In the practice of block cipher design, there seems to have grown a consensus about the diffusion function that designers choose linear functions with large branch numbers to achieve provable bounds against differential and linear cryptanalysis. In this paper, we propose two types of nonlinear functions as alternative diffusing components. One is based on a nonlinear code with parameters (16,25...

Using two models that incorporate a nonlinear forward-backward heat equation, we demonstrate the existence of well-deened weak solutions containing shocks for diiusive problems. Occurrence of shocks is connected to multivalued inverse solutions and non-monotone potential functions. Unique viscous solutions are determined from perturbation theory by matching to a shock layer condition. Results o...

Existence of wavefronts for discrete two-dimensional evolution models involving diifusive terms with a nonlinear dependence on the discrete ‘grsdients’ is studied. For small values of a control parameter, we prove existence of steady wavefronts. We investigate numerically the transition of steady fronts to traveling waves as the control parameter increases. @ 2002 Elsevier Science Ltd. All righ...

Self similar solutions u(x,t) = f(x//t) of the one-dimensional porousmedium equation are studied in this paper. These solutions emerge frominitial values that consist of two constant states: one non-positive forx < 0 and one non-negative for x > 0. With a diffusivity of the form|u| , we consider for m > 0 sign change solutions and for m e (-1,0]non-negative solutions. Th...