Recall that an algebraic module is aKG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module on its component of the (stable) Auslander–Re...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

This research is motivated by the need to provide teaching materials in form of electronic-based modules (e-modules) integrated with numeracy literacy learning. Where math books are less able delivery related literacy. Given lack a learning process during covid 19 period improve students' abilities field numeracy. The objective develop an e-module for multiplication and division fractions grade...

We present a novel randomized algorithm to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f ∈ Fq[x] to be factored) with respect to a random Drinfeld module φ with complex multiplication. Factors of f supported on prime ideals with supersin...

In this paper, a parallel, power-efficient and scalable word-based crypto architecture is proposed that performs the operations required for scalar point multiplication including add, multiplication and inversion operations on GF(2) operands. The proposed architecture distinguishes itself from exiting architectures, including our prior architecture, by the fact that its resource usage and power...

In Diffi-Hellman type key agreement (Idrissi et al., 2012), Elliptic Curve Digital Signature Algorithm (Shivkumar and Umamaheswari, 2014) and Elgamal crypto systems (Jie and Kamarulhaili, 2011; Ismail and Hijazi, 2012), we use elliptic curve Point Multiplication (PM) (Hankerson et al., 2004). Several hardware solutions are already available for elliptic curve Point Multiplication, (Ghosh et al....

This paper presents the comparison and optimization of Galois field algorithm and IDEA(International data encrypted algorithm) using VHDL(xc2v40-6cs144)with the help of Xilinx-Ise (9.2) .In terms of security IDEA algorithm is very much superior where as in terms of timings Galois field is much better and is already patented of Ascom. These are cryptographic algorithm used for security purpose. ...

For an extension $K/\mathbb{F}_q(T)$ of the rational function field over a finite field, we introduce notion virtually $K$-rational Drinfeld modules as analogue $\mathbb{Q}$-curves. Our goal in this article is to prove that all rank two with no complex multiplication are parametrized up isogeny by points quotient curve modular $Y_0(\mathfrak{n})$ some square-free level $\mathfrak{n}$. This Elki...

In the light of information security it is highly desirable to avoid a “single point of failure” because this would be an attractive target for attackers. Cryptographic protocols for distributed computations are important techniques in pursuing this goal. An essential module in this context is the secure multiparty multiplication of two polynomially shared values over Zq with a public prime num...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...