Abstract The purposes of this paper are to introduce generalizations quasi-prime ideals the context $$\phi $$ ? -quasi-prime ideals. Let : {\mathcal {I}}(S) \rightarrow \cup \left\{ \emptyset \right\} : I ( S ) </m...

In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattices [14]. Some...

NTRUEncrypt is a fast lattice-based cryptosystem and a probable alternative of the existing public key schemes. The existing provable-secure NTRUEncrypts are limited by the cyclotomic field it works on the prime-power cyclotomic field. This is worth worrying, due to the subfield attack methods proposed in 2016. Also, the module used in computation and security parameters rely heavily on the cho...

This note investigates modules having quasi-injective and duo submodules. We introduce a new generalization of C_1-module. The main method that was adopted in this is how to obtain submodule N M the characteristic Quasi-injective. investigate relationship between pseudo-injective module Quasi-injective property Finally, we anti-hopfian module.

Modules (also known as profunctors or distributors) and morphisms among them subsume categories and functors and provide more general and abstract framework to explore the theory of structures. In this book we generalize and redevelop the basic notions and results of category theory using this framework of modules. Topics Chapter 1 introduces modules and cells among them. A moduleM ∶ X⇢A from a...

Let LD8(1, 0) and LE8(1, 0) be the simple vertex operator algebras associated to untwisted affine Lie algebra ĝD8 and ĝE8 with level 1 respectively. In the 1980s by I. Frenkel, Lepowsky and Meurman as one of the many important preliminary steps toward their construction of the moonshine module vertex operator algebra, they use roots lattice showing that LD8(1, 0) can embed into LE8(1, 0) as a v...

A quasi-identifier refers to a subset of attributes that can uniquely identify most tuples in a table. Incautious publication of quasi-identifiers will lead to privacy leakage. In this paper we consider the problems of finding and masking quasi-identifiers. Both problems are provably hard with severe time and space requirements. We focus on designing efficient approximation algorithms for large...

We describe a concept to employ Trusted Computing technology to secure Conditional Access Systems (CAS) for DVB. Central is the embedding of a trust anchor, e.g. a trusted platform module (TPM) into the set-top box or Conditional Access Module. Various deployment scenarios exhibit possibilities of charging co-operation with mobile network operators (MNO) via trusted mobile devices, or with othe...