The area of lattice-based cryptography is growing ever-more prominent as a paradigm for quantum-resistant cryptography. One of the most important hard problem underpinning the security of latticebased cryptosystems is the shortest vector problem (SVP). At present, two approaches dominate methods for solving instances of this problem in practice: enumeration and sieving. In 2010, Micciancio and ...

There is an inherent difficulty in building 3-move ID schemes based on combinatorial problems without much algebraic structure. A consequence of this, is that most standard ID schemes today are based on the hardness of number theory problems. Not having schemes based on alternate assumptions is a cause for concern since improved number theoretic algorithms or the realization of quantum computin...

Let I be a non-zero left ideal of r-ring M satisfying the condition alpha b beta c= c for all a,b,c, e and alpha, r. We show that contains non-trivial central if is semiprime which admits an appropriate derivations on I, also commutative prime admitting centralizing derivation I. next give some characterizations when generalized act as homomorphisms anti-homomorphisms or two-sided ideals gamma ...

‎Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$‎. ‎Let $I$ be an ideal of $R$ with $grade(I,M)=c$‎. ‎In this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎The main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎Tor^{R}_c(k,H^c_I(M))to kotim...

in this paper, we introduce n-jordan homomorphisms and n-jordan *-homomorphisms and also investigate the hyers-ulam-rassiasstability of n-jordan *-homomorphisms on c*-algebras.

Let $L$ be a lattice in $ZZ^n$ of dimension $m$. We prove that there exist integer constants $D$ and $M$ which are basis-independent such that the total degree of any Graver element of $L$ is not greater than $m(n-m+1)MD$. The case $M=1$ occurs precisely when $L$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. As a corollary, we show t...

We consider the fuzzification of the notion of implicative hyper BCK-ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative hyper BCK-ideal. We establish a condition for a fuzzy hyper BCK-ideal to be a fuzzy implicative hype...

‎let $m$ be a non-zero finitely generated module over a commutative noetherian local ring $(r,mathfrak{m})$ with $dim_r(m)=t$‎. ‎let $i$ be an ideal of $r$ with $grade(i,m)=c$‎. ‎in this article we will investigate several natural homomorphisms of local cohomology modules‎. ‎the main purpose of this article is to investigate when the natural homomorphisms $gamma‎: ‎tor^{r}_c(k,h^c_i(m))to kotim...

The categorical dualities presented are: (first) for the category of bi-algebraic lattices that belong to variety generated by smallest non-modular lattice with complete (0,1)-lattice homomorphisms as morphisms, and (second) non-trivial (0,1)-lattices belonging same morphisms. Although two categories coincide on their finite objects, essentially differ mostly but not only fact duality second us...