An attacker who breaks into an authentication server and steals all of the cryptographic password hashes is able to mount an offline-brute force attack against each user's password. Offline brute-force attacks against passwords are increasingly commonplace and the danger is amplified by the well documented human tendency to select low-entropy password and/or reuse these passwords across multiple accounts. Moderately hard password hashing functions are often deployed to help protect passwords against offline attacks by increasing the attacker's guessing cost. However, there is a limit to how "hard" one can make the password hash function as authentication servers are resource constrained and must avoid introducing substantial authentication delay. Observing that there is a wide gap in the strength of passwords selected by different users we introduce DAHash (Distribution Aware Password Hashing) a novel mechanism which reduces the number of passwords that an attacker will crack. Our key insight is that a resource-constrained authentication server can dynamically tune the hardness parameters of a password hash function based on the (estimated) strength of the user's password. We introduce a Stackelberg game to model the interaction between a defender (authentication server) and an offline attacker. Our model allows the defender to optimize the parameters of DAHash e.g., specify how much effort is spent in hashing weak/moderate/high strength passwords. We use several large scale password frequency datasets to empirically evaluate the effectiveness of our differentiated cost password hashing mechanism. We find that the defender who uses our mechanism can reduce the fraction of passwords that would be cracked by a rational offline attacker by up to 15%.
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