周期为2p2 的四阶二元广义分圆序列的线性复杂度

该文基于分圆理论,构造了一类周期为2p2的四阶二元广义分圆序列。利用有限域上多项式分解理论研究序列的极小多项式和线性复杂度。结果表明,该序列具有良好的线性复杂度性质,能够抗击B-M算法的攻击。是密码学意义上性质良好的伪随机序列。     

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.     

周期为pm的广义割圆序列的线性复杂度

该文将周期为pm(p为奇素数,m为正整数)广义割圆的研究推广到了任意阶的情形,构造了一类新序列,确定了该序列的极小多项式,指出线性复杂度可能的取值为pm-1, pm,(pm-1)/2和(pm+1)/2。并且指出,当选取的特征集满足一定条件时,对应序列的线性复杂度取值总是以上4种情形。结果表明,该类序列具有较好的线性复杂度性质。     

Legendre序列在GF(p)上的线性复杂度

线性复杂度是度量流密码安全性的一个重要指标.GF(2)上序列可以把它看成GF(p)上的序列,因此需要研究序列在GF(p)(p是较小的奇素数)上的线性复杂度.从这个观点出发,讨论了Legendre序列在GF(p)上的线性复杂度,在应用部分发现了Legendre序列在分圆多项式分解上一个应用,并对此做了一些扩展.     

一类周期为pq阶为2的Whiteman广义分圆序列研究

线性复杂度是度量序列随机性质最重要的指标之一。该文基于Whiteman-广义分圆,构造了一类周期为pq阶为2的广义分圆序列。证明了适当的选取参数p和q,该类序列的线性复杂度的下界为pq-p-q+1,且该类序列为平衡序列。最后指出了准确计算该序列的线性复杂度所必须解决的问题。     

一类新的 pqr长2阶广义分圆序列的线性复杂度

具有良好随机性质的伪随机序列在流密码和通信领域中有着广泛的应用。本文构造出一类新的长为pqr的2阶广义分圆序列,并且计算其线性复杂度和极小多项式。结果显示这种序列具有高线性复杂度。     

计算有限域GF(q)上2pn-周期序列的k-错线性复杂度及其错误序列的算法

序列的k-错线性复杂度是序列线性复杂度稳定性的重要评价指标。在求得一个序列k-错线性复杂度的同时,也需要求出是哪些位置的改变导致了序列线性复杂度的下降。该文提出一个在GF(q)上计算2pn-周期序列s的k-错线性复杂度以及对应的错误序列e的算法,这里p和q是素数,且q是一个模p2的本原根。该文设计了一个追踪代价向量的trace函数,算法通过trace函数追踪最小的代价向量来求出对应的错误序列e,算法得到的序列e使得(s+e)的线性复杂度达到k-错线性复杂度的值。     

确定周期为2~n的二元序列的复杂度的一种快速算法

一个周期序列(S)的复杂度定义为产生(S)的线性反馈移位寄存器中最少的级数。本文阐述了一种确定周期为2~n的二元序列的复杂度的一种快速算法。此算法利用了基序列((?)=(?)(?)(?)…)的性质。     

自相关性和线性复杂度的关系

自相关性和线性复杂度是衡量序列伪随机性质的两个独立的指标.针对周期为2^<em>n的伪随机序列,本文首次指出了自相关性和线性复杂度之间存在的一个关系.该关系可应用于以下两个方面:(1)由序列的线性复杂度来估计/确定序列的自相关函数值;(2)通过线性复杂度来检验给定序列族的互相关性质.进一步的,针对一类周期为2^<em>n的伪随机序列,我们指出这类序列的自相关函数值和线性复杂度以及k-错线性复杂度存在着关系.     

