Semi-Finite Length Analysis for Secure Random Number Generation
Semi-Finite Length Analysis for Secure Random Number Generation
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DOI：
10.1109/isit.2019.8849241
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发表时间：
2019-07
期刊：
影响因子：
--
通讯作者：
Masahito Hayashi
中科院分区：
文献类型：
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作者：
Masahito Hayashi
为了讨论从不完美随机数生成安全密钥，我们讨论安全密钥生成长度。有几项关于其渐近展开到 $\sqrt n $ 或 log n 阶的研究。然而，这些展开式具有 $o\left( {\sqrt n } \right)$ 或 o(logn) 数量级的错误，并且不会渐近趋于零。为了解决这个问题，我们将这些最优值的上限和下限推导出至常数阶。虽然上键和下键的展开式不匹配，但它们澄清了这些最优值的范围，其误差渐近趋于零。
To discuss secure key generation from imperfect random numbers, we address the secure key generation length. There are several studies for its asymptotic expansion up to the order $\sqrt n $ or log n. However, these expansions have errors of the order $o\left( {\sqrt n } \right)$ or o(logn), which does not go to zero asymptotically. To resolve this problem, we derive the asymptotic expansion up to the constant order for upper and lower bounds of these optimal values. While the expansions of upper and lower bonds do not match, they clarify the ranges of these optimal values, whose errors go to zero asymptotically.