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Updating the Parameters of a Threshold Scheme by Minimal Broadcast
Authors: S. G. Barwick, W. -A. Jackson, K. M. MartinAbstract:
Threshold schemes allow secret data to be protected amongst a set
of participants in such a way that only a pre-specified threshold
of participants can reconstruct the secret from private
information (shares) distributed to them on system setup using
secure channels. We consider the general problem of designing
threshold schemes whose defining parameters (the threshold and the
number of participants) can later be changed by using only public
channel broadcast messages. In this paper we are interested in the
efficiency of such threshold schemes, and seek to minimise storage
costs (size of shares) as well as optimise performance in low
bandwidth environments by minimising the size of necessary
broadcast messages. We prove a number of lower bounds on the
smallest size of broadcast message necessary to make general
changes to the parameters of a threshold scheme in which each
participant already holds shares of minimal size. We establish the
tightness of these bounds by demonstrating optimal schemes.
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