Canteaut, Anne Duval, Sébastien Perrin, Léo

Nonlinear functions, also called S-Boxes, are building blocks for symmetric cryptography primitives. The robustness of S-Boxes is measured using properties of Boolean functions, such as differential uniformity and non-linearity. In particular, the lower the differential uniformity, the better the resistance to differential attacks. Functions which ...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Canteaut, Anne Duval, Sébastien Perrin, Léo

The existence of Almost Perfect Nonlinear (APN) permutations operating on an even number of variables was a long-standing open problem, until an example with six variables was exhibited by Dillon et al. in 2009. However it is still unknown whether this example can be generalised to any even number of inputs. In a recent work, Perrin et al. describe...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Anbar Meidl, Nurdagül Meidl, Wilfried

For c is an element of F(2)n, a c-bent4 function f from the finite field F(2)n to F-2 is a function with a fiat spectrum with respect to the unitary transform V-f(c), which is designed to describe the component functions of modified planar functions. For c = 0 the transform V-f(c) reduces to the conventional Walsh transform, and hence a 0-bent4 fun...

Broutin, Nicolas Mailler, Cécile

We present here a new and universal approach for the study of random and/or trees,unifying in one framework many different models, including some novel models, not yet understood in the literature.An and/or tree is a Boolean expression represented in (one of) its tree shape.Fix an integer $k$, take a sequence of random (rooted) trees of increasing ...