Now, say we define two of these points as u and v: we can then draw a straight line through two of these points to find another intersecting point, at w. We can then draw a vertical line through w to find the final intersecting point at x. This rule works, when we define another imaginary point, the Origin, or O, which exists at theoretically extreme points on the curve. As strange as this problem may seem, it does permit for an effective encryption system, but it does have its detractors.
On the positive side, the problem appears to be quite intractable, requiring a shorter key length thus allowing for quicker processing time for equivalent security levels as compared to the Integer Factorization Problem and the Discrete Logarithm Problem. On the negative side, critics contend that this problem, since it has only recently begun to be implemented in cryptography, has not had the intense scrutiny of many years that is required to give it a sufficient level of trust as being secure. This leads us to more general problem of cryptology than of the intractability of the various mathematical concepts, which is that the more time, effort, and resources that can be devoted to studying a problem, then the greater the possibility that a solution, or at least a weakness, will be found.
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Analysis, assessment, and data management are core competencies for operation research analysts. This volume addresses a number of issues and developed methods for improving those skills. It is an outgrowth of a conference held in April at the Hellenic Military Academy, and brings together a broad variety of mathematical methods and theories with several applications.
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