Choosing Coordinate Forms for Solving ECDLP Using Shor's Algorithm
Abstract
Shor's algorithm is well-known for its capability to address the elliptic curve discrete logarithm problem (ECDLP) in polynomial time. The enhancement of its quantum resources continues to be a crucial focus of research. Nevertheless, the application of projective coordinates for quantum resource optimization remains an unresolved issue, mainly because the representation of projective coordinates lacks uniqueness without employing modular division operations. Our study reveals that projective coordinates do not provide the same advantages as affine coordinates when utilizing Shor's method to tackle the ECDLP.
Cite
@article{arxiv.2502.12441,
title = {Choosing Coordinate Forms for Solving ECDLP Using Shor's Algorithm},
author = {Yan Huang and Fangguo Zhang and Fei Gao and Zijian Zhou and Longjiang Qu},
journal= {arXiv preprint arXiv:2502.12441},
year = {2025}
}
Comments
The primary concerns lie in the limited significance and novelty. While the paper explores the use of projective coordinates, quantum resource requirements are worse than those achieved with previously studied affine coordinates, as carefully documented in the manuscript