基于母函数的非线性反馈函数及其子序列研究

 针对非线性最大长度移位寄存器反馈函数难以构造问题,本文提出了一种基于母函数构造非线性最大长度移位寄存器反馈函数方法.首先,我们阐述了母函数模3分类法,证明了各类母函数新的特征状态集,提取了母函数的特征式;其次,根据特征式对母函数的筛分特性合成了非线性m子序列移位寄存器反馈函数;最后,分析了该移位寄存器生成的伪随机序列,对其自相关值和线性复杂度进行了大量搜索.结果一致表明该序列不仅具有良好的周期特性、平衡特性、游程特性,还具有尖锐的自相关特性和理想的线性复杂度.     

四元本原序列最高权位的线性复杂度

极小多项式和线性复杂度是序列用于保密通信和扩频通信的重要参数，本文利用有限域上迹函数理论和组合数学的知识决定了四元本原序列的最高权位序列的极小多项式和线性复杂度。     

基于余数系统与置换多项式的高速长周期伪随机序列生成方法

低复杂度长周期数字伪随机序列在现代加密、通信等系统中具有广泛的应用。该文提出一种基于余数系统和有限域置换多项式的伪随机序列生成方法。该方法基于中国剩余定理将多个互质的小周期有限域随机序列进行单射扩展生成长周期数字伪随机序列,置换多项式的迭代计算在多个并行的小动态范围有限域上进行,从而降低了硬件实现中迭代环路的计算位宽,提高了生成速率。该文还给出构建长周期伪随机序列的置换多项式参数选择方法和中国剩余定理优化方法,在现有技术平台下可轻易实现2100以上的序列周期。同时,该方法具有极大的迭代多项式选择自由度,例如仅在q2(mod)3且q503的有限域上满足要求的置换多项式就有10905种。硬件实现结构简单,基于Xilinx XC7Z020芯片实现290的随机序列仅需20个18 kbit的BRAM和少量逻辑资源,无需乘法器,生成速率可达449.236 Mbps。基于NIST的测试表明序列具有良好的随机特性。     

一种二进制伪随机序列盲识别方法

针对二进制伪随机序列生成多项式盲识别方法存在的需要预先知道生成多项式阶数、算法容错性能较差且复杂度较高的问题。该文提出首先将接收序列按照估计的生成多项式阶数建立分析矩阵,然后利用伽罗华域高斯列消元的方法识别出接收序列生成多项式的阶数,最后根据生成多项式的阶数构造关于生成多项式系数的方程组。为降低算法复杂度,在有限的多项式库中进行匹配搜索,能够满足该方程组的多项式就是接收序列的生成多项式。仿真结果表明,提出的方法能够区分接收序列是m序列、Gold序列或者是其他二进制伪随机序列,并有效识别其各自的生成多项式,且具有较好的容错性能。     

单圈函数序列研究

在流密码的设计中,通常要用一个随机源。常用线性反馈移位寄存器作为随机源。在Klimov A和Shamir A提出单圈T函数的概念后,许多学者在设计流密码时用单圈T函数作为随机源。为了得到新的随机源,单圈T函数的概念被扩展,单圈函数和单圈函数序列的概念被定义,单圈函数序列的最小周期被计算,有限域上分圆多项式的表达式被给出,与分圆多项式相关的两个定理被介绍。以这两个定理为基础,单圈函数序列的线性复杂度的下界被推导,猜测在许多情况下,单圈函数序列的线性复杂度远远大于这个下界。     

Fq上一类周期为2p2的四元广义分圆序列的线性复杂度

该文基于广义分圆理论,通过计算Fq(q=rm)上的序列生成多项式的零点个数,确定了一类周期为2p2的四元广义分圆序列的极小多项式和线性复杂度.结果表明,该序列的线性复杂度大于其周期的1/2,能够有效地抵抗Berlekamp-Massey(B-M)算法的攻击,是密码学意义上一类良好的周期伪随机序列.     

背包函数控制的钟控序列

本文给出了两种基于背包函数控制的钟控序列的实现方法,并证明了在一般条件下,它们的极小多项式均为h(x~q),复杂度为qn,周期为q(2~n-1),其中h(x)为GF(2)上某—n级本原不可约多项式,q为某一二元序列的周期。     

一类推广的二元Legendre-Sidelnikov序列的自相关分布

推广的Legendre-Sidelnikov序列较之原序列有更好的平衡性质,但是关于该序列的周期自相关函数,迄今仅知道一些特殊移位的情形。该文利用有限域上特征和的相关性质,给出了推广的二元Legendre-Sidelnikov序列的自相关函数的完整分布。结果表明当p3(mod 4)且qp 时,推广的Legendre-Sidelnikov序列较之原序列有更好的周期自相关函数的分布。     

GF(3)上新型自缩控序列的周期与线性复杂度

自缩控(SSC)序列是一类重要的伪随机序列,而伪随机序列在通信加密、编码技术等很多领域中有着广泛的应用.在这些应用中,通常要求序列具有大周期和高的线性复杂度.为了构造出周期更大、线性复杂度更高的伪随机序列,该文基于GF(3)上的m-序列构造了一种新型自缩控序列模型,利用有限域理论研究了生成序列的周期和线性复杂度,得到的生成序列周期和线性复杂度大大提高,且得到生成序列线性复杂度更精确的一个上界值,从而提高了生成序列在通信加密中的防攻击能力和安全性能.     

