Why Botnets Work: Distributed Brute-Force Attacks Need No Synchronization
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In September 2017, McAffee Labs quarterly report estimated that brute force attacks represent 20 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 password queries (guesses) before the correct one is found in an optimal attack, which is a direct surrogate for the time and the computational effort. We model the lack of synchronization by a worst-case optimization in which the queries are received in the worst possible order, 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.
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