(An) efficient implementation of elliptic curve point counting algorithm based on SST-algorithm with a GNB

Abstract

In this paper, we describe the implementation of the elliptic curve point counting algorithm of Kim et al.. We survey the algorithms including the SST-algorithm proposed by Satoh et al., We also described the modified SST-algorithm by Kim et al. using the Gaussian normal basis, which is of the lowest time complexity of $O(N^{2μ+\frac{1}{μ+1}})$ where $O(N^μ)$ is the complexity of multiplying two N-bit numbers. All algorithms which is required for its implementation is fully given. Every step is explained in detail, and the actual running time result is also included.