  In September 2017, McAffee Labs quarterly report estimated that brute force
attacks represent 20\% of total network attacks, making them the most prevalent
type of attack ex-aequo with browser based vulnerabilities. These attacks have
sometimes catastrophic consequences, and understanding their fundamental limits
may play an important role in the risk assessment of password-secured systems,
and in the design of better security protocols. While some solutions exist to
prevent online brute-force attacks that arise from one single IP address,
attacks performed by botnets are more challenging. In this paper, we analyze
these distributed attacks by using a simplified model. Our aim is to understand
the impact of distribution and asynchronization on the overall computational
effort necessary to breach a system. Our result is based on Guesswork, a
measure of the number of queries (guesses) required of an adversary before a
correct sequence, such as a password, is found in an optimal attack. Guesswork
is a direct surrogate for time and computational effort of guessing a sequence
from a set of sequences with associated likelihoods. We model the lack of
synchronization by a worst-case optimization in which the queries made by
multiple adversarial agents are received in the worst possible order for the
adversary, resulting in a min-max formulation. We show that, even without
synchronization, and for sequences of growing length, the asymptotic optimal
performance is achievable by using randomized guesses drawn from an appropriate
distribution. Therefore, randomization is key for distributed asynchronous
attacks. In other words, asynchronous guessers can asymptotically perform
brute-force attacks as efficiently as synchronized guessers.
