Properties of associated Boolean functions of quadratic APN functions A. A. Gorodilova
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ArticleSubject(s): булевы функции | дифференциальная эквивалентность | APN-функцииGenre/Form: статьи в журналах Online resources: Click here to access online
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Прикладная дискретная математика. Приложение № 12. С. 77-79Abstract: For a function F : Fn Fn, it is defined the associated Boolean function yF in 2n variables as follows: yF(a, b) = 1 if a = 0 and equation F(x) + F(x + a) = b has solutions. A vectorial Boolean function F from F2n to F2n is called almost perfect nonlinear (APN) if equation F(x) + F(x + a) = b has at most 2 solutions for all vectors a, b 6 F2n, where a is nonzero. In case when F is a quadratic APN function its associated function has the form yF(a, b) = Фр(a) • b + ^F(a) + 1 for appropriate functions Фр : Fn Fn and : Fn F2. We study properties of functions Фр and ^F, in particular their degrees.
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For a function F : Fn Fn, it is defined the associated Boolean function yF in 2n variables as follows: yF(a, b) = 1 if a = 0 and equation F(x) + F(x + a) = b has solutions. A vectorial Boolean function F from F2n to F2n is called almost perfect nonlinear (APN) if equation F(x) + F(x + a) = b has at most 2 solutions for all vectors a, b 6 F2n, where a is nonzero. In case when F is a quadratic APN function its associated function has the form yF(a, b) = Фр(a) • b + ^F(a) + 1 for appropriate functions Фр : Fn Fn and : Fn F2. We study properties of functions Фр and ^F, in particular their degrees.
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