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We introduce password strength signaling as a potential defense against password cracking. Recent breaches have exposed billions of user passwords to the dangerous threat of offline password cracking attacks. An offline attacker can quickly check millions (or sometimes billions/trillions) of password guesses by comparing a candidate password’s hash value with a stolen hash from a breached authentication server. The attacker is limited only by the resources he is willing to invest. We explore the feasibility of applying ideas from Bayesian Persuasion to password authentication. Our key idea is to have the authentication server store a (noisy) signal about the strength of each user password for an offline attacker to find. Surprisingly, we show that the noise distribution for the signal can often be tuned so that a rational (profit-maximizing) attacker will crack fewer passwords. The signaling scheme exploits the fact that password cracking is not a zero-sum game i.e., it is possible for an attacker to increase their profit in a way that also reduces the number of cracked passwords. Thus, a well-defined signaling strategy will encourage the attacker to reduce his guessing costs by cracking fewer passwords. We use an evolutionary algorithm to compute the optimal signaling scheme for the defender. We evaluate our mechanism on several password datasets and show that it can reduce the total number of cracked passwords by up to 12% (resp. 5%) of all users in defending against offline (resp. online) attacks. While the results of our empirical analysis are positive we stress that we view the current solution as a proof-of-concept as there are important societal concerns that would need to be considered before adopting our password strength signaling solution.