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An efficient elliptic curve scalar multiplication algorithm against side channel attacks

Shichun Pang, Shouyu Tong, Fuzong Cong, Haiyan Qiu

Open publisher page 3 citations

Abstract

This paper proposes a fast elliptic curve scalar multiplication algorithm applicable for any types of curves over finite fields. A new mixed coordinates strategy is proposed, which significantly reduces the number of basic operations needed for elliptic curve point addition formulas. A particular kind of addition chains,which involving only additions, is proposed and this provides a natural protection against side channel attacks. Algorithm improves efficiency by taking advantage of combination of the chosen mixed coordinates strategy and the structure of addition chains.

About this research paper

What this paper is about

This paper proposes a fast elliptic curve scalar multiplication algorithm applicable for any types of curves over finite fields. A new mixed coordinates strategy is proposed, which significantly reduces the number of basic operations needed for elliptic curve point addition formulas. A particular kind of addition chains,which involving only additions, is proposed and this provides a natural protection against side channel attacks. Algorithm improves efficiency by taking advantage of combination of the chosen mixed coordinates strategy and the structure of addition chains.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper proposes a fast elliptic curve scalar multiplication algorithm applicable for any types of curves over finite fields. A new mixed coordinates strategy is proposed, which significantly reduces the number of basic operations needed for elliptic curve point addition formulas. A particular kind of addition chains,which involving only additions, is proposed and this provides a natural protection against side channel attacks. Algorithm improves efficiency by taking advantage of combination of the chosen mixed coordinates strategy and the structure of addition chains.

Key concepts: Scalar multiplication, Side channel attack, Elliptic curve point multiplication, Elliptic curve, Scalar (mathematics), Tripling-oriented Doche–Icart–Kohel curve, Hessian form of an elliptic curve, Homogeneous coordinates

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