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Additional info for Applied Cryptography and Network Security: 13th International Conference, ACNS 2015, New York, NY, USA, June 2-5, 2015, Revised Selected Papers
This is accomplished with hyper-invertible matrices to ensure robustness. The protocol Reco opens a batch of secrets by sending each share to whichever party is supposed to learn the secret. That party then performs error detection/correction to interpolate the secrets in the presence of (possibly) corrupt shares. The protocol RanDouSha from  is also used as a subprotocol in our redistribution protocol. The protocol RanDouSha generates random sharings of degree d and additional sharings of the same secrets using degree 2d polynomials with constant amortized communication bandwidth.
5 (while some of the subprotocols are deferred to the full version of this paper ). In Sect. 6 we describe how the threshold may be raised in the statistical security setting. We show how our DPSS scheme can be applied to secure multiparty computation in Sect. 7. Security deﬁnitions and proofs are given in the full version of this paper . 2 Related Work The same work  introducing the proactive security model also contained the ﬁrst proactive secret sharing (PSS) scheme and proactively-secure multiparty computation (PMPC) protocol.
Then the Q and the Rj are generated simultaneously so that each party in the old group only learns her share of Q + Rj for each j. This technique preserves security but would not yield the optimal communication bandwidth that we aim for. Generating one polynomial for each party in the new group would result in a communication complexity of at least O(n2 ) for masking O(n) secrets while our goal is O(1) (amortized) communication per secret. In this paper we provide a solution that generates the polynomials Q without revealing any share of Q to the parties in the old group, and maintains optimal communication eﬃciency.