二元互补序列的两个重要性质的研究

就互补序列的两个重要性质———频域互补性与保密性进行了深入研究与分析,提出了一种衡量互补序列结构复杂性的抽象概念———线性复杂度,且利用LFSR(Berlakamp-Massylinearfeedbackshiftregister)合成算法计算出了从长为4到长为32768的互补序列的线性复杂度,结果证明二元互补序列具有良好的非线性,适用于保密通信和扩频通信系统。     

Optimal biphase sequences with large linear complexity derived fromsequences over Z4

New families of biphase sequences of size 2^r-1+1, r being a positive integer, are derived from families of interleaved maximal-length sequences over Z₄ of period 2(2^r-1). These sequences have applications in code-division spread-spectrum multiuser communication systems. The families satisfy the Sidelnikov bound with equality on &thetas;_max, which denotes the maximum magnitude of the periodic cross-correlation and out-of-phase autocorrelation values. One of the families satisfies the Welch bound on &thetas;_max with equality. The linear complexity and the period of all sequences are equal to r(r+3)/2 and 2(2 ^r-1), respectively, with an exception of the single m-sequence which has linear complexity r and period 2^r-1. Sequence imbalance and correlation distributions are also computed     

Binary sequence sets with favorable correlations from differencesets and MDS codes

We propose new families of pseudorandom binary sequences based on Hadamard difference sets and MDS codes. We obtain, for p=4k-1 prime and t an integer with 1⩽t⩽(p-1)/2, a set of p^t binary sequences of period p² whose peak correlation is bounded by 1+2t(p+1). The sequences are balanced, have high linear complexity, and are easily generated     

Linear complexity over F/sub p/ and trace representation of Lempel-Cohn-Eastman sequences

In this article, the linear complexity over F/sub p/ of Lempel-Cohn-Eastman (1977) sequences of period p/sup m/-1 for an odd prime p is determined. For p=3,5, and 7, the exact closed-form expressions for the linear complexity over F/sub p/ of LCE sequences of period p/sup m/-1 are derived. Further, the trace representations for LCE sequences of period p/sup m/-1 for p=3 and 5 are found by computing the values of all Fourier coefficients in F/sub p/ for the sequences.     

Fast algorithms for determining the linear complexity of sequences over GF(p/sup m/) with period 2/sup t/n

We prove a result which reduces the computation of the linear complexity of a sequence over GF(p^m) (p is an odd prime) with period 2n (n is a positive integer such that there exists an element bisinGF(p^m), bⁿ=-1) to the computation of the linear complexities of two sequences with period n. By combining with some known algorithms such as the Berlekamp-Massey algorithm and the Games-Chan algorithm we can determine the linear complexity of any sequence over GF(p^m) with period 2^tn (such that 2 ^t|p^m-1 and gcd(n,p^m-1)=1) more efficiently     

Computing the error linear complexity spectrum of a binary sequence of period 2/sup n/

Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed. We present an algorithm which computes the error linear complexity for binary sequences of period /spl lscr/=2/sup n/ using O(/spl lscr/(log/spl lscr/)/sup 2/) bit operations. The algorithm generalizes both the Games-Chan (1983) and Stamp-Martin (1993) algorithms, which compute the linear complexity and the k-error linear complexity of a binary sequence of period /spl lscr/=2/sup n/, respectively. We also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of Reed-Muller codes.     

二元周期序列的4-错线性复杂度

 k-错线性复杂度是衡量序列伪随机性的重要指标之一.对线性复杂度第一下降点为4的以2的方幂为周期的二元序列,本文通过分析Games-Chan算法,给出了其4-错线性复杂度的所有可能取值形式以及具有给定4-错线性复杂度的序列的计数.更进一步,给出了其4-错线性复杂度的期望.结果表明,其4-错线性复杂度的期望与线性复杂度相差不大.     

Linear Complexity of Least Significant Bit of Polynomial Quotients

Binary sequences with large linear com-plexity have been found many applications in communi-cation systems. We determine the linear complexity of a family of p2-periodic binary sequences derived from poly-nomial quotients modulo an odd prime p. Results show that these sequences have high linear complexity, which means they can resist the linear attack method.