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Space Selection and Abstraction in Set Theoretic Estimation

Set Theoretic Estimation has been used in diverse applications for quite some time. Most applications use a Hilbert space for problem solving; however, if a distance metric is not needed, the complexities and features of Hilbert space may not be required. A recent attempt to extend STE methodology to cryptography has led to a refinement of the set space used for this application. In some cases, such as cryptography, a topological space provides the necessary functions and structure. Solving this problem in a less restrictive space allows for ease of implementation and increased computational speed. A less ordered topological set space in which data is set and manipu-lated is described, along with the required functions to operate on the data. Possible extensions of this space abstraction are also presented for problems exhibiting similar characteristics. Cryptography is considered a difficult problem in any space, so the problem is both a relevant and illustrative demonstration of the results of solution space selection. We employ set methods and select an appropriate space in which to solve cryptography problems.