I am new to Oblivious Transfer (OT) and am having trouble finding a definitive answer regarding if/when/how baseOTs can be reused in a computation when using OT-extension (for passive security only).
Say two parties are running a secure function evaluation (SFE) protocol and need to use multiple rounds of oblivious transfer for some part of it (e.g., evaluating a 1-out-of-4 OT for each AND gate in the GMW protocol). It is my understanding that the parties can use, for example, k = 128 baseOTs in the “offline” phase to exchange symmetric keys and then later use these baseOTs to transfer the actual inputs in the “online” phase.
For each round of OT required by the SFE protocol, do the parties need to run the baseOTs again, or can one initial set of baseOTs be re-used for each SFE OT round?
Now say that, after computing the secure function evaluation protocol, both parties disconnect from each other and go offline. Later, they come back online and want to engage in another evaluation of the SFE protocol (e.g. over a different set of inputs).
Again, do the parties need to run the baseOTs again, or can the same baseOTs from before be re-used here?
Finally, say the parties want to evaluate a different type of secure function evaluation protocol that also uses OT. Can the same baseOTs be re-used here?
My intuition is that the answers to all of these questions are yes, but I cannot find any confirmation of this. I assume that it is probably good for the parties to repeat the baseOT step anyway every so often in case the seeds get compromised, but I am mostly just wondering if reusing the baseOTs in this way would be secure theoretically.