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Periods on the Cascade Connection of an LFSR and an NFSR

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Chinese Journal of Electronics 2019年第2期28卷 301-308页

作者： YANG Yinghua zeng xiangyong XU Yunge Hubei Key Laboratory of Applied Mathematics Hubei University

We study the periods of sequences produced by the cascade connection of two Feedback shift registers（FSRs）. The period of the cascade connection is the period of the longest sequences it produces. An upper bound for the period of the cascade connection of a Nonlinear feedback shift register（NFSR） into a Linear feedback shift register（LFSR） is established. In addition,the cascade connection of an n-stage maximum-length LFSR into an n-stage NFSR is called an（n + n）-stage Grain-like NFSR, and we propose two families of（n + n）-stage Grain-like NFSRs such that the minimal period 2~n-1 is achievable for a positive integer n.

关键词： Stream cipher Cascade connection Grain-like NFSR Period

FAMILIES OF p-ARY SEQUENCES WITH LOW CORRELATION AND LARGE LINEAR COMPLEXITY

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Journal of Systems Science & Complexity 2014年第6期27卷 1305-1319页

作者： CAI Han zeng xiangyong HU Lei Faculty of Mathematics and Statistics Hubei University State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences

This paper generalizes a method of generating shift sequences in the interleaved construction proposed by *** the new shift sequences,some new families of p-ary sequences with desired properties can be obtained.A lowe... 详细信息

关键词： Auto-correlation cross-correlation linear complexity low correlation p-ary sequence.

The Periods of a Class of Nonlinear Feedback Shift Register Sequences

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Chinese Journal of Electronics 2016年第2期25卷 296-303页

作者： LIANG Wanwan zeng xiangyong XU Yunge Hubei Key Laboratory of Applied Mathematics Hubei University

In this paper, we discuss a class of n-stage Nonlinear feedback shift registers(NFSRs). Applying the knowledge of algebra, the least periods of the sequences generated by these NFSRs with symmetric feedback functions can be characterized. This approach simplifies the problem of determining the periods of the NFSR sequences and it generalizes some Cheng's results.

关键词： Stream cipher Nonlinear feedback shift register(NFSRs) Period Boolean function

A Class of New Quadratic Vectorial Bent Functions

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Chinese Journal of Electronics 2020年第5期29卷 873-879页

作者： PANG Tingting zeng xiangyong LI Nian XU Yunge The Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University

A class of quadratic vectorial bent functions having the form F（x）=Trm~n(ax~(2s1+1))+Tr1~n(bx~(2s2+1)) is investigated,where n,m,s1,s2are positive integers and the coefficients a,b belong to the finite field F2~*** some discussions on the permutation property of certain linearized polynomials over F2~n,several classes of quadratic vectorial bent functions are presented for special cases of n,and it is also verified by computer that some vectorial bent functions proposed are extended affine inequivalent to all known quadratic vectorial bent functions.

关键词： Finite field Extended affine equivalence quadratic vectorial bent functions linearized polynomial Permutation polynomial Boolean functions Vectorial bent function polynomials affine transforms permutation property

More permutation polynomials with differential uniformity six

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Science China(Information Sciences) 2018年第3期61卷 223-225页

作者： Ziran TU xiangyong zeng Zhiyong ZHANG School of Mathematics and Statistics Henan University of Science and Technology Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University School of Information Engineering Henan University of Science and Technology

Differential analysis is one of the most important attacks threatening iterated block *** resist against differential attacks[1],the multioutput Boolean functions used in designing Sboxes should have low differential *** a positive integer n,the lowest differential uniformity of the functions from the finite field F;(for a prime power q,F;denotes the finite field with

关键词： More permutation polynomials with differential uniformity six

On the bit-based division property of S-boxes

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Science China(Information Sciences) 2022年第4期65卷 261-263页

作者： Zejun XIANG xiangyong zeng Shasha ZHANG Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied MathematicsHubei University

Dear editor,The S-box, which is one of the most popular cipher components, has been extensively applied in modern symmetrickey primitives. Moreover, it is often the case that S-boxes are the only nonlinear components ... 详细信息

关键词： division property Sbox ANF divisional optimal divisional suboptimal

A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties

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Journal of Systems Science & Complexity 2018年第4期31卷 1042-1064页

作者： SHAN Jinyong HU Lei zeng xiangyong LI Chunlei SKLOIS Institute of Information Engineering Chinese Academy of Sciences Beijing 100093 China DCS Chinese Academy of Sciences Beijing 100093 China School of Cyber Security University of Chinese Academy of Sciences Beijing 100049 China Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University Wuhan 430062 China SKLOIS Institute of Information Engineering Chinese Academy of Sciences Beijing 100093China Department of Informatics University of Bergen N-5020 Bergen Norway

This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.

关键词： Algebraic immunity Boolean functions correlation immunity nonlinearity resilient

The weight distributions of a class of non-primitive cyclic codes with two nonzeros

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Science China Mathematics 2015年第6期58卷 1285-1296页

作者： ZHENG DaBin ZHOU FengLi HU Lei zeng xiangyong Faculty of Mathematics and Statistics Hubei University State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of Sciences Beijing Center for Mathematics and Information Interdisciplinary Sciences

Recently, a class of non-primitive cyclic codes with two nonzeros have received much attention of researchers and their weight distributions have been obtained for several cases of two key parameters related to the nonzeros. In this paper, by evaluating certain Jacobi sums, we determine the weight distributions of this class of cyclic codes for one more special case.

关键词： primitive codes Jacobi multiplicative evaluating integer multiplicity exponential simplify details

Two families of Niho sequences having four-valued cross correlation with m-sequences Dedicated to Professor Yingbo Zhang on the Occasion of His 70th Birthday

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Science China Mathematics 2017年第12期60卷 2377-2390页

作者： FAN JinMei XU YunGe XIA YongBo zeng xiangyong Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied MathematicsHubei University College of Science Guilin University of Technology Department of Mathematics and Statistics South-Central University for Nationalities

For two odd integers m and s with 1≤s < m and gcd(m, s) = 1, let h satisfy h(2~s-1) ≡1(mod 2~m+ 1) and d =(h + 1)(2~m-1) + 1. The cross correlation function between a binary m-sequence of period 22~m-1 and its d-decimation sequence is proved to take four values, and the correlation distribution is completely determined. Let n be an even integer and k be an integer with 1≤k≤n/2. For an odd prime p and a p-ary m-sequence {s(t)} of period p^n-1, define u(t) =∑(p^k-1)/2 i=0 s(d_it), where d_i = ip^(n/2) + p^k-i and i = 0, 1,...,(p^k-1)/2. It is proved that the cross correlation function between {u(t)} and {s(t)} is three-valued or four-valued depending on whether k is equal to n/2 or not, and the distribution is also determined.

关键词： m-sequence decimation sequence correlation distribution Niho exponent exponential sum