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Computing the k-error joint linear complexity of binary periodic multisequences

The Journal of China Universities of Posts and Telecommunications 2013年第6期20卷 96-101页

作者： LI Fu-lin ZHU Shi-xin School of Mathematics Hefei University of Technology

complexity measures for multisequences over finite fields, such as the joint linear complexity and the k-error joint linear complexity, play an important role in cryptology. In this paper we study a fast algorithm, presented by Venkateswarlu A, to computer the k-error joint linear complexity of a binary periodic multisequence. In this paper, the aim is mainly to complement the theoretical derivation and proof of the existing algorithm. Moreover, our algorithm reduces computation.

关键词： cryptology multisequence algorithm joint linear complexity k-error joint linear complexity

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Improved results on the probabilistic theory of the joint linear complexity of multisequences

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Science China(Information Sciences) 2012年第1期55卷 165-170页

作者： NIEDERREITER Harald VIELHABER Michael Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Department of Mathematics University of Salzburg

We improve previous results on the asymptotic behavior and the expected value of the joint linear complexity of random multisequences over finite *** results are of interest for word-based stream ciphers in cryptology.

关键词： multisequences joint linear complexity stream ciphers

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joint linear complexity of arbitrary multisequences consisting of linear recurring sequences

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FINITE FIELDS AND THEIR APPLICATIONS 2009年第4期15卷 475-496页

作者： Fu, Fang-Wei Niederreiter, Harald Ozbudak, Ferruh Middle E Tech Univ Dept Math TR-06531 Ankara Turkey Middle E Tech Univ Inst Appl Math TR-06531 Ankara Turkey Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China Nankai Univ Key Lab Pure Math & Combinator Tianjin 300071 Peoples R China Natl Univ Singapore Dept Math Singapore 117543 Singapore

Let g(1),..., g(s) is an element of F-q[x] be arbitrary nonconstant monic polynomials. Let M(g(1),..., g(s)) denote the set of s-fold multisequences (sigma(1),...,sigma(s)) such that sigma(i) is a linear recurring sequence over F-q with characteristic polynomial g(i) for each 1 <= i <= s. Recently, we obtained in some special cases (for instance when gl,..., gs are pairwise coprime or when g(1) = ... = g(s)) the expectation and the variance of the joint linear complexity of random multisequences that are uniformly distributed over M(g(1),..., gs). However, the general case seems to be much more complicated. In this-paper we determine the expectation and the variance of the joint linear complexity of random multisequences that are uniformly distributed over M(g(1),..., g(s)) in the general case. (C) 2009 Elsevier Inc. All rights reserved.

关键词： joint linear complexity Multisequences linear recurring sequences

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joint linear complexity of multisequences consisting of linear recurring sequences

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2009年第1期1卷 3-29页

作者： Fu, Fang-Wei Niederreiter, Harald Ozbudak, Ferruh Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China Nankai Univ Key Lab Pure Math & Combinator Tianjin 300071 Peoples R China Natl Univ Singapore Dept Math Singapore 117543 Singapore Nanyang Technol Univ Sch Phys & Math Sci Div Math Sci Singapore 637616 Singapore Middle E Tech Univ Dept Math TR-06531 Ankara Turkey

The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. In this paper, we study the joint linear complexity of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random multisequences consisting of linear recurring sequences are determined. These results extend the corresponding results on the expectation and variance of the joint linear complexity of random periodic multisequences. Then we enumerate the multisequences consisting of linear recurring sequences with fixed joint linear complexity. A general formula for the appropriate counting function is derived. Some convenient closed-form expressions for the counting function are determined in special cases. Furthermore, we derive tight upper and lower bounds on the counting function in general. Some interesting relationships among the counting functions of certain cases are established. The generating polynomial for the distribution of joint linear complexities is determined. The proofs use new methods that enable us to obtain results of great generality.

关键词： joint linear complexity Multisequences linear recurring sequences Counting function Generating polynomial

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The asymptotic behavior of the joint linear complexity profile of multisequences

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MONATSHEFTE FUR MATHEMATIK 2007年第2期150卷 141-155页

作者： Niederreiter, Harald Wang, Ping Natl Univ Singapore Singapore 117548 Singapore

We prove a conjecture on the asymptotic behavior of the joint linear complexity profile of random multisequences over a finite field. This conjecture was previously shown only in the special cases of single sequences and pairs of sequences. We also establish an asymptotic formula for the expected value of the nth joint linear complexity of random multisequences over a finite field. Some more precise results are shown for triples of sequences.

