  Third-party cookies have been a privacy concern since cookies were first
developed in the mid 1990s, but more strict cookie policies were only
introduced by Internet browser vendors in the early 2010s. More recently, due
to regulatory changes, browser vendors have started to completely block
third-party cookies, with both Firefox and Safari already compliant.
  The Topics API is being proposed by Google as an additional and less
intrusive source of information for interest-based advertising (IBA), following
the upcoming deprecation of third-party cookies. Initial results published by
Google estimate the probability of a correct re-identification of a random
individual would be below 3% while still supporting IBA.
  In this paper, we analyze the re-identification risk for individual Internet
users introduced by the Topics API from the perspective of Quantitative
Information Flow (QIF), an information- and decision-theoretic framework. Our
model allows a theoretical analysis of both privacy and utility aspects of the
API and their trade-off, and we show that the Topics API does have better
privacy than third-party cookies. We leave the utility analyses for future
work.
