Vectorial boolean functions on distance one from apn functions
The metric properties of the class of vectorial Boolean functions are studied. A vectorial Boolean function F in n variables is called a differential 8-uniform function if the equation F(x) ф F(x ф а) = b has at most 8 solutions for any vectors а, b, where а = 0. In particular, if it is true for 8 = 2, then the function f is called APN. The distance between vectorial Boolean functions F and G is the cardinality of the set {x £ Zn : F(x) = G(x)}. It is proved that there are only differential 4-uniform functions which are on the distance 1 from an APN function.
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Keywords
векторная булева функция, дифференциально 8-равномерная функция, APN-функция, vectorial Boolean function, differentially 8-uniform function, APN functionAuthors
| Name | Organization | |
| Shushuev G.I. | g.shushuev@gmail.com |
References
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