The issue of this paper — efficient algorithms for calculating transformations based on elliptic curves - is a relatively new area of research. Transformations based on elliptic curves are widely used in public-key cryptosystems, and are also used in cryptanalysis of asymmetric ciphers based on integer factorization problem. Efficiency of point scalar multiplication on an elliptic curve defined over the prime fields on the basis of the binary Non-Adjacent Form representation of the scalar was also investigated. To assess effectiveness of the received and previously proposed algorithms the criterion of effectiveness, based on the average computational complexity was introduced. For new algorithms the effective operation in prime field, operations with point (addition and doubling); composite operation "double and add"; scaling operation; affine coordinate system properties; properties of the coordinate system of Jacobi were used. Formulated and proved assertion regarding computational complexity for the proposed algorithm.