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Construction of Balanced Boolean Functions with High Nonlinearity on Even Number Variables

Xiao Guo-zhen

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Abstract

A technique for constructing highly nonlinear balanced functions is described.It is shown that a balanced Boolean function with high nonlinearity on even number of variables can be obtained via modifying Maiorana-McFarland type bent functions.A conjecture about the upper bound of the nonlinearity of a balanced Boolean function on even number variables is given.

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What this paper is about

A technique for constructing highly nonlinear balanced functions is described.It is shown that a balanced Boolean function with high nonlinearity on even number of variables can be obtained via modifying Maiorana-McFarland type bent functions.A conjecture about the upper bound of the nonlinearity of a balanced Boolean function on even number variables is given.

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Available abstract

A technique for constructing highly nonlinear balanced functions is described.It is shown that a balanced Boolean function with high nonlinearity on even number of variables can be obtained via modifying Maiorana-McFarland type bent functions.A conjecture about the upper bound of the nonlinearity of a balanced Boolean function on even number variables is given.

Key concepts: Boolean function, Mathematics, Parity function, Nonlinear system, Conjecture, Discrete mathematics, Upper and lower bounds, Function (biology)

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