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Algorithms and Theory
Most of the work in the Algorithms and Theory group at the University of Illinois concerns computational geometry and cryptography. Both involve the study of mathematical algorithms. Computational geometry solves problems stated in terms of geometry, the branch of mathematics that deals with spatial relationships. These terms include basic geometrical objects like points, lines, polygons, curves, and surfaces. Applications of computational geometry range from computer graphics, visualization, robotics, integrated circuit design, computational biology, pattern recognition, and scientific computing. It is estimated that about 80 percent of all data have spatial context or reference, hence the importance of this field will continue to grow. Cryptography keeps communications private by transforming data so that it is only recognizable or useful to an authorized person. Cryptographic techniques can hide information contact, protect data from theft or alteration, and prevent its unauthorized use. The most secure techniques in modern cryptography are based on problems that are difficult to solve, either because they require some secret knowledge or because they are intrinsically difficult or computationally impractical to complete. Applications of cryptography are found anywhere that decisions and agreements are communicated electronically (online banking, trading, data distribution, e-commerce), to control access (to shared disk drives, high security installations, ATM machines, pay-per-view TV), and to provide privacy (for e-mail, cell phones). With the continued growth of the Internet and electronic commerce, this field is expanding.
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