Analysis and design of stream ciphers
Analysis and design of stream ciphers
Linear complexity, k-error linear complexity, and the discrete Fourier transform
Journal of Complexity
Remarks on the k-error linear complexity of pn-periodic sequences
Designs, Codes and Cryptography
The characterization of 2n-periodic binary sequences with fixed 1-error linear complexity
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
A relationship between linear complexity and k-error linear complexity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On the stability of 2n-periodic binary sequences
IEEE Transactions on Information Theory
Counting Functions and Expected Values for the k-Error Linear Complexity
Finite Fields and Their Applications
A counterexample concerning the 3-error linear complexity of 2n-periodic binary sequences
Designs, Codes and Cryptography
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The linear complexity of sequences is an important measure of the cryptographic strength of key streams used in stream ciphers. The instability of linear complexity caused by changing a few symbols of sequences can be measured using k-error linear complexity. In their SETA 2006 paper, Fu et al. (SETA, pp. 88---103, 2006) studied the linear complexity and the 1-error linear complexity of 2 n -periodic binary sequences to characterize such sequences with fixed 1-error linear complexity. In this paper we study the linear complexity and the k-error linear complexity of 2 n -periodic binary sequences in a more general setting using a combination of algebraic, combinatorial, and algorithmic methods. This approach allows us to characterize 2 n -periodic binary sequences with fixed 2- or 3-error linear complexity. Using this characterization we obtain the counting function for the number of 2 n -periodic binary sequences with fixed k-error linear complexity for k = 2 and 3.