Description: The article provides a short description of national and international standards for digital signatures and describes conditions for the generation general system parameters of elliptic curves of high and ultra-high levels of security. We show theoretical analysis of existing algorithms for calculating the number of points on elliptic curves defined over the binary field. Implementing in practice algorithms that were analyzed, and the obtained results were compared by the criterion of difficultyresistance with other works in this direction. Showing perspective algorithms to calculate the order of elliptic curves with the possibility of using as basic parameters for a national standard of digital signature.
Keywords: order of the elliptic curve, Satoh's algorithm, arithmetic-geometry mean, electronic digital signature