Efficient Implementation of Cryptography on Points of an Elliptic Curve in Residue Number System

The article explores the question of the effective implementation of arithmetic operations with points of an elliptic curve given over a prime field. Given that the basic arithmetic operations with points of an elliptic curve are the operations of adding points and doubling points, we study the question of implementing the arithmetic operations of adding and doubling points in various coordinate systems using the weighted number system and using the Residue Number System (RNS). We have shown that using the fourmodule RNS allows you to get an average gain for the operation of adding points of the elliptic curve of 8.67% and for the operation of doubling the points of the elliptic curve of 8.32% compared to the implementation using the operation of modular multiplication with special moduli from NIST FIPS 186.