International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 11 April 2012

Brajesh Kumar Singh
ePrint Report ePrint Report
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}

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