Secret sharing schemes for infinite sets of participants: A new design technique

We propose a new design technique for constructing secret sharing schemes over a potentially infinite set of participants. Our findings leverage on a nice property of secret sharing schemes for finite sets of participants based on the Chinese remainder theorem: the possibility of providing shares of different sizes to participants. We successful apply the technique to the (3,∞)-threshold access structure. The scheme we exhibit improves over the best construction currently available. Most importantly, the idea underlying the technique is of independent interest. Hopefully, it could be employed for other access structures, and in other areas of secure computation for potentially infinite sets of players.