## Cryptology ePrint Archive: Report 2009/502

On second order nonlinearities of cubic monomial Boolean functions

Abstract: We study cubic monomial Boolean functions of the form $Tr_1^n(\mu x^{2^i+2^j+1})$ where $\mu \in \mathbb{F}_{2^n}$. We prove that the functions of this form do not have any affine derivative. A lower bound on the second order nonlinearities of these functions is also derived.

Category / Keywords: secret-key cryptography /

Date: received 16 Oct 2009, last revised 25 Nov 2009

Contact author: gsugata at gmail com

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Version: 20091126:061050 (All versions of this report)

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