哈希块源的严格边界
Tight Bounds for Hashing Block Sources
摘要：
已知如果2-通用散列函数$H$被应用于{ \em块源} $(X_1,...,X_T)$的元素，其中每个项目$X_i$具有以先前项目为条件的足够的最小熵，则输出分布$(H,H(X_1),...,H(X_T))$将“接近”均匀分布。我们提供了改进的边界上有多少最小熵每个项目是需要这个举行，无论是当我们要求输出接近均匀的统计距离，当我们只要求它在统计上接近一个小碰撞概率的分布。在这两种情况下，我们减少的最小熵的项目数$T$从$2\log T$在以前的工作中的$\log T$，我们证明是最佳的依赖。当数据项来自块源时，这导致对Mitzenmacher和Vadhan（SODA '08）关于基于散列的算法和数据结构的分析的最近结果的相应改进。
英文摘要：
It is known that if a 2-universal hash function $H$ is applied to elements of a {\em block source} $(X_1,...,X_T)$, where each item $X_i$ has enough min-entropy conditioned on the previous items, then the output distribution $(H,H(X_1),...,H(X_T))$ will be ``close'' to the uniform distribution. We provide improved bounds on how much min-entropy per item is required for this to hold, both when we ask that the output be close to uniform in statistical distance and when we only ask that it be statistically close to a distribution with small collision probability. In both cases, we reduce the dependence of the min-entropy on the number $T$ of items from $2\log T$ in previous work to $\log T$, which we show to be optimal. This leads to corresponding improvements to the recent results of Mitzenmacher and Vadhan (SODA `08) on the analysis of hashing-based algorithms and data structures when the data items come from a block source.
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