An Improved Entropy Measure for Web Browser Fingerprinting Risk

Browser fingerprinting is the practice of tracking users across the Web by collecting attributes from their devices and combining them to create unique identifiers. This practice poses major privacy risks to users, and more than a decade of research has quantified fingerprinting risks due to various attributes, leading browser developers to implement many privacy-enhancing changes. Early work used Shannon entropy to quantify risks. However, Shannon entropy can grow with dataset size, limiting the ability to compare datasets and results. Researchers then introduced normalized entropy as a measure for comparing browser fingerprinting datasets of different sizes and numerous works followed using normalized entropy for this purpose.

We identify and address a resulting problem in the fingerprinting literature. We show normalized entropy is ill-suited to compare datasets of different sizes — it decreases as dataset size increases. We show this both analytically and empirically, leveraging a recently published dataset of browser attributes commonly used for fingerprinting.
Given the unmet need for a better fingerprinting risk measure, we define a minimal set of desired properties for such a measure: scale-invariance, monotonicity and estimability. We then propose to use Tsallis entropy as a more interpretable fingerprinting risk measure. We evaluate Shannon, normalized, and Tsallis entropy with respect to the properties, and prove that only Tsallis entropy satisfies all of them.