在微小的概率格子上,列举
Yoshinori Aono1, Phong Q Nguyen2
1National Institute of Information and Communications Technology, 4-2-1, Nukui-Kitamachi, Koganei, 1848795 Tokyo Japan.
概括
这项研究表明,当高斯启发式失败时,修剪格子计数可能比预测慢,特别是在成功概率低的情况下. 研究人员提出了更新的成本预测和格子计数算法的下限.
科学领域:
- 计算数学是指计算数学.
- 数学理论是数的理论.
- 密码学 密码学 密码学 密码学
背景情况:
- 格子计数对于计算格子问题至关重要,使用基于树的算法.
- 现有的算法面临相对于格子排名的超指数时间复杂性.
- 极端修剪策略提供了指数加速度,但依赖于准确的成本预测.
研究的目的:
- 为了调查切割格子计数的实际成本超过预测成本的场景.
- 确定高斯启发式的失败是导致这种差异的原因.
- 建议修改成本预测和格子计数中的下限讨论.
主要方法:
- 分析在特定条件下修剪格子计数成本.
- 确定高斯启发式在预测格子点计数方面的失败.
- 修改成本预测模型的开发和更新下限讨论.
主要成果:
- 经过实践证明,剪裁计数成本远远超过预测的实际情况.
- 将这种差异与高斯启发式的失败联系在一起,因为在修剪时成功概率非常低.
- 拟议修订的下限在加密相关设置中是20-30倍大.
结论:
- 高斯启发式可以低估格子点计数,导致在削减的计数中不准确的成本预测.
- 将搜索区域限制在子空间中被确定为可能的原因.
- 更新的成本预测和下限是必要的,以便更可靠地分析削减格子计数.
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