Delaying and Merging Operations in Scalar Multiplication: Applications to Curve-Based Cryptosystems

In this paper we introduce scalar multiplication algorithms for several classes of elliptic and hyperelliptic curves. The methods are variations on Yao's scalar multiplication algorithm where independent group operations are shown in an explicit way. We can thusmerge several group operations and reduce the number of field operations by means of Montgomery's trick. The results are that scalar multiplication on elliptic curves in even characteristic based on point halving can be improved by at least 10% and the performance of Koblitz curves by 25% to 32%.

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