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It is a well known fact that user-chosen passwords are somewhat predictable: by using tools such as dictionaries or probabilistic models, attackers and password recovery tools can drastically reduce the number of attempts needed to guess a password. Quite surprisingly, however, existing literature does not provide a satisfying answer to the following question: given a number of guesses, what is the probability that a state-of-the-art attacker will be able to break a password? To answer the former question, we compare and evaluate the effectiveness of currently known attacks using various datasets of known passwords. We find that a "diminishing returns" principle applies: in the absence of an enforced password strength policy, weak passwords are common; on the other hand, as the attack goes on, the probability that a guess will succeed decreases by orders of magnitude. Even extremely powerful attackers won't be able to guess a substantial percentage of the passwords. The result of this work will help in evaluating the security of authentication means based on user- chosen passwords, and our methodology for estimating password strength can be used as a basis for creating more effective proactive password checkers for users and security auditing tools for administrators.