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Private set intersection: New generic constructions and feasibility results

  • * Corresponding author

    * Corresponding author 
The first three and the last author were partially supported by the Spanish Ministerio de Economía y Competitividad through the project grant MTM-2010-15167. This research is also partially supported by the Italian PRIN project GenData 2020.
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  • In this paper we focus on protocols for private set intersection (PSI), through which two parties, each holding a set of inputs drawn from a ground set, jointly compute the intersection of their sets. Ideally, no further information than which elements are actually shared is compromised to the other party, yet the input set sizes are often considered as admissible leakage.

    In the unconditional setting we evidence that PSI is impossible to realize and that unconditionally secure size-hiding PSI is possible assuming a set-up authority is present in an set up phase. In the computational setting we give a generic construction using smooth projective hash functions for languages derived from perfectly-binding commitments. Further, we give two size-hiding constructions: the first one is theoretical and evidences the equivalence between PSI, oblivious transfer and the secure computation of the AND function. The second one is a twist on the oblivious polynomial evaluation construction of Freedman et al. from EUROCRYPT 2004. We further sketch a generalization of the latter using algebraic-geometric techniques. Finally, assuming again there is a set-up authority (yet not necessarily trusted) we present very simple and efficient constructions that only hide the size of the client's set.

    Mathematics Subject Classification: Primary: 94A60; Secondary: 68P99.


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  • Figure 1.  An unconditionally secure size-hiding set intersection protocol

    Figure 2.  A generic PSI protocol from smooth projective hashing

    Figure 3.  A computationally secure size-hiding set intersection protocol

    Figure 4.  OT protocol based on trapdoor permutations

    Figure 5.  Polynomial-based construction for $|\mathcal{C}|,|\mathcal{S}| \le M$

    Figure 6.  Algebraic PSI construction for $|\mathcal{C}|,|\mathcal{S}| \le M$

    Figure 7.  The PRF-PSI-protocol

    Figure 8.  Setup phase of the OPRF-PSI-protocol

    Table 1.  Performance comparison of SPH-based implementations vs prior public key implementations for PSI

    Protocol Comm. Overhead Server Exp. Client Exp.
    [20] $\mathcal{O}(v + w)$ $\mathcal{O}(w(\log\log v))$ $\mathcal{O}(w+v)$
    [31] $\mathcal{O}(w +v)$ $\mathcal{O}(vw)$ $\mathcal{O}(v+w)$
    SPH-DDH $\mathcal{O}(vw)$ $\mathcal{O}(vw)$ $\mathcal{O}(v)$
     | Show Table
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