Speeding up the Elliptic Curve Scalar Multiplication Using Non Adjacent Form

Improvement in the implementation of elliptic curves cryptography and reducing its complexity are still being actively researched. The representation of integers in non adjacent form has been the subject of various investigations in slightly different contexts. The n - digit Non Adjacent Form (NAF) representation of an integer has no two consecutive non zero digits. Fewer non zero elements mean fewer point additions and therefore more efficient when we need to compute the most popular operation: elliptic curve scalar multiplication. In the present paper we reduce the number of required operations using this representation.