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The Good lower bound of Second-order nonlinearity of a class of Boolean function
Boolean function Higher-order derivatives Second-order nonlinearit Walsh-spectrum
2012/3/26
this paper we find the lower bound of second-order nonlinearity of Boolean function $f_{\lambda}(x) = Tr_{1}^{n}(\lambda x^{p})$ with $p = 2^{2r} + 2^{r} + 1$, $\lambda \in \mathbb{F}_{2^{r}}^{*}$ and...
Maiorana-McFarland Functions with High Second-Order Nonlinearity
secret-key cryptography / boolean functions
2012/3/28
The second-order nonlinearity, and the best quadratic approximations, of Boolean functions are studied in this paper. We prove that cubic functions within the Maiorana-McFarland class achieve very hig...
The Lower Bounds on the Second Order Nonlinearity of Cubic Boolean Functions
cryptography derivative the second nonlinearity
2010/1/18
It is a difficult task to compute the r-th order nonlinearity of a given function with algebraic degree strictly greater than r > 1. Even the lower bounds on the second order nonlinearity is known onl...
On the Lower Bounds of the Second Order Nonlinearity of some Boolean Functions
Boolean functions derivative second order nonlinearity
2009/6/12
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 impor-
tant in coding theory as it ...