Приводится краткий обзор основных результатов в области бент-функций. Рассматриваются их теоретические и практические приложения. Ключевые слова: булева функция, АНФ, преобразование Уолша Адамара, нелинейность, бент-функция. 1 Исследование выполнено при финансовой поддержке интеграционного проекта СО РАН № 35 Древовидный каталог математических интернет-ресурсов mathtree.ru , РФФИ (проекты 07-01-00248, 08-01-00671, 09-01-00528-а) и Фонда содействия отечественной науке.
Threshold implementation (TI) is a masking method that provides security against first-order DPA with minimal assumptions on the hardware. It is based on multi-party computation and secret sharing. In this paper, we provide an efficient technique to find TIs for all 3 and 4-bit permutations which also covers the set of 3 × 3 and 4 × 4 invertible S-boxes. We also discuss alternative methods to construct shared functions by changing the number of variables or shares. Moreover, we further consider the TI of 5-bit almost bent and 6-bit almost perfect nonlinear permutations. Finally, we compare the areas of these various TIs.
Bent functions (Boolean functions with extreme nonlinearity properties) are actively studied for their numerous applications in cryptography, coding theory, and other fields. New statements of problems lead to a large number of generalizations of the bent functions many of which remain little known to the experts in Boolean functions. In this article, we offer a systematic survey of them.
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