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We introduce password strength information signaling as a novel, yet counter-intuitive, defense mechanism against password cracking attacks. 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 their hash value with the stolen hash from a breached authentication server. The attacker is limited only by the resources he is willing to invest. 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., the attacker's profit is given by the value of the cracked passwords minus the total guessing cost. 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. As a proof-of-concept, 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.