Characterization of 2n-periodic binary sequences with fixed 2-error or 3-error linear complexity
نویسنده
چکیده
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, Niederreiter, and Su [3] studied linear complexity and 1-error linear complexity of 2-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-periodic binary sequences in a more general setting using a combination of algebraic, combinatorial, and algorithmic methods. This approach allows us to characterize 2-periodic binary sequences with fixed 2-error or 3-error linear complexity. Using this characterization we obtain the counting function for the number of 2-periodic binary sequences with fixed k-error linear complexity for k = 2 and 3. Using the characterization we also show that there many 2-periodic binary sequences with high linear complexity and high 2-error or 3-error linear complexity.
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ورودعنوان ژورنال:
- Des. Codes Cryptography
دوره 53 شماره
صفحات -
تاریخ انتشار 2009