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Would you mind telling me based on the attached file, why in case 3(corrupted client B), the authors did not use the real input which is $S_B$ and instead they have generated $S'_B$? In this case, I think the reason why authors have generated $S'_A$ is that party B has no access to $S_A$(belongs to party A), but why did they generate $S'_B$, considering that party B has access to $S_B$(the real input)? So, based on this security proof, the input $S_B$ has no role in the process of the simulation by the simulator!

It would be highly appreciated if you could help me with this.


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