Computing A^X mod n or A^XB^Y mod n for large X, Y, and n is very important in many ElGamal-like public key cryptosystems. In this paper, we proposed using block method in sparse form to improve the performance of modular exponentiation and analyzing the computational cost by state transition diagram. We also extended the concept of Block Method and make it more general. This method is suitable for some devices with limited storage space, such as smart card.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 301-314). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 301-314). Also available on the Internet.

Thesis (M.A.(Afrikaans))--Universiteit van Pretoria. / Afrikaans text with summaries in English and Afrikaans. Includes bibliographical references (leaves 183-189). Also available on the Internet via World Wide Web.

Thesis (M.A.(Afrikaans))--Universiteit van Pretoria. / Afrikaans text with summaries in English and Afrikaans. Includes bibliographical references (leaves 183-189). Available on the Internet via World Wide Web.

This project investigates laser cutting in relation to textile manipulation and creating three-dimensional form. More precisely, this collection of nine outfits becomes an exploration about expressions of laser cut lines and their interrelation to the body through folding and draping the textile material. The laser cut bridge line used, will be the guiding part for a garments construction and through this different shapes are tested. This way of working with the material, its character and added manipulation will propose a new understanding of and an alternative for constructing a garment. This investigation is also a proposal for a new mind-set when it comes to using laser cutting in fashion design. Laser cutting has mainly been regarded as a technique for decoration, yet the machine could have a much greater role in the design process. Textile manipulation in this work is seen not only as a surface decoration but as a method of creating a 3D form from a 2D material which in this case is a method of design for shaping a garment. Through this, the work will hopefully challenge the industry in terms of working with laser cutting, garment construction and also textile manipulation.

The focus of this degree work is on material interaction within the field of knitwear. Material combinations are often seen in fashion as a decorative effect to add shine, transparency or blocks of colour. The materials are put together as one flat material. This work embraces the different qualities and explores the possibilities to use material interaction as a way of creating form on the body. To achieve this, material experiments have been made to find combinations that had a big impact on each other. The materials that were found to be most suitable for this were the combination of metal and lycra yarn. This combination showed contrast in both volume and in density. The result is a collection of seven examples that is based from square knitted pieces where the interaction changes the form of the material and the garment. Creating form from material combination could lead to a new method of creating garments with larger form possibilities than is seen today in ready to wear knitted garments.

This report is an exploration of theoretical and applied aspects of form-based coding. First, it presents an in-depth look at conventional zoning, conditions surrounding its origins around the turn of the twentieth century, the system of legal precedents that supports zoning, the evolution of the zoning “toolkit”, and the scope of zoning policies which are prevalent today. Second, form-based codes are defined and differentiated from conventional codes as well as design guidelines. The organizing principles on which FBCs are based are explained and the components of FBCs are described. Issues and controversy surrounding FBCs are discussed. Third, diverse case studies from around the country are carried out in order to examine how form-based codes are developed and applied in various real-world contexts. Case studies are presented in two different tiers, primary and secondary. Primary case studies involve in-depth research, whereas secondary case studies receive a brief, overview-style treatment. Primary case studies are: St. Lucie County, Florida and Sarasota County, Florida. Secondary case studies are: Leander, Texas; Peoria, Illinois; Montgomery, Alabama; Arlington County, Virginia; Hercules, California; and Miami, Florida. Fourth, conclusions are drawn from the research and point towards best practices in form-based coding. The report concludes that form-based codes are not a cure-all, should be developed in the context of a visioning process, and should strike a balance in terms of regulation. Additionally, market factors play a major role. The high cost of coding is a major concern. Furthermore, code writers should be prepared to educate the public as part of their profession. / text

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