A Parallel Algorithm for determining the inverse of a matrix for use in blockcipher encryption/decryption

In the current world that we live in, of rapid growing technology, and especially reliance on the Internet for our daily lively hood (Banking, shopping, entertainment, news), and also with current crimes (Identity-theft, hacking, spyware), computer security is becoming more and more important. By “computer security” we often refer to addressing three important aspects of a computer-related system: Confidentiality, integrity, and availability. Encryption clearly addresses the need for confidentiality of data, both in storage and transmission. However, the use of encryption can be cumbersome and time consuming. It is important to have a fast algorithm to both encrypt and decrypt data as needed. Public key encryption, though secure, is definitely not fast enough to be used for large size data. We introduce a Parallel Algorithm for computation of inverses of matrices modulo n. This is used in conjunction with Block Ciphers and Hill Ciphers in symmetric encryption and decryption of data for transmission on open lines. Experimental studies were done to compare the run-time of this algorithm on parallel machines, to the traditional one. The new algorithm was found to perform much better than the traditional one, and would be useful to use in encryption/decryption of large sensitive data.

DC测量：电压与电流

这解释了为什么电压测量成为长距离应用中较常用的一种方式。例如,如果你想从一个单独的控制室测量通过直流电机的电流,你需要一种将电流测量转换为电压测量的方法。     

A Fair, Secure and Trustworthy Peer-to-Peer Based Cycle-Sharing System

The increased popularity of Grid systems and cycle sharing across organizations requires scalable systems that provide facilities to locate resources, to be fair in the use of those resources, to allow resource providers to host untrusted applications safely, and to allow resource consumers to monitor the progress and correctness of jobs executing on remote machines. This paper presents such a framework that locates computational resources with a peer-to-peer network, assures fair resource usage with a distributed credit accounting system, provides resource contributors a safe environment, for example Java Virtual Machine (JVM), to host untrusted applications, and provides the resource consumers a monitoring system, GridCop, to track the progress and correctness of remotely executing jobs. We present the details of the credit accounting subsystem and the GridCop remote job monitoring subsystem. GridCop and the distributed credit accounting system together enable incremental payments so that the risk for both resource providers and resource consumers is bounded.*This work was supported by NSF CAREER award grant ACI-0238379 and NSF grants CCR-0313026 and CCR-0313033.     

Incremental reconstruction of sharp edges on mesh surfaces

Limited by the regular grids in computing, many modelling approaches (e.g. field-based methods) sample 3D shape insensitive to sharp features therefore exhibit aliasing errors, by which a lot of sharp edges and corners are lost on the reconstructed surface. An incremental approach for recovering sharp edges on an insensitive sampled triangular mesh is presented in this paper, so that shape approximation errors are greatly reduced. Either chamfered or blended sharp edges on an input triangular mesh could be successfully reconstructed by the signals inherent in the mesh. As a non-iterative method, our approach could be finished in a very short time comparing to those diffusion-based sharp-feature reproducers. The region embedding sharp features is first identified through normal variations. The positions of vertices in the sharp-feature embedded region are then predicted progressively from outer to the inner of sharp regions so that sharp edges could be recovered in the sense of region shrinking.     

Feature based 3D garment design through 2D sketches

This paper presents a new approach for intuitively modeling a three-dimensional (3D) garment around a 3D human model by two-dimensional (2D) sketches input. Our approach is feature based—every human model has pre-defined features, and the constructed garments are related to the features on human models. Firstly, a feature template for creating a customized 3D garment is defined according to the features on a human model; secondly, the profiles of the 3D garment are specified through 2D sketches; finally, a smooth mesh surface interpolating the specified profiles is constructed by a modified variational subdivision scheme. The resulting mesh surface can be cut and flattened into 2D patterns to be manufactured. Our approach provides a 3D design tool to create garment patterns directly in the 3D space through 2D strokes, which is a characteristic not available in other computer aided garment design systems. The constructed garment patterns are related to the features on a human model, so the patterns can be regenerated automatically when creating the same style of garment for other human models. Our technique can greatly improve the efficiency and the quality of pattern making in the garment industry.     

