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Stability of nonlinear feedback shift registers

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Science China(Information Sciences) 2016年第1期59卷 201-212页

作者： Jianghua ZHONG dongdai lin State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences Institute of Complexity Science Qingdao University

Convolutional codes have been widely used in many applications such as digital video, radio, and mobile communication. Nonlinear feedback shift registers(NFSRs) are the main building blocks in convolutional decoders. A decoding error may result in a succession of further decoding errors. However, a stable NFSR can limit such an error-propagation. This paper studies the stability of NFSRs using a Boolean network approach. A Boolean network is an autonomous system that evolves as an automaton through Boolean functions. An NFSR can be viewed as a Boolean network. Based on its Boolean network representation, some sufficient and necessary conditions are provided for globally(locally) stable NFSRs. To determine the global stability of an NFSR with its stage greater than 1, the Boolean network approach requires lower time complexity of computations than the exhaustive search and the Lyapunov’s direct method.

关键词： nonlinear feedback shift register stability Boolean function Boolean network semi-tensor product

Analyzing Boolean Functions via Solving Parametric Polynomial Systems

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Journal of Systems Science & Complexity 2021年第2期34卷 792-808页

作者： HUANG Zhenyu SUN Yao lin dongdai SKLOIS Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China

In this paper,a new method to analyze Boolean functions is *** this method,one can analyze the balancedness,the nonlinearity,and the input-output correlation of vectorial Boolean *** basic idea of this method is to compute the refined covers of some parametric Boolean polynomial systems which are equivalent to these *** a refined cover,the parameter space is divided into several disjoint components,and on each component,the parametric Boolean polynomial system has a fixed number of *** efficient algorithm based on the characteristic set method to compute refined covers of parametric Boolean polynomial systems is *** experimental results about some instances generated from cryptanalysis show that this new method is efficient and can solve some instances which can not be solved in reasonable time by other methods.

关键词： Boolean functions characteristic set method correlation nonlinearity parametric Boolean polynomial systems

Observability of Galois nonlinear feedback shift registers

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Science China(Information Sciences) 2022年第9期65卷 219-234页

作者： Wenhui KONG Jianghua ZHONG dongdai lin State Key Laboratory of Information Security Institute of Information Engineering Chinese Academy of Sciences School of Cyber Security University of Chinese Academy of Sciences

Nonlinear feedback shift registers(NFSRs) have been used in many recent stream ciphers. They are generally classified into Fibonacci NFSRs and Galois NFSRs according to their implementation configurations. An NFSR is observable if any two distinct initial states can be distinguished from their corresponding output sequences. From the security perspective, NFSR-based stream ciphers should select observable NFSRs; otherwise, they will be subject to weak key attacks. Any Fibonacci NFSR is observable as the first n bits of its output sequence is just its initial state, where n is the stage number of the Fibonacci *** paper considers the observability of Galois NFSRs. Some necessary and/or sufficient conditions are presented, using the semi-tensor product-based Boolean network theory. In particular, a new observability matrix is proposed to facilitate the observability determination.

关键词： shift register stream cipher observability Boolean network semi-tensor product

Algebraic-Differential Attacks on a Family of Arithmetization-Oriented Symmetric Ciphers

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Journal of Systems Science & Complexity 2023年第6期36卷 2681-2702页

作者： LI Zhengnan WU Baofeng lin dongdai Institute of Information Engineering Chinese Academy of SciencesBeijing100085China State Key Laboratory of Cryptology Beijing100878China School of Cyber Security University of Chinese Academy of SciencesBeijing100049China

Motivated by applications in advanced cryptographic protocols,research on arithmetizationoriented symmetric primitives has been rising in the field of symmetric cryptography in recent *** this paper,the authors focus on on the collision attacks for a family of arithmetization-oriented symmetric ciphers *** authors firstly enhance the algebraically controlled differential attacks proposed by introducing more ***,combining algebraic attacks and differential attacks,the authors propose algebraic-differential attacks on GMi *** attack method is shown to be effective by experiments on toy versions of GMi *** authors further introduce some tricks to reduce the complexities of algebraic-differential attacks and improve the success probability of finding collisions.

关键词： Algebraic attacks collisions differential attacks GMiMCHash Grobner basis

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

linearization of Multi-Valued Nonlinear Feedback Shift Registers

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Journal of Systems Science & Complexity 2017年第2期30卷 494-509页

作者： WANG Haiyan ZHONG Jianghua lin dongdai State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China

Nonlinear feedback shift registers(NFSRs) have been used in many stream ciphers for cryptographic security. The linearization of NFSRs is to describe their state transitions using some matrices. Such matrices are called their state transition matrices. Compared to extensive work on binary NFSRs, much less work has been done on multi-valued NFSRs. This paper uses a semi-tensor product approach to investigate the linearization of multi-valued NFSRs, by viewing them as logical networks. A new state transition matrix is found for a multi-valued NFSR, which can be simply computed from the truth table of its feedback function. The new state transition matrix is easier to compute and is more explicit than the existing results. Some properties of the state transition matrix are provided as well, which are helpful to theoretically analyze multi-valued NFSRs.

关键词： Logic network nonlinear feedback shift register semi-tensor product state transition matrix stream ciphers.

On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers

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Science China(Information Sciences) 2017年第5期60卷 84-95页

作者： Yupeng JIANG Qun-Xiong ZHENG dongdai lin State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences State Key Laboratory of Mathematical Engineering and Advanced Computing Zhengzhou Information Science and Technology Institute

Let Z/（p;） be the integer residue ring modulo pewith p an odd prime and e 2. We consider the suniform property of compressing sequences derived from primitive sequences over Z/（p;）. We give necessary and sufficient conditions for two compressing sequences to be s-uniform with α provided that the compressing map is of the form φ(x;, x;,..., x;) = g(x;) + η(x;, x;,..., x;), where g(x;) is a permutation polynomial over Z/（p） and η is an（e-1）-variable polynomial over Z/（p）.

关键词： compressing map linear recurring sequence primitive sequence permutation polynomial s uniform

Decomposition of nonlinear feedback shift registers based on Boolean networks

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Science China(Information Sciences) 2019年第3期62卷 217-219页

作者： Jianghua ZHONG dongdai lin State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences

Dear editor,The Boolean network (BN) was introduced by Kauffman [1] to model a genetic network. In such a network, the nodes (genes, proteins, or other molecules) assume only two values, 1 (ON) and0 (OFF), and the interactions between nodes are determined by Boolean functions. Owing to the complexity of nonlinear logical relations, a con-

关键词： In Decomposition of nonlinear feedback shift registers based on Boolean networks

On enumeration of polynomial equivalence classes

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Science China Mathematics 2012年第6期55卷 1137-1152页

作者： WANG TianZe lin dongdai State Key Laboratory of Information Security Institute of SoftwareChinese Academy of SciencesBeijing 100190China Graduate University of Chinese Academy of Sciences Beijing 100149China

The isomorphism of polynomials （IP）, one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials. Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate publi9 key cryptosystem. In this paper we show the enumeration of the equivalence classes containing ∑n-1 i=0 aiX^2qi when char（Fq） = 2, which implies that these polynomials are all weak IP instances. Moreover, we study the cardinality of an equivalence class containing the binomial aX2qi ＋ bX2qj （i ≠ j） over Fqn without the restriction that char（Fq） = 2, which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.

关键词： enumerative problem isomorphism of polynomials finite geometry