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I was thinking of the problem of naming&shaming, victims don't want to reveal themselves. Yet the public wants to know, and have some confidence in the veracity of statements. Such confidence could arise for instance from multiple victims naming the same person. I was thinking cryptography could come to the rescue.

I'm having trouble even in the formal definition part. Initially I though multi party computation could allow a group of people to each name (or not) and only if a name passes a threshold is it revealed, and all members of the group could attest the name passed the threshold. But thinking of practice issues, we may want a async process, where after setup different people submit their testimony separately with minimal back and forth. We may not know in advance who will participate and want to be able to work with a subset members. The minimal number of people to ensure reasonable anonymity is rather small say 100, but we may want to increase the requirement significantly if we are thinking about minimum number of colluding members to reveal which specific member named someone.

I quickly run into impossibilities, If we allow ad-hoc groups to form and vote together then a not so large malicious group could break anonymity. I'm looking for a solvable variant of this problem.

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    $\begingroup$ So, how is this different from voting? You want the votes to disappear if they don't pass a threshold? $\endgroup$ – Elias Jan 23 '18 at 10:29
  • $\begingroup$ yes, we want the votes to disappear if they don't have a threshold. $\endgroup$ – Meir Maor Jan 23 '18 at 11:17
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There is a very recent paper that solves this problem at a large scale using secure computation techniques:

How to (not) share a password: Privacy preserving protocols for finding heavy hitters with adversarial behavior: Moni Naor, Benny Pinkas, Eyal Ronen

They motivate the problem from the point of view of passwords (they want to identify passwords that are too common), but it seems like the same problem you propose.

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    $\begingroup$ This isn't much more than a link only answer. Can you add more details? $\endgroup$ – mikeazo Jan 23 '18 at 21:10
  • $\begingroup$ It took me a bit to find time to read the paper itself, almost too good to be true. Very cool result. $\endgroup$ – Meir Maor Jan 24 '18 at 19:34
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    $\begingroup$ It does however allow for low probavility false positives,more problematic for shaming the password heavy hitters. But it also gives some relevant references I haven't yet gone through. $\endgroup$ – Meir Maor Jan 24 '18 at 19:44

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