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Let $F(x_1,…,x_n)\mapsto(y_1,…,y_n)$ be some arbitrary computable function.

Suppose there are $n$ parties, where each party $i$ encrypt its message $m_i$ with a public key $\mathrm{pk}_i$ and obtain $c_i$. Is it possible for parties to execute a secure multi party computation $A$ with the same functionality as $F$, such that $A(c_1,…,c_n)=(c'_1,…,c'_n)$ where $c'_i = E_{\mathrm{pk}_i}(y_i)$ over public ledger (any public platform), so that no information is leaked during the execution?

I though it may be possible using fully homomorphic encryption as it can evaluate every circuit, though we have now several public key, so I am not sure if that's possible.

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    $\begingroup$ So I edited the question to be more formal. Public ledger can be any public blackboard where everyone see each step of the computation. $\endgroup$
    – Doron
    Commented Sep 14, 2022 at 18:31
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    $\begingroup$ You might be interested in Multi-key FHE. $\endgroup$
    – Mark Schultz-Wu
    Commented Sep 14, 2022 at 20:18
  • $\begingroup$ Thanks @Mark, that indeed seems promising. $\endgroup$
    – Doron
    Commented Sep 15, 2022 at 10:37

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