Analysis of password authentication strength

Abstract

The article develops an approach to assessing the strength of password authentication based on numerical, probabilistic, and entropy metrics. For this purpose, mathematical expressions were formulated to determine the time required to crack a password using brute-force methods, as well as the probability of successfully guessing it within its validity period. The proposed formulas made it possible to identify the key parameters affecting password security, including length, alphabet size, character complexity, and password lifetime. Particular attention is paid to the analysis of password entropy according to Shannon and heuristic entropy recommended by NIST. Based on these approaches, criteria were established for determining whether a password can be considered resistant to attacks. To confirm the research results, examples of entropy calculations for different password lengths and alphabets were provided, along with statistical data on password usage in Google services. This made it possible to reveal that a significant number of users continue to employ overly simple combinations that are highly vulnerable to attacks. In addition, the article presents a comparative analysis of traditional approaches and modern methods for improving security. In particular, the integration of classical password-based methods with new technologies, such as graphical passwords and steganographic mechanisms based on digital watermarks, is proposed. This approach makes it possible to enhance the robustness of authentication systems and provide additional protection against unauthorized access to information resources.