Continual leakage-resilient dynamic secret sharing in the split-state model

Traditional secret sharing assume the absolute secrecy of the private shares of the uncorrupted users. It may not hold in the real world due to the side-channel attacks. Leakage-resilient cryptography is proposed to capture this situation. In the continual leakage model, the attacker can continuously leak the private value owned by the user with the constraint that the information leaked should be less than ℓ between updates. We propose continual leakage-resilient dynamic secret sharing under split-state model in this paper. After a preprocessing stage, the dealer is able to dynamically choose a set of n users and to allow a threshold of t users to reconstruct different secrets in different time instants, by using the same broadcast message. The secrets are protected even if an adversary corrupts up to t - 1 users and obtains continual leakage from the rest of them. Our scheme can provide the security for secret sharing under continual leakage model while at the same time allowing the users to join and quit the scheme dynamically.