A Study of Probabilistic Password Models

A probabilistic password model assigns a probability value to each string. Such models are useful for research into understanding what makes users choose more (or less) secure passwords, and for constructing password strength meters and password cracking utilities. Guess number graphs generated from password models are a widely used method in password research. In this paper, we show that probability-threshold graphs have important advantages over guess-number graphs. They are much faster to compute, and at the same time provide information beyond what is feasible in guess-number graphs. We also observe that research in password modeling can benefit from the extensive literature in statistical language modeling. We conduct a systematic evaluation of a large number of probabilistic password models, including Markov models using different normalization and smoothing methods, and found that, among other things, Markov models, when done correctly, perform significantly better than the Probabilistic Context-Free Grammar model proposed in Weir et al., which has been used as the state-of-the-art password model in recent research.