Abstract
The nonlinearity of a Boolean function is the minimum number of substitutions required in its truth table to change it into an affine function. Hence, in a cryptographic context, it is used to measure the strength of cryptosystems when facing linear attacks. As for the nonlinearity of order r of a Boolean function, which equals the least number of substitutions needed to change it into a function of degree at most r, it is examined when dealing with low-degree approximation attacks [7,14].
Many studies aimed at the distribution of Boolean functions according to the r-th order nonlinearity. Asymptotically, a lower bound is established in the higher order cases for almost all boolean functions, whereas a concentration point is shown in the (first order) nonlinearity case. We present a more accurate distribution by proving a concentration point in the second-order nonlinearity case.
This work has been done with the support of the Région Provence-Alpes-Côte d’Azur.
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Dib, S. (2010). Distribution of Boolean Functions According to the Second-Order Nonlinearity. In: Hasan, M.A., Helleseth, T. (eds) Arithmetic of Finite Fields. WAIFI 2010. Lecture Notes in Computer Science, vol 6087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13797-6_7
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DOI: https://doi.org/10.1007/978-3-642-13797-6_7
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