Welcome to the resource topic for 2007/370
Title:
FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY
Authors: Claude Carlet, Xiangyong Zeng, Chunlei Li, Lei Hu
Abstract:Thanks to a method proposed by Carlet, several classes of balanced Boolean functions with optimum algebraic immunity are obtained. By choosing suitable parameters, for even n\geq 8, the balanced n-variable functions can have nonlinearity 2^{n-1}-{n-1\choose\frac{n}{2}-1}+2{n-2\choose\frac{n}{2}-2}/(n-2), and for odd n, the functions can have nonlinearity 2^{n-1}-{n-1\choose\frac{n-1}{2}}+\Delta(n), where the function \Delta(n) is describled in Theorem 4.4. The algebraic degree of some constructed functions is also discussed.
ePrint: https://eprint.iacr.org/2007/370
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