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According to me, every OT takes a constant number of rounds and since we have to do an OT for every input of one party, we'll have to do O(n) OTs which would correspond to O(n) rounds. But I have read at various places that the number of rounds in Yao's Protocol is constant. Am I missing something?

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The OT inputs/outputs don't depend on each other, so they can all be done in parallel.

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