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The Signal client establishes a normal TLS connection with the proxy, and the proxy simply forwards any bytes it receives to the actual Signal service. Any non-Signal traffic is blocked. Additionally, the Signal client still negotiates its standard TLS connection with the Signal endpoints through the tunnel.
This means that in addition to the end-to-end encryption that protects everything in Signal, all traffic remains opaque to the proxy operator.
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Probably helpful context: [Help people in Iran reconnect to Signal – a request to our community] https://signal.org/blog/run-a-proxy/
And the people that are protesting and hurting right now are not the most tech savvy one - so expect a lot of naivete about opsec. I doubt that the majority of them even know signal exists.