  Consider a sub-population of rebels that wish to initiate a revolution. In
order to avoid initializing a failed revolution, rebels would first strive to
estimate their relative "power", which is often correlated with their fraction
in the population. However, and especially in non-democratic countries, rebels
refrain from disclosing themselves. This poses a significant challenge for
rebels: estimating their fraction in the population while minimizing the risk
of being identified as rebels. This paper introduces a distributed computing
framework aiming to study this question. Our main takeaway message is that the
communication pattern has a crucial role in achieving such a task.
Specifically, we show that relying on the inherent noise in the communication,
"public communication", characterized by the fact that each message announced
by an individual can be viewed by all its neighbors, allows rebels to estimate
their fraction in the population while keeping a negligible risk of each rebel
being identified as such. The suggested estimation protocol, inspired by
historical events, is extremely simple and can be executed covertly even under
extreme conditions of surveillance. Conversely, we show that under peer-to-peer
communication, protocols of similar simplicity are either inefficient or
non-covert.
