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Consider the problem of guessing the realization of a random vector$\textbf{X}$ by repeatedly submitting queries (guesses) of the form "Is$\textbf{X}$ equal to $\textbf{x}$?" until an affirmative answer is obtained.In this setup, a key figure of merit is the number of queries required untilthe right vector is identified, a number that is termed the \emph{guesswork}.Typically, one wishes to devise a guessing strategy which minimizes a certainguesswork moment.  In this work, we study a universal, decentralized scenario where the guesserdoes not know the distribution of $\textbf{X}$, and is not allowed to use astrategy which prepares a list of words to be guessed in advance, or evenremember 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 apassword or decrypt a message, yet cannot coordinate the guesses between themor even know how many bots actually participate in the attack.  We devise universal decentralized guessing strategies, first, for memorylesssources, and then generalize them for finite-state sources. In each case, wederive the guessing exponent, and then prove its asymptotic optimality byderiving a compatible converse bound. The strategies are based on randomizedguessing using a universal distribution. We also extend the results to guessingwith side information. Finally, for all above scenarios, we design efficientalgorithms in order to sample from the universal distributions, resulting instrategies which do not depend on the source distribution, are efficient toimplement, and can be used asynchronously by multiple agents.

Universal Randomized Guessing with Application to Asynchronous Decentralized Brute-Force Attacks