Welcome to the resource topic for 2012/186
Title:
Third-order nonlinearities of some biquadratic monomial Boolean functions
Authors: Brajesh Kumar Singh
Abstract:In this paper, we estimate the lower bounds on third-order nonlinearities of some biquadratic monomial Boolean functions of the form Tr_1^n(\lambda x^d) for all x \in \mathbb F_{2^n}, where \lambda \in \BBF_{2^n}^{*}, \begin{itemize} \item [{(1)}]d = 2^i + 2^j + 2^k + 1, i, j, k are integers such that i > j > k \geq 1 and n > 2 i. \item [{(2)}] d = 2^{3\ell} + 2^{2\ell} + 2^{\ell} + 1, \ell is a positive integer such that \gcd (i, n) = 1 and n > 6. \end{itemize}
ePrint: https://eprint.iacr.org/2012/186
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