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Construction of k-ary pseudorandom Elliptic Curve sequences

Wuhan University Journal of Natural Sciences 2011年第5期16卷 452-456页

作者： WU Chenhuang WENG Xin CHEN Zhixiong Department of Mathematics Putian University Putian351100 Fujian China State Key Laboratory of Information Security/Institute ofSoftware Chinese Academy of Sciences Beijing 100049 China School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

We present a method for constructing k-ary sequences over elliptic curves. Using the multiplicative character of order k of finite fields, we construct a family of k-ary pseudorandom elliptic curve sequences. The pseudorandom measures, such as the well-distribution measure, the correlation measure of order e, and the linear complexity are estimated by using certain character sums. Such sequences share the same order of magnitude on the well-distribution measure, the correlation measure of order e as the ＇truly＇ random sequences. The method indicates that it is possible to construct ＇good＇ pseudorandom sequences over elliptic curves widely used in public key cryptography.

关键词： pseudorandom sequences discrete logarithms elliptic curves character sums

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Linear complexity problems of level sequences of Euler quotients and their related binary sequences

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Science China(Information Sciences) 2016年第3期59卷 75-86页

作者： Zhihua NIU Zhixiong CHEN Xiaoni DU School of Computer Engineering and Science Shanghai University School of Mathematics Putian University College of Mathematics and Information Science Northwest Normal University

The Euler quotient modulo an odd-prime power pr(r > 1) can be uniquely decomposed as a p-adic number of the form(up-1pr-1- 1)/pr≡ a0(u) + a1(u)p + ··· + ar-1(u)pr-1(mod pr), gcd(u, p) = 1, where0≤aj(u) 1. We firstly study certain arithmetic properties of the level sequences(aj(u))u≥0over Fp via introducing a new quotient. Then we determine the exact values of linear complexity of(aj(u))u≥0 and values of k-error linear complexity for binary sequences defined by(aj(u))u≥0.

关键词： cryptography Euler quotients Fermat quotients pseudorandom sequences binary sequences lin ear complexity k-error linear complexity

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Assessment and improvement of autocorrelation performance of chaotic sequences using a phase space method

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Science China(Information Sciences) 2011年第12期54卷 2667-2679页

作者： CHEN Bin School of Software and Communication Engineering, JiangXi University of Finance and Economy, Nanchang 330032, China School of Software and Communication Engineering JiangXi University of Finance and Economy Nanchang China

Chaotic sequences have been widely used as pseudorandom sequences. However, how to judge whether their autocorrelation performance is good remains a problem because we have no simple method for assessing and improving the autocorrelation performance. Using a phase space method, we have discovered that the autocorrelation performance of a chaotic sequence is determined by whether its phase space trajectory is axis symmetrical, and have deduced theorems to describe and solve these problems. This paper presents a simple yet effective method to assess and improve the autocorrelation performance of chaotic sequences. Several simulations are presented to validate the theorems and method.

关键词： chaos autocorrelation pseudorandom sequences phase space

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AUTOCORRELATIONS OF l-sequences WITH CERTAIN SHIFTS

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Journal of Electronics(China) 2007年第4期24卷 439-442页

作者： Xu Hong Qi Wenfeng Department of Applied Mathematics Zhengzhou Information Engineering University Zhengzhou 450002 China

In this paper, the autocorrelations of maximal period Feedback with Carry Shift Register sequences （l-sequences） are discussed. For an l-sequence a with connection integer q = p^e（e ≥ 2） and period T = p^t-1（p- 1）, and for any integer i, 1 ≤ i ≤ e/2, by calculating the number of certain sets, it is shown that the autocorrelation of a with shift τ= kT/2p^i is Ca（τ） =（-1）^k-1 T/p^2i-1, where 1 ≤ k ≤ 2p^i - 1, and gcd（k,2p^i） = 1. This result shows there do exist some shifts such that the autocorrelations of l-sequences are high although most autocorrelations are low. Such result also holds for the decimations of l-sequences.

关键词： pseudorandom sequences l-sequences Feedback with Carry Shift Register (FCSR) sequences Autocorrelations

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