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I will first restate the question as I understand it after the clarifying comment. If I'm misunderstanding something, please let me know. Let $M$ be a set of size $n$. There are two parties $A$ and $B$. We are looking for a protocol that does the following. $A$ chooses a subset $N\subseteq M$ with $|N|=2n/3$ and computes some message $m$ with $|m|=\ell$, ...

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