A Dynamic Proactive Secret Sharing Scheme for Quadratic Functions

Dynamic proactive secret sharing (DPSS) allows a client to share a secret
$s$
among a committee of
$n$
participants and allows the committee to reshare the secret among a new committee of
$n$
participants such that the secret
$s$
can be reconstructed by any authorized subset of the new committee but an adversary that corrupts both members from the old committee and members from the new committee learns no information about
$s$
. The existing DPSS schemes only allow the old committee to reshare the same secret
$s$
to the new committee. In this paper, we consider dynamic proactive functional secret sharing (DPFSS), a new model for DPSS that allows the old committee to reshare functions of the original secret
$s$
among the new committee, and construct a DPFSS scheme for resharing the evaluation results of quadratic functions on the original secret. We discuss the applications of our DPFSS scheme in distributed systems such as those for health data sharing and smart meter billing. Our scheme is efficient and achieves a communication complexity of
${\mathcal{ O}}(n^{2})$
and a time complexity of
${\mathcal{ O}}(n)$
. Our experimental results show that for a committee of size
$n=100$
, the communication cost is
$\approx 1.166$
MB and the time cost is
$\approx 10.72$
s.