New point addition formulae for ECC applications

Abstract

In this paper we propose a new approach to point scalar multiplication on elliptic curves defined over fields of characteristic greater than 3. It is based on new point addition formulae that suit very well to exponentiation algorithms based on Euclidean addition chains. However finding small chains remains a very difficult problem, so we also develop a specific exponentiation algorithm, based on Zeckendorf representation (i.e. representing the scalar k using Fibonacci numbers instead of powers of 2), which takes advantage of our formulae. © Springer-Verlag Berlin Heidelberg 2007.