|
Privacy-preserving Computational Geometry
Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. Classical problems of computational geometry reconsidered from the point of view of SMC include shape intersection, private point inclusion problem, range searching, convex hull In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ..., and more.Kaitai LIANG, Bo YANG, Dake HE, Min ZHOUPrivacy-Preserving Computational Geometry Problems on Conic Sections Journal of Computational Information Systems 7: 6 (2011) 1910–1923 A pioneering work in this area was a 2001 paper by Atallah and Du, Atallah M J, Du WSecure Multiparty Computational Geometry In Proc. Algorithms and Data Structures: 7th International Workshop, WADS 2001, Lectur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secure Multi-party Computation
Secure multi-party computation (also known as secure computation, multi-party computation (MPC) or privacy-preserving computation) is a subfield of cryptography with the goal of creating methods for parties to jointly compute a function over their inputs while keeping those inputs private. Unlike traditional cryptographic tasks, where cryptography assures security and integrity of communication or storage and the adversary is outside the system of participants (an eavesdropper on the sender and receiver), the cryptography in this model protects participants' privacy from each other. The foundation for secure multi-party computation started in the late 1970s with the work on mental poker, cryptographic work that simulates game playing/computational tasks over distances without requiring a trusted third party. Note that traditionally, cryptography was about concealing content, while this new type of computation and protocol is about concealing partial information about data while comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity. Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(''n''2) and O(''n'' log ''n'') may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Searching
In computer science, the range searching problem consists of processing a set ''S'' of objects, in order to determine which objects from ''S'' intersect with a query object, called the ''range''. For example, if ''S'' is a set of points corresponding to the coordinates of several cities, find the subset of cities within a given range of latitudes and longitudes. The range searching problem and the data structures that solve it are a fundamental topic of computational geometry. Applications of the problem arise in areas such as geographical information systems (GIS), computer-aided design (CAD) and databases. Variations There are several variations of the problem, and different data structures may be necessary for different variations. In order to obtain an efficient solution, several aspects of the problem need to be specified: * Object types: Algorithms depend on whether ''S'' consists of points, lines, line segments, boxes, polygons.... The simplest and most studied obje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Hull
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Atallah
Mikhail Jibrayil (Mike) Atallah is a Lebanese American computer scientist, a distinguished professor of computer science at Purdue University. Biography Atallah received his bachelor's degree from the American University of Beirut in 1975. He then moved to Johns Hopkins University for his graduate studies, earning a master's degree in 1980 and a Ph.D. in 1982 under the supervision of S. Rao Kosaraju. Since that time he has been a member of the Purdue University faculty.Department faculty profile Purdue University, retrieved 2011-09-29. In 2001, Atallah co-founded Arxan Technologies, Inc., a provider of internet anti-piracy and anti-tampering software, and in 2007, he became its chief technology officer. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point In Polygon
In computational geometry, the point-in-polygon (PIP) problem asks whether a given point in the plane lies inside, outside, or on the boundary of a polygon. It is a special case of point location problems and finds applications in areas that deal with processing geometrical data, such as computer graphics, computer vision, geographic information systems (GIS), motion planning, and computer-aided design (CAD). An early description of the problem in computer graphics shows two common approaches ( ray casting and angle summation) in use as early as 1974. An attempt of computer graphics veterans to trace the history of the problem and some tricks for its solution can be found in an issue of the ''Ray Tracing News''. Ray casting algorithm One simple way of finding whether the point is inside or outside a simple polygon is to test how many times a ray, starting from the point and going in any fixed direction, intersects the edges of the polygon. If the point is on the outside of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alice And Bob
Alice and Bob are fictional characters commonly used as placeholders in discussions about cryptographic systems and protocols, and in other science and engineering literature where there are several participants in a thought experiment. The Alice and Bob characters were invented by Ron Rivest, Adi Shamir, and Leonard Adleman in their 1978 paper "A Method for Obtaining Digital Signatures and Public-key Cryptosystems". Subsequently, they have become common archetypes in many scientific and engineering fields, such as quantum cryptography, game theory and physics. As the use of Alice and Bob became more widespread, additional characters were added, sometimes each with a particular meaning. These characters do not have to refer to people; they refer to generic agents which might be different computers or even different programs running on a single computer. Overview Alice and Bob are the names of fictional characters used for convenience and to aid comprehension. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Cryptography
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and compreh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity. Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(''n''2) and O(''n'' log ''n'') may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
