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I'm reading papers related to the IPS compiler.

I'm confused about one point: The paper IPS08 (PDF) proposed a protocol with $O(s)$ communication for a circuit of size $s$ in the OT-Hybrid model.

Are they actually assuming a bit-OT Hybrid model, where parties can perform OT on single bits? For example, the communication of GMW is counted as $O(m^2 s)$ for m parties with circuit size s.

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They do not specifically assume a bit-OT… but at least in the semi-honest case, it seems that having an ideal bit-OT is indeed sufficient.

If you are wondering about the fact that they do not specify which kind of OT they use: their purpose was to focus on a black box use of the primitive; bit OT and string OT can be easily reduced in black box to each other.

And if you are wondering about the fact that the communication is only $O(s)$: the costs of the OTs are not counted, as they are replaced by an ideal primitive to which all the players have access.

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