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Head of the Signal app threatens to withdraw from Europe
(www.bluewin.ch)
This is a most excellent place for technology news and articles.
That makes the assumption you want to use your phone number at all. And I'm sure the overhead of encryption would break SMS due to the limits on character counts.
Can't use Signal without a phone number.
You CAN use it to interact with people without them knowing your number. The only current requirement is specific to registration.