Sustainability and Time Complexity Estimation of Сryptographic Algorithms Main Operations on Elliptic Curves

This paper presents the time complexity estimates for the methods of points exponentiation, which are basic for encrypting information flows in computer systems. As a result of numerical experiments, it is determined that the method of doubling-addition-subtraction has the lowest complexity. Mathematical models for determining the execution time of each considered algorithm for points exponentiation on elliptic curves were developed, which allowed to conduct in-depth analysis of their performance and resistance to special attacks, in particular timing analysis attack. The dependences of the cryptographic operations execution time on the key length and the sustainability of each method on the Hamming weight are investigated. It is proved that under certain conditions the highest sustainability of the system is achieved by the doubling-addition-subtraction algorithm. This allows to justify the choice of algorithm and its parameters for the implementation of cryptographic information security, which is resistant to special attacks.