Application of mathematical optimization in elliptic curve arithmetic

Currently, a lot of standardized elliptic curve cryptographic algorithms are widely used. Due to the constantly increasing execution speed demands, implementation optimization problem become actual. Using elliptic curve arithmetic on a different information security devices require to form an mathematical programming problem of elliptic curves calculation. Solution of this problem allows to find optimal way of calculation in the current condition. This approach increases the speed of cryptographic algorithms on information security devices. The paper present one of the possible ways to optimize computations in elliptic curve arithmetic by using mathematical programming. An optimization problem is formed that describes the calculation of scalar multiplication. Operations composition and multiplication methods composition are introduced to form the corresponding optimization problem. Adduction of elliptic curve calculations to the mathematical programming problem allow to research applicability of known optimization methods to computations in elliptic curves.