Trading Inversions for Multiplications in Elliptic Curve Cryptography
- Mathieu Ciet ,
- Marc Joye ,
- Kristin Lauter ,
- Peter Montgomery
Designs, Codes, and Cryptography | , Vol 2003: pp. 257
Recently, Eisentraeger-Lauter-Montgomery proposed a method for speeding up scalar multiplication on elliptic curves. That method relies on improved formulae for evaluating S = 2P + Q from given points P and Q on an elliptic curve. Compared to the naive approach, the improved formulae 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 or quadrupling a point, and present a ternary/binary method to perform efficient scalar multiplication.