Abstract. Transformations of points of a nonsupersingular elliptic curve are selected as a promising way for further development of cryptographic systems. Statements are proved for the estimation of the number of isomorphic transformations of a nonsupersingular elliptic curve over a dilation of a finite field, which is dependent on the characteristics of the finite field. The estimates can be used to improve elliptic curve cryptosystems.

Keywords: elliptic curve, transformation of an elliptic curve, isomorphic elliptic curve, isomorphic transformation.