Very strong multiplication ideals and the ideal θ(I) over a commutative semirings

Let R a commutative semiring with identity. An ideal I is called a multiplication ideal if every ideal contained in I is a multiple of I. We consider the associated ideal θ(I). It is proved that the strong ideal θ(I) is important in the study of multiplication ideals. Among various applications given, the following results are proved: if I is a faithful very strong multiplication ideal, then the strong ideal θ(I) is an idempotent ideal of R such that θ(θ(I)) = θ(I), and every secondary representable ideal of R which is also a very strong multiplication ideal is finitely generated

On primarily multiplication modules over pullback rings

The purpose of this paper is to present a new approach to the classification of indecomposable primarily multi-plication modules with finite-dimensional top over pullback of two Dedekind domains. We extend the definition and results given in [10] to a more general primarily multiplication modules case

Weak comultiplication modules over a pullback of commutative local Dedekind domains

The goal point of recent attempts to classify indecomposable modules over non-artinian rings has been pullback rings. The purpose of this paper is to outline a new approach to the classification of indecomposable weak comultiplication modules with finite-dimensional top over certain kinds of pullback rings

On DPA-Resistive Implementation of FSR-based Stream Ciphers using SABL Logic Styles

The threat of DPA attacks is of crucial importance when designing cryptographic hardware. This contribution discusses the DPA-resistant implementation of two eSTREAM finalists using SABL logic styles. Particularly, two Feedback Shift Register (FSR) based stream ciphers, Grain v.1 and Trivium are designed in both BSim3 130nm and typical 350nm technologies and simulated by HSpice software. Circuit simulations and statistical power analysis show that DPA resistivity of SABL implementation of both stream ciphers has a major improvement. The paper presents the tradeoffs involved in the circuit design and the design for performance issues