Algebraic grid generation on trimmed parametric surface using non‐self‐overlapping planar Coons patch

Using a Coons patch mapping to generate a structured grid in the parametric region of a trimmed surface can avoid the singularity of elliptic PDE methods when only C¹ continuous boundary is given; the error of converting generic parametric C¹ boundary curves into a specified representation form is also avoided. However, overlap may happen on some portions of the algebraically generated grid when a linear or naïve cubic blending function is used in the mapping; this severely limits its usage in most of engineering and scientific applications where a grid system of non‐self‐overlapping is strictly required. To solve the problem, non‐trivial blending functions in a Coons patch mapping should be determined adaptively by the given boundary so that self‐overlapping can be averted. We address the adaptive determination problem by a functional optimization method. The governing equation of the optimization is derived by adding a virtual dimension in the parametric space of the given trimmed surface. Both one‐ and two‐parameter blending functions are studied. To resolve the difficulty of guessing good initial blending functions for the conjugate gradient method used, a progressive optimization algorithm is then proposed which has been shown to be very effective in a variety of practical examples. Also, an extension is added to the objective function to control the element shape. Finally, experiment results are shown to illustrate the usefulness and effectiveness of the presented method. Copyright © 2004 John Wiley & Sons, Ltd.     

Achieving developability of a polygonal surface by minimum deformation: a study of global and local optimization approaches

Surface developability is required in a variety of applications in product design, such as clothing, ship hulls, automobile parts, etc. However, most current geometric modeling systems using polygonal surfaces ignore this important intrinsic geometric property. This paper investigates the problem of how to minimally deform a polygonal surface to attain developability, or the so-called developability-by-deformation problem. In our study, this problem is first formulated as a global constrained optimization problem and a penalty-function-based numerical solution is proposed for solving this global optimization problem. Next, as an alternative to the global optimization approach, which usually requires lengthy computing time, we present an iterative solution based on a local optimization criterion that achieves near real-time computing speed.     

Parameterization and parametric design of mannequins

This paper presents a novel feature based parameterization approach of human bodies from the unorganized cloud points and the parametric design method for generating new models based on the parameterization. The parameterization consists of two phases. First, the semantic feature extraction technique is applied to construct the feature wireframe of a human body from laser scanned 3D unorganized points. Secondly, the symmetric detail mesh surface of the human body is modeled. Gregory patches are utilized to generate G¹ continuous mesh surface interpolating the curves on feature wireframe. After that, a voxel-based algorithm adds details on the smooth G¹ continuous surface by the cloud points. Finally, the mesh surface is adjusted to become symmetric. Compared to other template fitting based approaches, the parameterization approach introduced in this paper is more efficient. The parametric design approach synthesizes parameterized sample models to a new human body according to user input sizing dimensions. It is based on a numerical optimization process. The strategy of choosing samples for synthesis is also introduced. Human bodies according to a wide range of dimensions can be generated by our approach. Different from the mathematical interpolation function based human body synthesis methods, the models generated in our method have the approximation errors minimized. All mannequins constructed by our approach have consistent feature patches, which benefits the design automation of customized clothes around human bodies a lot.     

Non-self-overlapping Hermite interpolation mapping: a practical solution for structured quadrilateral meshing

This paper addresses the problem of constructing a structured quadrilateral grid inside a given four-sided 2D region by a particular boundary-conforming mapping scheme—Hermite Interpolation Mapping (HIM). When the four given boundary curves are concave and convoluted, all boundary-conform mapping methods suffer from potential self-overlapping problem. Under HIM, the geometry of the grid depends on both the four boundary curves and the tangent vector functions associated with the curves. While the four boundary curves are fixed, the tangent functions in HIM can be varied to suit the need of controlling the characteristics of the mesh inside the given region to prevent self-overlapping. Besides tangent functions, the four twist vectors at the corners of the region can also be adjusted to influence the distribution of the inner grid elements. In our approach, a constrained functional optimization scheme is adopted to adjust the tangent functions and the twist vectors, adaptive to the geometry of the boundary curves, so that the resulting HIM will be free of self-overlapping. The optimization is carried out on the shape control energy that measures the overall mesh quality of the underlying HIM while the self-overlapping is strongly prevented in the form of constraints to the optimization. Experimental results show the promise of the proposed method as a practical and effective solution for structured grid generation.