Practical Multi-party Private Set Intersection from Symmetric-Key Techniques

\begin{algorithm}
  \small
  \caption{Zero Sharing Protocol}
  \begin{algorithmic}[1]
    There are $n$ parties $P_1,\cdots,P_n$. There is a PRF $F:\{0,1\}^{\kappa}\times \{0,1\}^{\ell}\rightarrow\{0,1\}^{\kappa}$.

    Protocol:
    \begin{enumerate}
      \item Each party $P_i$ picks a random seed $r_{i,j}$ for $j\in [i+1,n]$ and sends $r_{i,j}$ to $P_j$.
      \item Compute $S(K_i,x) = \left(\oplus\limits_{j=1}^{i-1}F(r_{j,i},x)\right)\oplus \left(\oplus\limits_{j=i+1}^n F(r_{i,j},x)\right)$
    \end{enumerate}
  \end{algorithmic}
\end{algorithm}