共查询到20条相似文献,搜索用时 46 毫秒
1.
We determined the linear complexity of a family of p2 -periodic binary threshold sequences and a family of p2 -periodic binary threshold sequences constructed using the Legendre symbol, both of which are derived from Fermat quotients modulo an odd prime p . If 2 is a primitive element modulo p2 , the linear complexity equals to p2 -p or p2-1, which is very close to the period and it is large enough for cryptographic purpose. 相似文献
2.
3.
Multiresolution analysis via decomposition into wavelets has been established as an important transform technique in signal processing. A wealth of results is available on this subject, and particularly, the framework has been extended to treat finite length sequences of size 2n (for positive integers n) over finite fields. The present paper extends this idea further to provide a framework for dealing with arbitrary finite data lengths. This generalization is largely motivated in part by the need for such transforms for building error correcting codes in the wavelet transform domain. Here we extend the previous two-band formulation of the transform to treat a p-band case in general (i.e. for data length pn), where p is a prime number, and we also give a general result for developing transforms over composite-length sequences. Potential applications and computational complexity issues are discussed as well. 相似文献
4.
Based on element statistics in a matrix,a new efficient computing method for computing the k-error linear complexity of q-ary sequence of period p2was proposed,where p,q were odd primes and q modulo p2was primitive.A general result and a concrete proof were showed.To verify the correctness of the result,two kinds of q-ary sequence of period p2were illustrated.Because the new method does not need iterative calculation and when it is implemented by program and compared with existing algorithms,the results show that the proposed new algorithm is significantly more efficient in calculating k-error linear complexity of q-ary sequence of period p2. 相似文献
5.
Paterson K.G. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1998,44(1):172-180
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 pt 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 相似文献
6.
7.
pmqn周期q元序列线性复杂度与k错复杂度的关系 总被引:3,自引:0,他引:3
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. 相似文献
8.
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. 相似文献
9.
Based on the Ding-generalized cyclotomy,a new class of generalized cyclotomic sequences with length pm over the finite field of power of odd prime order was constructed,and the sequence was balanced.The linear complexity of the sequences was determined using the relationship between h and p and the theory of polynomial over finite field.It is shown that the sequence has good linear complexity,and it can resist attacks from the application of the Berlekamp-Massey algorithm. 相似文献
10.
11.
12.
Meidl W. Niederreiter H. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2002,48(11):2817-2825
Rueppel (1986) conjectured that periodic binary sequences have expected linear complexity close to the period length N. In this paper, we determine the expected value of the linear complexity of N-periodic sequences explicitly and confirm Rueppel's conjecture for arbitrary finite fields. Cryptographically strong sequences should not only have a large linear complexity, but also the change of a few terms should not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity of N-periodic sequences. We present a method to establish a lower bound on the expected k-error linear complexity of N-periodic sequences based on the knowledge of the counting function 𝒩N,0(c), i.e., the number of N-periodic sequences with given linear complexity c. For some cases, we give explicit formulas for that lower bound and we also determine 𝒩N,0(c) 相似文献
13.
14.
Etzion T. Kalouptsidis N. Kolokotronis N. Limniotis K. Paterson K.G. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2009,55(10):4681-4686
This paper studies the error linear complexity spectrum of binary sequences with period 2n. A precise categorization of those sequences having two distinct critical points in their spectra, as well as an enumeration of these sequences, is given. An upper bound on the maximum number of distinct critical points that the spectrum of a sequence can have is proved, and a construction which yields a lower bound on this number is given. In the process simpler proofs of some known results on the linear complexity and k-error linear complexity of sequences with period 2n are provided. 相似文献
15.
在序列密码中,输出序列的线性复杂度是一种非常重要的特征性质,因为已知的Berlekamp-massey算法对滚动密钥生成器是一种有效而且威胁极大的攻击手段,所以在设计滚动密钥序列生成器时必须能产生具有极大线性复杂度的密钥序列,虽然这只是个必要非充分的条件。利用m-序列的良好特性与代数上的逆矩阵理论提出了一种用本原多项式生成的线性反馈移位寄存器序列置换生成的具有良好性质的伪随机序列。新生成的二元序列不但保持了m-序列的良好特性,同时还极大提高了序列的线性复杂度,在一定范围内具有良好实用价值。 相似文献
16.
17.
THE 2-ERROR LINEAR COMPLEXITY OF 2^n-PERIODIC BINARY SEQUENCES WITH LINEAR COMPLEXITY 2^n -1 总被引:9,自引:0,他引:9
Zhu Fengxiang Qi Wenfeng 《电子科学学刊(英文版)》2007,24(3):390-395
Linear complexity and k-error linear complexity of the stream cipher are two important standards to scale the randomicity of keystreams. For the 2n -periodicperiodic binary sequence with linear complexity 2n 1and k = 2,3,the number of sequences with given k-error linear complexity and the expected k-error linear complexity are provided. Moreover,the proportion of the sequences whose k-error linear complexity is bigger than the expected value is analyzed. 相似文献
18.
Computing the error linear complexity spectrum of a binary sequence of period 2/sup n/ 总被引:1,自引:0,他引:1
Lauder A.G.B. Paterson K.G. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2003,49(1):273-280
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. 相似文献
19.