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Period tracking app refuses to disclose data to American authorities
(www.newsweek.com)
This is a most excellent place for technology news and articles.
They could do it by not uploading any of the data, or if they do, uploading it encrypted with the only key being on the user's device or a passcode.
Both are well established ways to secure data, but the company itself would not be able to interact with the data at all past storing it, so any features/revenue there would end.