Abstract
We use combinatorial methods and permutation groups to classify homogeneous boolean functions. The property of symmetry of a boolean function limits the size of the function’s class. We exhaustively searched for all boolean functions on V 6. We found two interesting classes of degree 3 homogeneous boolean functions: the first class is degree 3 homogeneous bent boolean functions; and the second is degree 3 homogeneous balanced boolean functions. Both the bent and balanced functions discovered have nice algebraic and combinatorial structures. We note that some structures can be extended to a large boolean space. The application of homogeneous boolean functions for fast implementation on parallel architectures is mooted.
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Qu, C., Seberry, J., Pieprzyk, J. (1999). On the Symmetric Property of Homogeneous 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_3
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DOI: https://doi.org/10.1007/3-540-48970-3_3
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