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Optimizing Implementations of Boolean Functions



Meltem Sonmez Turan


Symmetric cryptography primitives are constructed by iterative applications of linear and nonlinear layers. Constructing efficient circuits for these layers, even for the linear one, is challenging. In 1997, Paar proposed a heuristic to minimize the number of XORs (modulo 2 addition) necessary to implement linear layers. In this study, we slightly modify Paar's heuristics to find implementations for nonlinear Boolean functions, in particular to homogeneous Boolean functions. Additionally, we show how this heuristic can be used to construct circuits for generic Boolean functions with small number of AND gates, by exploiting affine equivalence relations


Boolean functions, circuit complexity, implementation


Sonmez Turan, M. (2024), Optimizing Implementations of Boolean Functions, [online], (Accessed July 21, 2024)


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Created January 31, 2024, Updated February 1, 2024