关键词： multisequences joint linear complexity joint linear complexity profile

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A lattice-based minimal partial realization algorithm for matrix sequences of varying length

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2011年第1期3卷 29-42页

作者： Wang, Li-Ping Tsinghua Univ Inst Adv Study Beijing 100084 Peoples R China

In this paper we first extend a minimal partial realization algorithm from vector sequences to matrix sequences of equal length by means of a lattice basis reduction algorithm over polynomial rings. We also give all minimal partial realizations for such matrix sequences and a sufficient and necessary condition for the uniqueness issue. Then we improve the above algorithm to solve the minimal partial realization problem for matrix sequences of varying length.

关键词： Minimal partial realization linear feedback register synthesis linear complexity joint linear complexity linear system theory

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Improved results on periodic multisequences with large error linear complexity

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FINITE FIELDS AND THEIR APPLICATIONS 2010年第6期16卷 463-476页

作者： Venkateswarlu, Ayineedi Niederreiter, Harald CR Rao AIMSCS Hyderabad 500046 Andhra Pradesh India Austrian Acad Sci Johann Radon Inst Computat & Appl Math A-4040 Linz Austria

For multisequences there are various possibilities of defining analogs of the k-error linear complexity of single sequences. We consider the k-error joint linear complexity, the k-error F(q)-linear complexity, and the (k) over right arrow -error joint linear complexity. Improving the existing results, several results on the existence of, and lower bounds on the number of, multisequences with large error linear complexity are obtained. Improved lower bounds are shown for the case of prime-power periodic multisequences. An asymptotic analysis for the prime-power period case is carried out. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Multisequences joint linear complexity Error linear complexity Word-based stream ciphers

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Enumeration results on the joint linear complexity of multisequences

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FINITE FIELDS AND THEIR APPLICATIONS 2006年第4期12卷 613-637页

作者： Wang, Li-Ping Niederreiter, Harald Natl Univ Singapore Temasek Labs Singapore 117508 Singapore Natl Univ Singapore Dept Math Singapore 117543 Singapore

Recent developments in stream ciphers point towards an interest in word-based or vectorized stream ciphers. Such stream ciphers suggest the study of the joint linear complexity of multisequences. In this paper, using the first author's multisequence linear feedback shift-register synthesis algorithm based on a lattice basis reduction algorithm in function fields, we present a method to determine the value of N-n((m)) (L), the number of in-fold multisequences of length n over a finite field F-q with nth joint linear complexity L. Furthermore, a closed-form expression for N-n((m)) (L) and formulas for the expected value of the joint linear complexity and its variance are given when m = 2. (c) 2005 Elsevier Inc. All rights reserved.

关键词： multisequence shift-register synthesis lattice basis reduction algorithm joint linear complexity

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The probabilistic theory of the joint linear complexity of multisequences

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4th International Conference on Sequences and Their Applications (SETA 2006)

作者： Niederreiter, Harald Natl Univ Singapore Dept Math Singapore 117543 Singapore

ISBN: (纸本)3540445234

The joint linear complexity and the joint linear complexity profile are standard complexity measures for multisequences in the context of word-based stream ciphers. The last few years have seen major advances in the theory of these complexity measures, especially with regard to probabilistic results on the behavior of random (periodic and nonperiodic) multisequences. This paper presents a survey of these developments as well as the necessary background for the results.

关键词： word-based stream ciphers multisequences linear complexity joint linear complexity joint linear complexity profile

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linear complexity over F_q and over F_qm for linear recurring sequences

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FINITE FIELDS AND THEIR APPLICATIONS 2009年第1期15卷 110-124页

作者： Meidl, Wilfried Ozbudak, Ferruh Middle E Tech Univ Dept Math TR-06531 Ankara Turkey Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Turkey

Since the F-q-linear spaces F-q(m) and F-qm are isomorphic, an m-fold multisequence S over the finite field F-q with a given characteristic polynomial f is an element of F-q[x], can be identified with a single sequence S over F-qm with characteristic polynomial f. The linear complexity of S, which will be called the generalized joint linear complexity of S, can be significantly smaller than the conventional joint linear complexity of S. We determine the expected value and the variance of the generalized joint linear complexity of a random m-fold multisequence S with given minimal polynomial. The result on the expected value generalizes a previous result oil periodic m-fold multisequences. Moreover we determine the expected drop of linear complexity of a random m-fold multisequence with given characteristic polynomial f, when one switches from conventional joint linear complexity to generalized joint linear complexity. (C) 2008 Elsevier Inc. All rights reserved.

关键词： joint linear complexity Generalized joint linear complexity Multisequences linear recurring sequences

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