This research is a study on the relationship of irrigation water treatments and soil moisture distribution uniformity (DU). Soil moisture distribution was based on long-term data sets that were collected during wet and dry soil conditions (from permanent wilting point to field capacity) using a novel electromagnetic sensor-based platform moving inside subsurface horizontal access-tubes. The irr...

Recently, a new concept called the c-differential uniformity was proposed by Ellingsen et al. (2020), which generalizes notion of differential measuring resistance against cryptanalysis. Since then, finding functions having low has attracted attention many researchers. However it seems that, at this moment, there are not non-monomial permutations uniformity. In paper, we present classes (almost...

Very recently, a new concept called multiplicative differential and the corresponding c-differential uniformity were introduced by Ellingsen et al. (IEEE Trans. Inform. Theory 66(9), 5781–5789 2020). A function F(x) over finite field GF(pn) to itself is said have δ, or equivalent, differentially (c,δ)-uniform, when maximum number of solutions x ∈GF(pn) F(x + a) − cF(x) = b, a,b,c ∈GF(pn), c≠ 1 ...

Functions with low differential uniformity can be used as the s-boxes of symmetric cryptosystems as they have good resistance to differential attacks. The AES (Advanced Encryption Standard) uses a differentially4 uniform function called the inverse function. Any function used in a symmetric cryptosystem should be a permutation. Also, it is required that the function is highly nonlinear so that ...

A partial differential equation (PDE) of order m is a relation of the form F (x, u,Du,Du, · · · , Du) = 0. (0.1) Here F is a given function of x ∈ R, ”unknown” function u = u(x), and its derivatives up to order m. We denote Du the set of all the derivatives of u of order k. Using multi-indices l = (l1, · · · , ln), i.e. vectors in R with nonnegative integer components, we can write Du = { Du = ...

We consider the boomerang uniformity of an infinite class (locally-APN) power maps and show that its over finite field $\F_{2^n}$ is $2$ $4$, when $n \equiv 0 \pmod 4$ 2 4$, respectively. As a consequence, we for this maps, differential strictly greater than uniformity.

Bundles are equivalence classes of functions derived from equivalence classes of transversals. They preserve measures of resistance to differential and linear cryptanalysis. For functions over G F(2n), affine bundles coincide with EA-equivalence classes. From equivalence classes (“bundles”) of presemifields of order pn , we derive bundles of functions over G F(pn) of the form λ(x)∗ρ(x), where λ...

We conjecture a strong property for the up and down maps U and D in an r-differential poset: DU + tI and UD + tI have Smith normal forms over Z[t]. In particular, this would determine the integral structure of the maps U, D, UD, DU , including their ranks in any characteristic. As evidence, we prove the conjecture for the Young-Fibonacci lattice YF studied by Okada and its r-differential genera...