Boolean Functions Derived from Pseudorandom Binary Sequences
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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- 6.Brandstätter, N., Winterhof, A.: Nonlinearity of binary sequences with small autocorrelation. In: Proceedings of the Second International Workshop on Sequence Design and its Applications in Communications (IWSDA 2005), pp. 44–47 (2005)Google Scholar
- 7.Carlet, C.: Boolean functions for cryptography and error correcting codes. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, pp. 257–397. Cambridge University Press (2010)Google Scholar
- 8.Cusick, T.W., Stănică, P.: Cryptographic Boolean functions and applications. Elsevier/Academic Press, Amsterdam (2009)Google Scholar
- 10.Lange, T., Winterhof, A.: Arne Interpolation of the discrete logarithm in F q by Boolean functions and by polynomials in several variables modulo a divisor of q − 1. In: International Workshop on Coding and Cryptography (WCC 2001), Paris. Discrete Appl. Math., vol. 128, pp. 193–206 (2003)Google Scholar
- 15.Shparlinski, I.E.: Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness. Birkhäuser (2003)Google Scholar