An efficient elliptic curve scalar multiplication algorithm against side channel attacks

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.