重用两次情况下ACORN v3的状态恢复攻击,攻击所需的计算复杂度为2122.5c,数据复杂度和存储复杂度可忽略不计,其中c是求解线性方程组的复杂度。针对Nonce多次重用时的情形进行了分析,发现ACORN v3较复杂的滤波函数,使由密钥流直接提取关于内部状态线性方程的方法变得不可行,从而有效规避了通过增加Nonce重用次数来显著降低攻击复杂度的安全风险。

关键词：认证加密密码分析 ACORN 状态恢复攻击