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In FSE 2005, transparency order was proposed as a parameter for the robustness of S-boxes to Differential Power Analysis (DPA): lower transparency order implying more resistance. However most cryptographically strong Boolean functions have been found to have high transparency order. In this paper, the authors characterize transparency order for various classes of Boolean functions by computing the upper and lower bounds of transparency order for both even and odd numbers of variables. The transparency order is defined in terms of diffusion properties of the structures of Boolean functions namely the number of bit flips in the output of the functions corresponding to the number of bit flips at the input of the function.
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