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It wouldn't be a strong signature, it would simply be the other half of the number pair. Numbers A and B both have easy access to A:B and B:A.

The hashes for a given user could still be attacked using their phone number, but a global table wouldn't work.

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That's clever. You can then even improve the algorithm by only sending the hash of A:B for every phone number, where A < B (numerically). Then you don't have to worry about whether it's Friend:Local or Local:Friend.

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