Trading Inversions for Multiplications in Elliptic Curve Cryptography

Recently, Eisenträger et al. proposed a very elegant method for speeding up scalar multiplication on elliptic curves. Their method relies on improved formulas for evaluating S = (2P + Q) from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulas save a field multiplication each time the operation is performed. This paper proposes a variant which is faster whenever a field inversion is more expensive than six field multiplications. We also give an improvement when tripling a point, and present a ternary/binary method to perform efficient scalar multiplication.