Efficient application of the residue number system in elliptic cryptography

Abstract

The article is devoted to the study of the efficiency of arithmetic operations with points of an elliptic curve using the residue number system. Based on the obtained data, it was found that the use of the residue number system with moduli of a special type from the operations with an elliptic curve from NIST FIPS 186 allows gaining 7.72% for the operation of addition and 7.50% for the operation of doubling points of an elliptic curve on average.