Methods of increasing the efficiency of data analysis based on topology and analytical geometry are becoming increasingly popular in modern information systems. However, due to the high degree of complexity of topological structures, the solution of the main tasks of processing and storing information is provided by spatial geometry in combination with modular arithmetic and analytical assignment of geometric structures, the description of which is involved in the development of new methods for solving optimization problems. The practical application of elliptic cryptography, including in network protocols, is based on the use of interpolation methods for approximating graphs of functions, since a loss of accuracy may occur when performing many sequential mathematical operations. This problem is related to the features of the computing architecture of modern devices. It is known that an error can have a cumulative effect, so data approximation methods must be used sequentially as calculations are performed.

Keywords: elliptic curve, information system, data analysis, discrete logarithm, point order, scalar, subexponential algorithm