Authenticating humans to computers remains a notable weak point in computer security despite decades of effort. Although the security research community has explored dozens of proposals for replacing or strengthening passwords, they appear likely to remain entrenched as the standard mechanism of human-computer authentication on the Internet for years to come. Even in the optimistic scenario of eliminating passwords from most of today's authentication protocols using trusted hardware devices or trusted servers to perform federated authentication, passwords will persist as a means of "last-mile" authentication between humans and these trusted single sign-on deputies. This dissertation studies the difficulty of guessing human-chosen secrets, introducing a sound mathematical framework modeling human choice as a skewed probability distribution. We introduce a new metric, alpha-guesswork, which can accurately models the resistance of a distribution against all possible guessing attacks. We also study the statistical challenges of estimating this metric using empirical data sets which can be modeled as a large random sample from the underlying probability distribution. This framework is then used to evaluate several representative data sets from the most important categories of human-chosen secrets to provide reliable estimates of security against guessing attacks. This includes collecting the largest-ever corpus of user-chosen passwords, with nearly 70 million, the largest list of human names ever assembled for research, the largest data sets of real answers to personal knowledge questions and the first data published about human choice of banking PINs. This data provides reliable numbers for designing security systems and highlights universal limitations of human-chosen secrets.
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