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I'm trying to figure out whether pseudorandom secret sharing (as described in this paper) requires a central dealer, i.e. one party who doles out keys to the other players and thus who would be able to generate all the pseudorandom numbers on their own.

I'm new to this, so the paper is almost completely opaque to me, and there doesn't seem to be any dumbed down versions of this technique anywhere on the internet.

The implementation of PRSS in VIFF appears to require a central person to generate everyone's initial keys, but this doesn't seem necessary, i.e. you could make an implementation where everyone generates their own random keys and shares them with the appropriate parties as necessary.

However, VIFF's use of "dealer keys" confuses me, and makes me think that at some point, some party could generate all the pseudorandom numbers on their own. I've tried to read through the code, but I've reached a point where it's just as opaque to me as the aforementioned paper.

Is there anyone who can explain this?

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In secret sharing, one person typically wants to share a secret. Only that one person knows that secret, so they are the dealer.

In MPC, which VIFF implements protocols for, you actually have multiple parties, each with a secret input(s). So, each of these parties is the dealer for their individual secret input(s). In this sense, there is no central dealer for the entire computation.

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  • $\begingroup$ And that includes PRSS? So to generate random numbers, every player uses their "dealer keys", sort of like regular MPC? Then what are the other keys in VIFF's implementation for? I assume it'd be too much to ask for an in-depth explanation, so do you know of any sources with explanations that are relatively easy to understand? $\endgroup$ – user124384 Jul 22 '15 at 23:36
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    $\begingroup$ @user124384 Take a look at Martin Geisler's PhD dissertation it has a lot of detail. Especially about PRSS as implemented in VIFF. It has been a while since I have looked that closely at the PRSS stuff. $\endgroup$ – mikeazo Jul 23 '15 at 1:19
  • $\begingroup$ Thanks for that. So he says, "The runtime can create a secret sharing of a uniformly pseudorandom number using no communication," and "pseudorandom secret-sharing (PRSS) is then based on the observation that we can create many random shared secrets by distributing once and for all one set of rA values." So basically, if I'm understanding this correctly, even if each player is able to generate and distribute their own random keys (i.e. without one central dealer), once that happens, every player has access to all the pseudorandom values and no longer needs to contact the rest of the group? $\endgroup$ – user124384 Jul 23 '15 at 1:34

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