Impact of optimized field operations AB,AC and AB + CD in scalar multiplication over binary elliptic curve

Abstract

A scalar multiplication over a binary elliptic curve consists in a sequence of hundreds of multiplications, squarings and additions. This sequence of field operations often involves a large amount of operations of type AB,AC and AB + CD. In this paper, we modify classical polynomial multiplication algorithms to obtain optimized algorithms which perform these particular operations AB,AC and AB + CD. We then present software implementation results of scalar multiplication over binary elliptic curve over two platforms: Intel Core 2 and Intel Core i5. These experimental results show some significant improvements in the timing of scalar multiplication due to the proposed optimizations. © 2013 Springer-Verlag Berlin Heidelberg.