Résumé
A scalar multiplication over a binary elliptic curve consists in a sequence of hundreds of multiplications, squarings and additions. This sequence of eld 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 signi cant improvements in the timing of scalar multiplication due to the proposed optimizations.