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Direct construction of balanced semi-bent functions and 1-resilient semi-bent functions of odd variables with optimal algebraic degree
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Semi-bent functions possess nearly optimal nonlinearity, making them important in symmetric cryptography and CDMA communication systems. In this paper, we present new constructions of semi-bent functions with optimal or near-optimal algebraic degrees, derived from Boolean functions with an odd number of variables. We also outline the conditions for their balancedness. One of the constructions derived 1-resilient semi-bent functions with maximal algebraic degree. Notably, our construction leads to the first family of 1-resilient semi-bent functions with maximal algebraic degree.
Title: Direct construction of balanced semi-bent functions and 1-resilient semi-bent functions of odd variables with optimal algebraic degree
Description:
Semi-bent functions possess nearly optimal nonlinearity, making them important in symmetric cryptography and CDMA communication systems.
In this paper, we present new constructions of semi-bent functions with optimal or near-optimal algebraic degrees, derived from Boolean functions with an odd number of variables.
We also outline the conditions for their balancedness.
One of the constructions derived 1-resilient semi-bent functions with maximal algebraic degree.
Notably, our construction leads to the first family of 1-resilient semi-bent functions with maximal algebraic degree.
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