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Discrete Functions
On connection between affine splitting of a Boolean function and its algebraic, combinatorial and cryptographic properties
A. A. Babueva Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Moscow
Abstract:
In this paper, the following results are obtained: 1) for an affine splitting of a Boolean function – an upper bound of algebraic degree; 2) for a dual bent function – some sufficient conditions to be affine splitting, and 3) for any Boolean function with a non-trivial subspace of the linear structures – an upper bound of nonlinearity. Besides, the following assertions are proved: 1) affine splitting is an invariant of complete affine group; 2) if a bent function is normal or weakly normal, then its dual function is normal or weakly normal respectively; 3) the coefficients of the incomplete Walsh–Hadamard transformation of a bent function and of its dual function are the same for zero values of variables; 4) a relation connecting the squares of the Walsh–Hadamard coefficients of a function over cosets of a subspace with the squares of the coefficients of the incomplete Walsh–Hadamard transformation of this function.
Keywords:
Boolean functions, bent functions, affine splitting.
Citation:
A. A. Babueva, “On connection between affine splitting of a Boolean function and its algebraic, combinatorial and cryptographic properties”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 33–34
Linking options:
https://www.mathnet.ru/eng/pdma313 https://www.mathnet.ru/eng/pdma/y2017/i10/p33
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