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首页> 外文期刊>Information Theory, IEEE Transactions on >Multi-User Guesswork and Brute Force Security
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Multi-User Guesswork and Brute Force Security

机译：多用户猜测和蛮力安全性

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摘要

The guesswork problem was originally motivated by a desire to quantify computational security for single user systems. Leveraging recent results from its analysis, we extend the remit and utility of the framework to the quantification of the computational security of multi-user systems. In particular, assume that users independently select strings stochastically from a finite, but potentially large, list. An inquisitor who does not know which strings have been selected wishes to identify of them. The inquisitor knows the selection probabilities of each user and is equipped with a method that enables the testing of each (user, string) pair, one at a time, for whether that string had been selected by that user. Here, we establish that, unless , there is no general strategy that minimizes the distribution of the number of guesses, but in the asymptote as the strings become long we prove the following: by construction, there is an asymptotically optimal class of strategies; the number of guesses required in an asymptotically optimal strategy satisfies a large deviation principle with a rate function, which is not necessarily convex, that can be determined from the rate functions of optimally guessing individual users’ strings; if all users’ selection statistics are identical, the exponential growth rate of the average guesswork as the string-length increases is determined by the specific Rényi entropy of the string-source with parameter , generalizing the known case; and that the Shannon entropy of the source is a lower bound on the average guesswork gr- wth rate for all and , thus providing a bound on computational security for multi-user systems. Examples are presented to illustrate these results and their ramifications for systems design.
机译：猜测问题最初是由量化单个用户系统的计算安全性的愿望引起的。利用最近的分析结果，我们将框架的职权范围和实用性扩展到了多用户系统的计算安全性的量化。特别是，假设用户从有限但可能很大的列表中随机随机选择字符串。不知道选择了哪些字符串的查询者希望识别它们。查询者知道每个用户的选择概率，并配备了一种方法，可以一次测试每个（用户，字符串）对，以检查该用户是否选择了该字符串。在这里，我们确定，除非，没有通用的策略使猜测数目的分布最小化，但是随着字符串的变长，在渐近线中，我们证明了以下内容：通过构造，存在渐近最优的策略类别；渐近最优策略所需的猜测次数满足一个大偏差原理，该比率函数具有不一定是凸的速率函数，该速率函数可以通过最佳猜测单个用户字符串的速率函数来确定。如果所有用户的选择统计都相同，则随着字符串长度的增加，平均猜测的指数增长率取决于带有参数的字符串源的特定Rényi熵，并推导已知情况；并且源的香农熵是所有和的平均猜测增长率的下界，从而为多用户系统的计算安全性提供了界限。举例说明了这些结果及其对系统设计的影响。

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