Exponential S-boxes

Construction of Highly Nonlinear Injective S-boxes With Application to CAST-like Encryption Algorithms

In this paper we present two methods for constructing highly nonlinear injective s-boxes. Both of these methods, which are based on exponential sums, outperform previously proposed methods. In particular, we are able to obtain injective 8 32 s-boxes with nonlinearity equal to 80 and maximum XOR table entry of 2. We also re-evaluate the resistance of the CAST-like encryption algorithms construct...

Exponential S-Boxes: a Link Between the S-Boxes of BelT and Kuznyechik/Streebog

The Bernoulli Sieve Revisited

We consider an occupancy scheme in which “balls” are identified with n points sampled from the standard exponential distribution, while the role of “boxes” is played by the spacings induced by an independent random walk with positive and nonlattice steps. We discuss the asymptotic behavior of five quantities: the index K n of the last occupied box, the number Kn of occupied boxes, the number Kn...

On exponential domination and graph operations

An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v  in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set....

Bringing Order to Special Cases of Klee's Measure Problem

Klee’s Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in R. Omitting logarithmic factors, the best algorithm has runtime O∗(nd/2) [Overmars,Yap’91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and kGro...