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Figure 1 on page 1249 of the “Multiparty Computation Secure Against Continual Memory Leakage” paper shows $m$ committees are elected in step 1 and then later in step 3 are each given a secret share.

But I was wondering if it is possible to pull out the election of $m$ committees from the pre-processing phase and do it in a different phase (like online phase)? The problem with the pre-processing phase is it is assumes no leakage so simplifying it is a step closer to completely getting rid of it.

I am essentially wondering if it is possible to distribute secret shares without knowing the committees (i.e. “don't run election protocol immediately, run it later”)?

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    $\begingroup$ I'm confused, you want to distribute shares w/o knowing who to distribute them to? That seems impossible. Maybe an example usage scenario would help? $\endgroup$ – mikeazo Dec 30 '13 at 14:47
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    $\begingroup$ @mikeazo - i think what i am asking is if it is possible to compute secret shares and distribute them at a later stage. I think in the paper authors figure out who the committees are first and then immediately distribute secret shares after they are computed. I'm wondering if the election could be done at a later (leaky) stage. In general doing it in a leaky environment is favorable because it makes a better protocol. $\endgroup$ – user1068636 Dec 30 '13 at 19:09
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As long as you know the reconstruction threshold a priori, I see no reason you can't generate a bunch of shares before knowing who you will distribute them to. Once you know who you are going to distribute them to, just send one share to each person.

On the other hand, if you don't know the reconstruction threshold, you wouldn't be able to construct, I don't see how you can do it. It would seem like an ill-posed problem at that point.

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