Choosing Coordinate Forms for Solving ECDLP Using Shor's Algorithm
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916854809755648 |
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| author | Huang, Yan Zhang, Fangguo Gao, Fei Zhou, Zijian Qu, Longjiang |
| author_facet | Huang, Yan Zhang, Fangguo Gao, Fei Zhou, Zijian Qu, Longjiang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_12441 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Choosing Coordinate Forms for Solving ECDLP Using Shor's Algorithm Huang, Yan Zhang, Fangguo Gao, Fei Zhou, Zijian Qu, Longjiang Cryptography and Security 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. |
| title | Choosing Coordinate Forms for Solving ECDLP Using Shor's Algorithm |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2502.12441 |