A usual way to construct block ciphers is to apply several rounds of a given structure. Many kinds of attacks are mounted against block ciphers. Among them, differential and linear attacks are widely used. In [18, 19], it is shown that ciphers that achieve perfect pairwise decorrelation are secure against linear and differential attacks. It is possible to obtain such schemes by introducing at l...

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Abstract We study quantitative equidistribution of random walks on the torus by affine transformations. Under assumption that Zariski closure group generated linear part acts strongly irreducibly ${{\mathbb{R}}}^d$ and is either connected or contains a proximal element, we give estimates (depending only walk) for how fast walk equidistributes unless initial point translation transformations can...

Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. Recently, researchers have begun to relax this restriction to include systems of affine recurrence equations. A system of uniform recurrence equations typically can be embedded in spacetime so that the distance between a variable and a depende...

Most work on the problem of synthesizing a systolic array from a system of recurrence equations is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. A system of uniform recurrence equations typically can be embedded in spacetime so that the distance between a variable and a dependent variable does...