Analyzing Password Strength: A Combinatorial Entropy Approach

Passwords have long served as a primary means for user authentication, facilitating access to restricted resources. The critical concern surrounding passwords lies in their quality or strength—determining how susceptible they are to being "guessed" by unauthorized entities attempting to gain entry by impersonating the legitimate user. In this research, we systematically examine diverse metrics assessing password quality, including a metric proposed within this study. Our investigation involves a comprehensive comparison of the strengths and weaknesses of these metrics, along with an exploration of the interrelationships among them. Furthermore, we present the outcomes of experiments designed to crack a set of passwords with varying quality levels. The results of these experiments demonstrate a notable positive correlation between the difficulty of guessing passwords and their overall quality. To provide a nuanced understanding, we employ a clustering analysis on the set of passwords, considering their quality measures as variables. This analysis reveals distinct groups based on password quality. Moreover, to bolster the strength of our passwords, we introduce the integration of a Combinatorial Entropy Calculation algorithm. This algorithm is designed to enhance password resilience by leveraging combinatorial methods. Through this combined approach, we aim to contribute to the broader discourse on password security and provide insights into developing more robust authentication practices.