Alice and Bob engage to compute a secure function f(a,b) where a and b must be present in a set U. Although both Alice and Bob know f(a,b), how can Alice confirm that b is present in U and Bob confirm that a is present in U?

  • $\begingroup$ If Alice revealed all of what is allegedly her information to Bob, then how would Bob confirm that the revealed a is present in U? $\endgroup$ – user991 Nov 4 '15 at 8:34
  • $\begingroup$ They should engage in a zero-knowledge proof to prove the membership. $\endgroup$ – MH Samadani Nov 4 '15 at 13:48
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    $\begingroup$ Why not just use MPC to compute set membership? MPC can compute anything, right. Are you using the garbled circuit variant of MPC or the secret sharing variant? $\endgroup$ – mikeazo Nov 4 '15 at 14:15
  • $\begingroup$ Could you clarify the question? One way for Bob and Alice to prove they know A and B is to send a hash of A or B along (hashed with challenge bytes from the other side) $\endgroup$ – Zaphod1001 Nov 4 '15 at 15:32

Try reading this paper https://www.math.ucla.edu/~tdokos/notes_files/garbledCircuits.pdf. It will answer your question.

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