一类可控序列的构造和分析

本文通过利用GF(2m)(m2)上L级m序列来控制其上的L级m序列的方法,构造出了一类具有较高线性复杂度的周期序列。这类序列的线性复杂度的下界为L((L+1)mLm)。     

一类可控序列线性复杂度的估计

本文运用指数集的概念，得到了任意有限域ＧＦ（ｑ）（ｑ＝ｐｍ）上Ｌ级ｍ－序列的多项式序列的线性复杂度，并导出了一类可控序列线性复杂度的上界，这个上界很可能是紧上界。当域特征ｐ＝２时，这类序列线性复杂度的上界为Ｌ＋１２［（Ｌ＋１）ｍ－１］，下界为［（Ｌ＋１）ｍ－１］。     

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${\rm{GF}}(3)$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。     

序列k-错线性复杂度算法

本文给出了一个测量流密码序列稳定性的重要指标Ｋ－错线性复杂度的算法,即求ＧＦ（ｑ）上（ｑ＝ｐ＾ｍ,ｐ：素数）周期为Ｎ＝ｐ＾ｎ序列的Ｋ－错线性复杂度的快速算法。在这里对广义ＧａｍｅｓＣｈａｎ算法－ＧＦ（ｑ）上ｐ＾ｎ序列线性复杂度算法进行了简化,并给出了ＧＦ（ｑ）上ｐ＾ｎ序列Ｋ－错线性复杂度算法及其证明。     

GF(p)上钟控序列

本文利用有限域GF(p)(p2为素数,1为正整数)上二次特征建立了GF(p)上一类互钟控序列,即LSRg[d0,d1,d2]-互钟控序列。讨论了当用作移位时钟控制的前馈函数g(x1,x2,,xn)为二次型时,LSRg[d0,d1,d2]-互钟控序列的周期和线性复杂度的特点。     

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     

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     

关于求周期序列k错线性复杂度的Stamp-Martin算法

在k错线性复杂度的实际应用中,误差向量的计算是非常重要的。因此改进了Stamp-Martin算法中cost向量的结构,从而使该算法求周期为2n的二元序列k错线性复杂度更加简洁且容易理解,同时给出了求相应误差向量的算法,即在该误差向量下,能够实现最小的k错线性复杂度。     

确定周期序列线性复杂度的快速算法

本文介绍了确定周期序列的线性复杂度的两个快速算法。一个适应于GF（q)上周期为p^n的序列,另一个适应于GF（p^m)上周期为p^n的序列,这里p是奇素数,q是素数并且是模p^2的本原根。     

Fast transform for decoding both errors and erasures of Reed-Solomon codes over GF(2/sup m/) for 8/spl les/m/spl les/10

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2/sup m/-1 points over GF(2/sup m/), where 8/spl les/m/spl les/10. Using these transforms, together with the Berlekamp-Massey algorithm, the complexity of the transform-domain decoder for correcting both errors and erasures of the Reed-Solomon codes of block length 2/sup m/-1 over GF(2/sup m/) for 8/spl les/m/spl les/10 is reduced substantially from the previous time-domain decoder. A computer simulation verifies these new results.     

On the linear complexity of functions of periodic GF(q)sequences

It is proved that the product of arbitrary periodic GF(q) sequences attains maximum linear complexity if their periods are pairwise coprime. The necessary and sufficient conditions are derived for maximum linear complexity of the product of two periodic GF(q ) sequences with irreducible minimal characteristic polynomials. For a linear combination of products of arbitrary periodic GF(q) sequences, it is shown that maximum linear complexity is achieved if their periods are pairwise coprime and the polynomial x -1 does not divide any of their minimal characteristic polynomials; assuming only that their periods are pairwise coprime, the author establishes a lower bound on the linear complexity which is of the same order of magnitude as maximum linear complexity. Boolean functions are derived that are optimal with respect to the maximum linear complexity. Possible applications of the results in the design of sequence generators are discussed     

GF(q)上周期序列的线性复杂度分析

给出了有限域上周期序列在改变几个比特的情况下,其极小多项式及线性复杂度的计算公式,并对其中只改变了一个比特的序列进行了深入的分析,最后得出m序列及周期为2~n序列在改变任意一个比特后的线性复杂度。     

pmqn周期q元序列线性复杂度与k错复杂度的关系

研究了q元周期序列线性复杂度和k错复杂度之间的关系,给出了k错复杂度严格小于线性复杂度的一个充要条件.当周期为N=pqn时,给出了使得LC(S+E)＜LC(S)成立的错误多项式EN(x)的确切表达式,以及使得LCk(S)＜LC(S)成立的最小的k值,即minerror(S)的值,结果表明minerror(S)与线性复杂度的重量密切相关;当周期为N=pmqn时,给出了使得LC(S+E)＜LC(S)成立的用错误多项式EN(x)表达的一个充分条件.这里P为奇素数,q是素数且是一个模p2的本原根.     

Irreducible Polynomials Which Divide Trinomials Over GF (2)

The simplest linear shift registers to generate binary sequences involve only two taps, which corresponds to a trinomial over GF(2). It is therefore of interest to know which irreducible polynomials f(x) divide trinomials over GF(2), since the output sequences corresponding to f(x) can be obtained from a two-tap linear feedback shift register (with a suitable initial state) if and only if f(x) divides some trinomial t(x)=x^m+x^a+1 over GF(2). In this paper, we develop the theory of which irreducible polynomials do, or do not, divide trinomials over GF(2). Then some related problems such as Artin's conjecture about primitive roots, and the conjectures of Blake, Gao, and Lambert, as well as of Tromp, Zhang, and Zhao are discussed     

Sets of complementary sequences

A set of complementary sequences is a set of sequences such that, for each nonzero offset, the out-of-phase aperiodic autocorrelations of all the sequences sum to zero. It is shown that the sequences from any coset of an (N, m) nondegenerate minimal linear cyclic code over GF(p) form a set of complex-valued complementary sequences of length N.     

一类平衡前馈序列的构造与性质

该文采用m序列选控传统前馈密码系统的方法,在继承了Bent函数谱值均匀优点的同时,使得产生的序列具有理想的平衡性、大的周期和高的线性复杂度,且能抵抗现有的线性逼近攻击和相关攻击。     

一种可重构的快速有限域乘法结构

在一种改进的串行乘法器的基础上,提出了一种可重构的快速有限域GF (2m )(1＜mM)乘法器结构。利用一组配置信号和逻辑电路来改变有限域的度m,使得乘法器可以重构和编程。同时采用门控时钟减小电路功耗。该乘法器结构具有可重构性、高灵活性和低电路复杂性等特点。与传统的移位乘法器相比,它将乘法器速度提高一倍。这种乘法器适合于变有限域,低硬件复杂度的高性能加密算法的VLSI设计。     

Maximizing Burst Erasure-Correction Capability of MDS Codes

In general, an (n,k) maximum distance separable (MDS) code over GF(p^m) can not correct all burst erasures of length (n-k)m over GF(p). In this letter, we constructively show that such a linear MDS code over GF(p^m) can be modified to correct all burst erasures of length up to (n-k)m over GF(p), while maintaining its MDS property over GF(p^m)     

Improved algorithm for division over GF(2/sup m/)

An improved algorithm for division over GF(2/sup m/) is proposed. It is based on a look-ahead procedure that allows division over GF(2/sup m/) to be performed in any number of clock cycles up to 2/sup m/-1. The hardware complexity of the divider depends on the level of look-ahead chosen and hence the speed of operation required. An example using this divider in solving the key equation for single-error correcting Reed-Solomon codes is also considered.<>     

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.