Duality of Boolean functions and its cryptographic significance
Recent advances in interpolation and high order differential cryptanalysis have highlighted the cryptographic significance of Boolean functions with a high algebraic degree. However, compared with other nonlinearity criteria such propagation, resiliency, differential and linear characteristics, apparently little progress has been made in relation to algebraic degree in the context of cryptography. The aim of this work is to research into relationships between algebraic degree and other nonlinearity criteria. Making use of duality properties of Boolean functions, we have obtained several results that are related to lower bounds on nonlinearity, as well as on the number of terms, of Boolean functions. We hope that these results would stimulate the research community's interest in further exploring this important area.
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