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We introduce and evaluate various methods for purely automated attacks against PassPoints-style graphical passwords. For generating these attacks, we introduce a graph-based algorithm to efficiently create dictionaries based on heuristics such as click-order patterns (e.g., five points all along a line). Some of our methods combine click-order heuristics with focus-of-attention scan-paths generated from a computational model of visual attention, yielding significantly better automated attacks than previous work. One resulting automated attack finds 7%-16% of passwords for two representative images using dictionaries of approximately 226 entries (where the full password space is 243). Relaxing click-order patterns substantially increased the attack efficacy albeit with larger dictionaries of approximately 235 entries, allowing attacks that guessed 48%-54% of passwords (compared to previous results of 1% and 9% on the same dataset for two images with 235 guesses). These latter attacks are independent of focus-of-attention models, and are based on image-independent guessing patterns. Our results show that automated attacks, which are easier to arrange than human-seeded attacks and are more scalable to systems that use multiple images, require serious consideration when deploying basic PassPoints-style graphical passwords.