Impact of Optimized Operations AB,AC and AB+CD in Scalar Multiplication over Binary Elliptic Curve

Christophe Negre 1, 2 Jean-Marc Robert 2, 1
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : 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.
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AFRICACRYPT: Cryptology in Africa, Jun 2013, Cairo, Egypt. 7th International Conference on Cryptology in Africa, LNCS (8469), pp.13-30, 2014, Progress in Cryptology – AFRICACRYPT 2014. 〈10.1007/978-3-642-38553-7_16〉
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Christophe Negre, Jean-Marc Robert. Impact of Optimized Operations AB,AC and AB+CD in Scalar Multiplication over Binary Elliptic Curve. AFRICACRYPT: Cryptology in Africa, Jun 2013, Cairo, Egypt. 7th International Conference on Cryptology in Africa, LNCS (8469), pp.13-30, 2014, Progress in Cryptology – AFRICACRYPT 2014. 〈10.1007/978-3-642-38553-7_16〉. 〈hal-00724785v2〉

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