Impact of Optimized Operations AB,AC and AB+CD in Scalar Multiplication over Binary Elliptic Curve
Résumé
A scalar multiplication over a binary elliptic curve consists of 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 duo and Intel core i5. These experimental results show some significant improvements due to the proposed optimizations and our results are better than the recently published implementation results (Taverne et al. - CHES 2011) of double-and-add scalar multiplication.
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