Linear Complexity Measures of Binary Multisequences

The joint linear complexity and k error joint linear complexity of an m fold 2 periodic multisequence can be efficiently computed using Modified Games Chan algorithm and Extended Stamp Martin Algorithm respectively. In this paper we derived an algorithm for finding the joint linear complexity of n 2 . 3 periodic binary multisequence with the help of Modified Games Chan algorithm. Here we derived the minimum value of k for which k-error joint linear complexity is strictly less than the joint linear complexity of binary m fold multisequences of period 2 and an algorithm which, given a constant c and an m fold 2 periodic binary multisequence S, computes the minimum number k of errors and the associated error multisequence needed over a period of S for bringing the joint linear complexity of S below c . General Terms Cryptography, Applied Number theory, Word Based Stream Ciphers, Linear Complexity of sequences, Joint Linear Complexity of sequences

[1]  Ana Salagean.  On the computation of the linear complexity and the k-error linear complexity of binary sequences with period a power of two , 2005, IEEE Transactions on Information Theory.

[2]  Harald Niederreiter.  The Probabilistic Theory of the Joint Linear Complexity of Multisequences , 2006, SETA.

[3]  Kaoru Kurosawa,et al.  A Relationship Between Linear Complexity and-Error Linear Complexity , 2022 .

[4]  Takayasu Kaida.  On the Generalized Lauder-Paterson Algorithm and Profiles of the k-Error Linear Complexity for Exponent Periodic Sequences , 2004, SETA.

[5]  Satoshi Uehara,et al.  A New Algorithm for the k -Error Linear Complexity of Sequences over GF(p m) with Period p n , 1998, SETA.

[6]  Mark Stamp,et al.  An algorithm for the k-error linear complexity of binary sequences with period 2n , 1993, IEEE Trans. Inf. Theory.

[7]  Cai Mian.  A fast algorithm for determining the linear complexity of a pseudo-random sequence with a period n2~v , 2001 .

[8]  Cunsheng Ding,et al.  The Stability Theory of Stream Ciphers , 1991, Lecture Notes in Computer Science.

[9]  Ayineedi Venkateswarlu,et al.  Remarks on the k-error linear complexity of pn-periodic sequences , 2007, Des. Codes Cryptogr..

[10]  Wilfried Meidl,et al.  Discrete Fourier Transform, Joint Linear Complexity and Generalized Joint Linear Complexity of Multisequences , 2004, SETA.

[11]  Ayineedi Venkateswarlu,et al.  Error linear complexity measures for multisequences , 2007, J. Complex..

[13]  戒田 高康.  On algorithms for the k-error linear complexity of sequences over GF(p[m]) with period p[n] , 1999 .

[15]  Kenneth G. Paterson,et al.  Computing the error linear complexity spectrum of a binary sequence of period 2n , 2003, IEEE Trans. Inf. Theory.

[16]  M. Sethumadhavan,et al.  Error Linear Complexity Measures of Binary Multisequences , 2011, Cyber Security, Cyber Crime and Cyber Forensics.

[17]  Kaoru Kurosawa,et al.  A relationship between linear complexity and kapa-error linear complexity , 2000, IEEE Trans. Inf. Theory.

[18]  Wilfried Meidl,et al.  Reducing the calculation of the linear complexity of u2v-periodic binary sequences to Games–Chan algorithm , 2008, Des. Codes Cryptogr..