Abstract

GLV method is an important research direction to accelerate the scalar multiplication on classes of elliptic curves with efficiently computable endomorphisms, which can reduce the number of doublings by using Straus-Shamir simultaneous multi-scalar multiplication technique. Researchers explore to generalize the method to higher dimension, and then evaluate the effect of accelerating the scalar multiplication. In this paper, we consider various multi-scalar multiplication algorithms, and analyze the computational cost of scalar multiplication under different dimensions to select the optimal multi-scalar multiplication algorithm and parameters. On this basis, the multi-scalar multiplication algorithm is applied to the GLV method, and the computational cost of scalar multiplication is analyzed. Higher dimension usually means fewer doublings, but more precomputation, there is a trade-off. The analysis results show that the limit of GLV method to accelerate the scalar multiplication is dimension 8, and the GLV method will lose its effect of speedup for higher dimension. In particular, dimension 3 or 4 may be the optimal choice for the case that resource constrained or the cost of endomorphism is large.

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