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Measuring Password Strength Using Expectation Entropy


Core Concepts
Expectation entropy is a newly developed metric that can estimate the strength of any random or random-like password on the same scale as entropy estimation tools, providing a more informative and practical measure of password security.
Abstract
The article presents a newly developed metric called "Expectation entropy" that can be used to estimate the strength of random or random-like passwords. The classical combinatorics-based password strength formula provides a result in bits, while the NIST Entropy Estimation Suite gives a result between 0 and 1 for min-entropy. The authors define four disjoint character sets (lowercase letters, uppercase letters, digits, and symbols) and calculate the expectation of a character appearing in a password based on the probability of each character set. They then express the Expectation entropy as the logarithm of the expected character value divided by the maximum entropy of the total character space. The authors evaluate the Expectation entropy using two datasets: 100,000 randomly generated passwords of varying lengths, and three publicly leaked password databases (LinkedIn, 10Million, and WPA2). The results show that the Expectation entropy value increases or decreases according to the length of the password and satisfies the theoretical bounds. The publicly leaked databases mostly contain passwords with short lengths and characters not chosen from all character sets, resulting in low Expectation entropy values. The authors conclude that having an Expectation entropy of a certain value, e.g., 0.4, means that an attacker has to exhaustively search at least 40% of the total number of guesses to find the password using brute-force.
Stats
The total character space K has a cardinality of |K| = 94, consisting of 26 lowercase letters, 26 uppercase letters, 10 digits, and 32 symbols.
Quotes
"Having an Expectation entropy of a certain value, for example, 0.4 means that an attacker has to exhaustively search at least 40% of the total number of guesses to find the password using brute-force."

Key Insights Distilled From

by Khan Reaz,Ge... at arxiv.org 04-29-2024

https://arxiv.org/pdf/2404.16853.pdf
Expectation Entropy as a Password Strength Metric

Deeper Inquiries

How could the Expectation entropy metric be extended to consider the context and user behavior in password selection, beyond just the character composition?

The Expectation entropy metric, while effective in evaluating the strength of a password based on character composition, can be extended to incorporate additional factors such as context and user behavior in password selection. One way to achieve this is by introducing weighting factors for different character sets based on common patterns observed in user-generated passwords. For example, if certain character combinations are frequently used by users, they could be assigned lower weights in the entropy calculation, as they may be more easily guessed by attackers. Additionally, considering the context in which the password is used, such as the specific application or system, could lead to the adjustment of entropy values based on the sensitivity of the data being protected. By integrating these contextual and behavioral aspects into the entropy calculation, the metric can provide a more comprehensive assessment of password strength tailored to individual user habits and security requirements.

What are the potential limitations or edge cases of the Expectation entropy approach, and how could it be further refined or combined with other password strength estimation methods?

One potential limitation of the Expectation entropy approach is its reliance on the assumption of uniform randomness in character selection, which may not always reflect real-world password creation patterns. Users tend to exhibit biases towards certain characters or patterns, leading to deviations from the expected uniform distribution. To address this limitation, the Expectation entropy metric could be refined by incorporating data-driven insights from password databases to adjust the probabilities of character occurrence based on observed patterns. Additionally, the metric could be combined with machine learning algorithms to analyze and adapt to evolving user behavior in password selection, enhancing its accuracy and relevance over time. By integrating these refinements and complementary approaches, the Expectation entropy metric can better account for the complexities and nuances of password creation, improving its effectiveness in assessing password strength.

How might the Expectation entropy concept be applied to other security-related domains beyond just password strength estimation, such as cryptographic key generation or random number evaluation?

The concept of Expectation entropy can be extended beyond password strength estimation to various other security-related domains, including cryptographic key generation and random number evaluation. In the context of cryptographic key generation, Expectation entropy can be utilized to assess the randomness and unpredictability of key sequences, ensuring that cryptographic keys exhibit sufficient entropy to resist brute-force attacks. By applying the same principles of character composition and probability distribution, the metric can provide insights into the strength and security of generated keys, guiding the selection of robust cryptographic algorithms and key lengths. Moreover, in random number evaluation, Expectation entropy can be leveraged to quantify the unpredictability and entropy of random number sequences used in cryptographic protocols or secure communication channels. By analyzing the distribution and composition of random numbers, the metric can help identify potential vulnerabilities or weaknesses in random number generation processes, enhancing the overall security of cryptographic systems. Through its application in these diverse security domains, the Expectation entropy concept offers a versatile and valuable tool for assessing and enhancing security measures beyond password strength estimation.
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