A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine spaces over various finite fields. Then algebro-geometric transformations on those spaces is transported back to provide encryption. For a specific block size <...

This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a ‘geometric product’ of vectors in 2and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods. Reflections and rotations are analysed in terms of bilinear spinor transforma...

Determining the precedence of machining features is a critical issue in feature-based process planning. It becomes more complex when geometric interaction occurs between machining features. STEP-NC, the extension of STEP (ISO 10303) standard developed for CNC controllers, is a feature-based data model. It represents all the geometric and topological product data minus feature interactions. In t...

For the aim of producing geometric models of critical infrastructures (e.g., governamental assets, nuclear plants, airports, railway and metro stations, hospitals, etc.) where various security tools and control systems may be easily integrated, we discuss here a fast and inexpensive construction of digital models of complex buildings and infrastructures from line drawings of architectural plans...

Advancements in 3D CAD allow product shape to act as a common language to represent and retrieve reusable product information in PLM systems. While shape-based retrieval techniques contribute to the part design reuse process by retrieving similar part models, selecting the optimal candidate for reuse remains a challenge. A more refined shape comparison process is required to locate single shape...

The purpose of this paper is to develop a geometric approach to Wall's finiteness obstruction. We will do this for equivariant CW-complexes. The main advantage will be that we can derive all the formal properties of the equivariant finiteness obstruction easily from this geometric description. Namely, the obstruction property, homotopy invariance, the sum and product formulas, and the restricti...

Geometric interpretation of turbodecoding has founded an analytical basis, and provided tools for the analysis of this algorithm. Based on this geometric framework, we extend the analytical results for turbo-decoding of product codes, and show how analysis tools can be practically adopted for this case. Specifically, we investigate the algorithm’s stability and its convergence rate. We present ...

In this paper we investigate possible patterns that component interactions can take in a component-based simulation environment by taking the communication between a behaviour simulator and an an-imator as a case study. The interaction between a functional simulator of an engineering product and a visualisation system that is used to animate the geometric model corresponding to that product, to...