<p>The prevalence of offline password attacks, resulting from attackers breaching authentication servers and stealing cryptographic password hashes, poses a significant threat. Users' tendency to select weak passwords and reuse passwords across multiple accounts, coupled with computation advancement,  further exacerbate the danger.</p> <p><br></p> <p>This dissertation addresses this issue by proposing password authentication mechanisms that aim to minimize the number of compromised passwords in the event of offline attacks, while ensuring that the server's workload remains manageable. Specifically, we present three mechanisms: (1) DAHash: This mechanism adjusts password hashing costs based on the strength of the underlying password. Through appropriate tuning of hashing cost parameters, the DAHash mechanism effectively reduces the fraction of passwords that can be cracked by an offline password cracker. (2) Password Strength Signaling: We explore the application of Bayesian Persuasion to password authentication. The 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. We demonstrate that by appropriately tuning the noise distribution for the signal, a rational attacker will crack fewer passwords. (3) Cost-Asymmetric Memory Hard Password Hashing: We extend the concept of password peppering to modern Memory Hard password hashing algorithms. We identify limitations in naive extensions and introduce the concept of cost-even breakpoints as a solution. This approach allows us to overcome these limitations and achieve cost-asymmetry, wherein the expected cost of validating a correct password is significantly smaller than the cost of rejecting an incorrect password.</p> <p><br></p> <p>When analyzing the behavior of a rational attacker it is important to understand the attacker’s guessing curve i.e., the percentage of passwords that the attacker could crack within a guessing budget B. Dell’Amico and Filippone introduced a Monte Carlo algorithm to estimate the guessing number of a password as well as an estimate for the guessing curve. While the estimated guessing number is accurate in expectation the variance can be large and the method does not guarantee that the estimates are accurate with high probability. Thus, we introduce Confident Monte Carlo as a tool to provide confidence intervals for guessing number estimates and upper/lower bound the attacker’s guessing curves.</p> <p><br></p> <p>Moreover, we extend our focus beyond classical attackers to include quantum attackers. We present a decision-theoretic framework that models the rational behavior of attackers equipped with quantum computers. The objective is to quantify the capabilities of a rational quantum attacker and the potential damage they could inflict, assuming optimal decision-making. Our framework can potentially contribute to the development of effective countermeasures against a wide range of quantum pre-image attacks in the future.</p>