Boolean Functions Derived from Pseudorandom Binary Sequences
- Cite this paper as:
- Pirsic G., Winterhof A. (2012) Boolean Functions Derived from Pseudorandom Binary Sequences. In: Helleseth T., Jedwab J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg
We study measures used to assess Boolean functions, where the functions are understood to be derived from binary sequences. We prove relations between two complexity measures for these Boolean functions and the correlation measure of order k of the corresponding sequence. More precisely, we study sparsity and combinatorial complexity of the Boolean function. Moreover, for a sequence with ’typical’ values of the correlation measure of order k we apply these relations to derive bounds on the complexity measures for the corresponding Boolean function. Finally, we apply our results to Sidelnikov sequences for which nice upper bounds on the correlation measure are known.
KeywordsBoolean functions sparsity correlation measure combinatorial complexity cryptography nonlinearity pseudorandomness
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