On optimal bounds for separating hash families
On optimal bounds for separating hash families
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发表时间：
2009
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通讯作者：
Marjan Bazrafshan;T. Trung
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作者：
Marjan Bazrafshan;T. Trung
本文讨论了分离{1，w}和{2，2}型散列族的最佳界和构造。我们首先证明了最佳界限分离哈希家庭类型{1，w}和家庭实现的界限显示建设。作为一个副产品的结果，我们得到了一个肯定的答案，提出了一个问题，布莱克本，Etzion，Stinson和Zaverucha最近。接下来，我们研究分离具有少量符号的{2，2}类型的哈希族的最佳界限。然后，我们证明了新的强界的一般情况下的类型{2，2}。本文展示了一个通用的结构，分离哈希家庭的类型{2，2}，这表明了新的界限的强度。
This paper concerns optimal bounds and constructions for separating hash families of type {1, w} and {2, 2}. We first prove optimal bounds for separating hash families of type {1, w} and show constructions of families achieving the bounds. As a by-product of the results we obtain a positive answer to a question put by Blackburn, Etzion, Stinson and Zaverucha recently. Next we study optimal bounds for separating hash families of type {2, 2} having a small number of symbols. We then prove new strong bounds for the general case of type {2, 2}. The paper exhibits a generic construction of separating hash families of type {2, 2} which shows the strength of the new bounds.