Consider the problem of guessing the realization of a random vector ${X}$ by repeatedly submitting queries (guesses) of the form “Is ${X}$ equal to ${x}$ ?” until an affirmative answer is obtained. In this setup, a key figure of merit is the number of queries required until the right vector is identified, a number that is termed the guesswork. Typically, one wishes to devise a guessing strategy which minimizes a certain guesswork moment. In this work, we study a universal, decentralized scenario where the guesser does not know the distribution of ${X}$ , and is not allowed to use a strategy which prepares a list of words to be guessed in advance, or even remember which words were already used. Such a scenario is useful, for example, if bots within a Botnet carry out a brute–force attack in order to guess a password or decrypt a message, yet cannot coordinate the guesses between them or even know how many bots actually participate in the attack. We devise universal decentralized guessing strategies, first, for memoryless sources, and then generalize them for finite–state sources. In each case, we derive the guessing exponent, and then prove its asymptotic optimality by deriving a compatible converse bound. The strategies are based on randomized guessing using a universal distribution. We also extend the results to guessing with side information. Finally, for all above scenarios, we design efficient algorithms in order to sample from the universal distributions, resulting in strategies which do not depend on the source distribution, are efficient to implement, and can be used asynchronously by multiple agents.

中文翻译：

---

通用随机猜测与异步分散暴力攻击的应用

考虑猜测一个随机向量的实现问题 ${X}$ 通过反复提交“是 ${X}$ 等于 ${x}$ ？” 直到得到肯定的答复。在这个设置中，一个关键的品质因数是在确定正确的向量之前所需的查询数量，这个数字被称为猜测. 通常，人们希望设计一种猜测策略来最小化某个猜测时刻。在这项工作中，我们研究了一个通用的、分散的场景，其中猜测者不知道 ${X}$ ，并且不允许使用预先准备要猜测的单词列表的策略，甚至不能记住哪些单词已经使用过。这种场景很有用，例如，如果僵尸网络中的机器人执行暴力攻击以猜测密码或解密消息，但无法协调它们之间的猜测，甚至无法知道实际有多少机器人参与了攻击. 我们首先针对无记忆源设计通用的分散猜测策略，然后将它们推广到有限状态源。在每种情况下，我们导出猜测指数，然后通过导出兼容逆界来证明其渐近最优性。这些策略基于使用通用分布的随机猜测。我们还将结果扩展到带有辅助信息的猜测。最后，对于上述所有场景，