Welcome to the resource topic for
**2009/094**

**Title:**

On the Lower Bounds of the Second Order Nonlinearity of some Boolean Functions

**Authors:**
Sugata Gangopadhyay, Sumanta Sarkar, Ruchi Telang

**Abstract:**

The r-th order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed-Muller code \mathcal{R}(r, n). In this paper we deduce the lower bounds of the second order nonlinearity of the two classes of Boolean functions of the form \begin{enumerate} \item f_{\lambda}(x) = Tr_1^n(\lambda x^{d}) with d=2^{2r}+2^{r}+1 and \lambda \in \mathbb{F}_{2^{n}} where n = 6r. \item f(x,y)=Tr_1^t(xy^{2^{i}+1}) where x,y \in \mathbb{F}_{2^{t}}, n = 2t, n \ge 6 and i is an integer such that 1\le i < t, \gcd(2^t-1, 2^i+1) = 1. \end{enumerate} For some \lambda, the first class gives bent functions whereas Boolean functions of the second class are all bent, i.e., they achieve optimum first order nonlinearity.

**ePrint:**
https://eprint.iacr.org/2009/094

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

**Example resources include:**
implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .