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Unconditional zero-sharing was presented in the following paper

Practical Multi-party Private Set Intersection from Symmetric-Key Techniques, by Vladimir Kolesnikov, Naor Matania, Benny Pinkas, Mike Rosulek, Ni Trieu

Unconditional zero-sharing allows all parties to obtain a share corresponding to each element in their set using the technique of zero-sharing.If they have a common element $x$,the sum of their corresponding shares equals $0$. Based on the above facts,I wonder if it is correct to directly obtain the final intersection by using only zero-sharing technique?

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  • $\begingroup$ If it was possible to easily get PSI from zero-sharing, without much extra effort, then I guess those authors would have done it? $\endgroup$
    – Mikero
    Commented Jan 13 at 17:40
  • $\begingroup$ Thanks for your response！I know that doing this should have issues, but I haven’t figured out what the problem is, or I’m not clear about the reason why the authors didn’t do it this way. $\endgroup$
    – Rui T.
    Commented Jan 14 at 13:23

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Did you read the paper NTY21? [NTY21] designed the zero-XOR protocol that includes zero-sharing and OPPRF. For $P_1$, OPPRF is used to get the other parties' share. If you don't use OPPRF to get the share, $P_1$ can't map the element $x$ to its corresponding share.

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  • $\begingroup$ I think the key point is that using OPPRF/OKVS can bind the element and its corresponding share. $\endgroup$
    – fixedpoint
    Commented Mar 14 at 6:41

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