Functions with low c-differential uniformity have optimal resistance to some types of differential cryptanalysis. In this paper, we investigate the power functions over finite fields odd characteristic. Based on known almost perfect nonlinear functions, present several classes $$f(x)=x^d$$ $$_{c}\varDelta _f\le 3$$ . Especially, two new c-nonlinear are proposed.

then dropping the last term, an operation that can be justified in terms of limits. Differential notation, in general, can be regarded as a shorthand for a formal limit argument. Still more informally, one can argue that du is small compared to u, so that the last term can be ignored at the level of approximation needed. After dropping du and dividing by du, one obtains the derivative, namely d...

Depleted uranium (DU) is an important by product in uranium enrichment process. Due toits applications in civilian and also military activity, DU emerged as environmental pollutant.The exposure to DU can occur via external or internal pathways. In external exposure, mainlybeta radiation from the decay products contributes to DU toxicity. Internal exposure to DUis more im...

Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce 4-differential uniform permutation function. Recently, [21] it was shown that this swapped version boomerang uniformity exactly 10, if n?0(mod6), 8, n?3(mod6), and 6, n?0(mod3). Based upon c-differential c-boomerang notions we defined [16], respectively, [30], paper characterize...

We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F (x, u, du, du) = 0 defined on a finite-dimensional Riemannian manifold M . Finest results (with hypothesis that require the function F to be degenerate elliptic, that is nonincreasing in the second order derivative variable, and uniformly...

We prove comparison, uniqueness and existence results for viscosity solutions to a wide class of fully nonlinear second order partial differential equations F (x, u(x), du(x), du(x)) = 0 defined on a finite-dimensional Riemannian manifold M . Finest results (with hypothesis that require the function F to be degenerate elliptic, that is nonincreasing in the second order derivative variable) are ...

Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm theorem for indefinite systems with Dirichlet boundary conditions of the form p2m du dx + p2m−2(x) du dx + · · ·+ p1(x) du dx + p0(x)u = 0, where pi is a smooth path of matrices on the comple...

We use the standard notations: differential forms ap, their exterior algebra A, exterior derivative d<p, Hodge's star operator *, coderivative 3f = (_ 1)nP + n 1*d*(P, Laplace-Beltrami operator A = d3 + Md, exterior product (pAg,, inner product (so,*) = fJmpA*4p, and the Dirichlet norm D(sp) = (dep, dp) + (a<p, 5op). For 0forms u the norm reduces to D(u) = (du, du), and Au has the representation

We look for necessary and sufficient conditions for the existence of solutions of the minimization problem (P) inf Ω f (P Du(x)) dx : u ∈ u ζ 0 + W m,∞ 0 (Ω; R N) where P D is a particular type of differential operator of order m, (which we identify as of divergence type) and the boundary data u ζ 0 satisfes P Du ζ 0 (x) = ζ0 for ζ0 ∈ R given.

In [9], the notion of c-differentials was introduced as a potential expansion differential cryptanalysis against block ciphers utilizing substitution boxes. Drawing inspiration from technique higher order cryptanalysis, in this paper we propose c-derivatives and differentials investigate their properties. Additionally, consider how several classes functions, namely multiplicative inverse functi...