The security of the signature scheme is destroyed because its secret information system leaked due to side channel attack. Ring has good application value, which can provide more flexibility and complete anonymity. It be used in some systems such as anonymous authentication ad hoc networks, electronic voting crypto coin based on blockchain. Because attack, private key ring may exposed, cause in...

we introduce center-like subsets z*(r,f), z**(r,f) and z1(r,f), where r is a ring and f is a map from r to r. for f a derivation or a non-identity epimorphism and r a suitably-chosen prime or semiprime ring, we prove that these sets coincide with the center of r.

for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

We study the initial evolution of coffee ring that is formed by evaporation a thin, axisymmetric, surface tension-dominated droplet containing dilute solute. When solutal P\'{e}clet number large, we show diffusion close to contact line controls coffee-ring structure in stages evaporation. perform systematic matched asymptotic analysis for two models -- simple, non-equilibrium, one-sided model (...

For various lattice gas models with nearest neighbour exclusion (and, in one case, second-nearest neighbour exclusion as well), we obtain lower bounds on m, the average number of particles on the non-excluded lattice sites closest ∗We dedicate this work to the memory of Ann Stell, beloved friend of OP and beloved wife of GS.

a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.