形成混沌码序列的一种方法

本文提出了用混沌迭代函数作为Mealy型有限状态机状态转换函数,用m 状态序列作为输入产生伪随机码序列,证明了系统的输出周期是m序列的整数倍;分析其输出序列近似具有独立均匀同分布的随机特性;还保持了混沌序列高复杂性等特点。     

STUDY ON STREAM CIPHERS USING GENERATING FUNCTIONS

Several kinds of stream ciphers—complementary sequences of period sequences,partial sum of period sequences,inverse order sequences and finitely generated sequences,arestudied by using techniques of generating functions.Their minimal polynomials,periods,as wellas generating functions are given.As to finitely generated sequences,the change of their linearcomplexity profiles as well as the relationship between the two generated sequences usder thecase in which the degree of connected polynomials are fixed,are discussed.     

从非奇异布尔函数对产生M序列

本文指出一种构造产生Ｍ序列的方法，它是基于圈的合并，给出一个计数公式，并给出一个简单的生成算法，不同的非奇异布尔函数生成不同的Ｍ序列，从而可以生成２＾２ｎ－１－１个ｎ＋１级Ｍ序列。     

Connection between primitive generators of GF(2n)

Primitive polynomials over GF(2) are used for generating maximal-length sequences. Powers of a root ? of such a polynomial are delay operators on the generated sequence. Given two primitive polynomials of degree n with ?1, and ?2 their roots, it is shown which parameter is needed in order to find ?1x from ?2x without knowledge of x.     

Generating 2-D FIR filter functions by Christoffel–Darboux formula for Chebyshev polynomials of the second kind

Global Christoffel–Darboux formula for different polynomials has already been used for the filter design. Here, this formula for orthonormal Chebyshev polynomials of the second kind and for two independent variables is applied in generating novel class linear-phase two-dimensional (2-D) finite impulse response (FIR) digital filter functions. In this way, 2-D filters with some specific features including economy, phase linearity, symmetry and selectivity are designed. Representative examples of the 2-D FIR digital filters of a new class obtained by the proposed approximation technique are given. A filter generated by the proposed approach is compared with the corresponding one generated by the procedure from literature.     

Interlacing properties of shift-register sequences with generator polynomials irreducible overGF(p)(Corresp.)

Interlacing properties of shift-register sequences with generator polynomials irreducible over GF(p)-herein called elementary sequences--are analyzed. The most important elementary sequences are maximal-length sequences (m-sequences). If the periodqof an elementary sequence is not prime, the sequence can always be constructed by interlacing shorter elementary sequences of periodq_{i}, providedq_{i}dividesq. It is proved that all interlaced elementary sequences are generated by one and the same irreducible polynomial. Some relationships between equal-length elementary sequences are derived, including some rather unexpected crosscorrelation properties. As an example of an application of the theory, a new time-division multiplex technique for generating high-speedm-sequences is presented.     

一种基于哈夫曼树的最大频繁序列挖掘算法

最大频繁序列挖掘是数据挖掘的重要内容之一.在深入分析频繁序列特点以及已有序列挖掘算法的基础上,提出一种新的最大序列挖掘算法Huffman-MaxSeq.与传统的"候选最大频繁序列集生成——测试"思路不同,该算法采用"边生成候选序列边测试"的思想,从而有效地减少了候选序列的生成.该算法基于构造哈夫曼树(最优树)的方法,对每个序列赋予权值,按权值的大小选取序列,连接生成新的候选频繁序列,再产生最大频繁序列.     

Image encryption method based on multiple-order fractional discrete Tchebichef transform and generating sequence

Fractional transform based image encryption methods have been widely studied in recent years.However,most of the existing fractional transform based image encryption methods are defined in the complex field.Thus,the encrypted images contain both phase and amplitude information,which is not conducive to transmission and storage.Moreover,some encryption methods that meet the requirements of reality-preserving have problems of relatively single keys,lacking of sensitivity and so on.An image encryption method was proposed based on multiple-order fractional discrete Tchebichef transform and generating sequence.The proposed method used randomly generated row and column vectors and generating sequence generated by Chaotic sequences as keys to encrypt images,which not only satisfied property of reality-preserving transmission but also greatly expanded the key space.The experimental results further demonstrate that the proposed encryption method can resist a variety of attacks,and decrypted images are almost non-distored,which indicate excellent encryption effect,sufficient security and robustness of the method.     

Application of Zero Correlation Zone Sequences in Quasi-synchronous CDMA Systems

In a quasi-synchronous code division multiple access （QS-CDMA） system, the correlation functions around the origin influence the system performance and odd functions are as important as the even functions. Three kinds of zero correlation zone（ZCZ） sequences are used to analyze and compare the correlation functions. Binary phase shift keying（BPSK） simulations of QS-CDMA system with the three kinds of QS sequences as spreading codes on additive white Gaussian noise（AWGN） channel show that these sequences are quasi-orthogonal, so they are suitable for QS-CDMA system. The correlation between the system performance and the zero correlation zone of the sequence is also proved.