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.
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Negre, C., Robert, JM. (2013). Impact of Optimized Field Operations AB,AC and AB + CD in Scalar Multiplication over Binary Elliptic Curve. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds) Progress in Cryptology – AFRICACRYPT 2013. AFRICACRYPT 2013. Lecture Notes in Computer Science, vol 7918. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38553-7_16
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DOI: https://doi.org/10.1007/978-3-642-38553-7_16
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