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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.09605 |
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| _version_ | 1866915337296936960 |
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| author | Zhuang, Jincheng Cheng, Qi |
| author_facet | Zhuang, Jincheng Cheng, Qi |
| contents | The principal ideal problem constitutes a fundamental problem in algebraic number theory and has attracted significant attention due to its applications in ideal lattice based cryptosystems. Efficient quantum algorithm has been found to address this problem. The situation is different in the classical computational setting. In this work, we delve into the relationship between the principal ideal problem and the class field computation. We show that the decision version of the problem can be solved efficiently if the class group is smooth, after pre-computation has been completed to collect information about the Hilbert class field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09605 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the Decision Principal Ideal Problem with Pre-processing Zhuang, Jincheng Cheng, Qi Number Theory 11T71, 11Y40 The principal ideal problem constitutes a fundamental problem in algebraic number theory and has attracted significant attention due to its applications in ideal lattice based cryptosystems. Efficient quantum algorithm has been found to address this problem. The situation is different in the classical computational setting. In this work, we delve into the relationship between the principal ideal problem and the class field computation. We show that the decision version of the problem can be solved efficiently if the class group is smooth, after pre-computation has been completed to collect information about the Hilbert class field. |
| title | Solving the Decision Principal Ideal Problem with Pre-processing |
| topic | Number Theory 11T71, 11Y40 |
| url | https://arxiv.org/abs/2506.09605 |