Mathematical models based on elliptic curves have been intensively studied since their applicability in data security systems was discovered. In this article, the authors describe the optimal way to select particular subspaces over which elliptic curves are defined, showing the applicability of these subspaces in secure data transfer. Access to large databases and analyses of the requests made to these databases are required daily by a variety of users, including legal entities. An attack on these communication systems causes violations in privacy and damage to/theft of data that can be worth EUR tens of billions annually. For requests made between computers, encryption methods can be used as these systems have adequate computing power and energy. For requests made from fixed and mobile systems, if the data are distributed heterogeneously, the computing power required to authenticate both the users and the answering entities determines the efficiency of the proposed solution. To address this limitation, our study proposes a double-authentication method based on particular elliptic-curve systems.
The detection of clear and encrypted data that are transported through computer networks is of particular importance both for protecting the data and the users to whom they belong and to whom they are intended, as well as the networks through which they are transmitted. The proposed method consists of an algorithm that classifies the data it receives by testing the belongingness of their standard deviation values to established confidence intervals. Following the evaluation of the algorithm, an accuracy of 94.73% was obtained and it appears that the results can be used with certainty in subsequent analyses of the data detection.
"The aim of this paper is to provide a characterization diagram for a family of B\'{e}zier flexible interpolation curves as well as to present an application of our results in cryptography. In our interpolation scheme, two parameters, $t_1,\ t_2\in (0,1)$ determine the position of the interpolation points on the B\'{e}zier curve. Consequently we obtain a family of B\'{e}zier interpolation curves depending on two parameters. Altering the values of the parameters we modify the intermediary control points and implicitly the shape of the interpolation curve. In order to control the shape of the interpolation curves from this family, we provide a partition of the domain $T=(0,1)\times (0,1)$ where the parameters lie according to the geometric characterization of these curves: with zero, one or two inflexion points; with loop; with cusp and degenerated in quadratic curves. The characterization diagram can be used as a tool for the choice of parameters, with possible applications in different fields. We present one of its application in cryptography, for finding certain subspaces over which particular elliptic sub-curves are defined. Computation, implementation and graphics are made using MATLAB."
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