Abstract
We introduce new ideas to tackle the enumeration problem for correlation immune functions and provide the best known lower and upper bounds. The lower bound is obtained from sufficient conditions, which are essentially construction procedures for correlation immune functions. We obtain improved necessary conditions and use these to derive better upper bounds. Further, bounds are obtained for the set of functions which satisfy the four conditions of correlation immunity, balancedness, nondegeneracy and nonaffinity. Our work clearly highlights the difficulty of exactly enumerating the set of correlation immune functions.
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Maitra, S., Sarkar, P. (1999). Enumeration of Correlation Immune Boolean Functions. In: Pieprzyk, J., Safavi-Naini, R., Seberry, J. (eds) Information Security and Privacy. ACISP 1999. Lecture Notes in Computer Science, vol 1587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48970-3_2
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DOI: https://doi.org/10.1007/3-540-48970-3_2
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