Lower Bounds on the Share Size of Leakage Resilient Cheating Detectable Secret Sharing.

Cheating detectable secret sharing schemes (CDSS) detects changes in the secret that is caused by an adversary who modifies shares of an unauthorized subset of participants. We consider leakage resilient cheating detectable secret sharing schemes (LRCDSS) where protection is against an adversary who, in addition to the shares of an unauthorized set, has access to the leakages from all other shares. We give lower bounds on the share size of these schemes when the scheme provides ϵ -indistinguishability security, and the adversary’s modification of shares can be detected with probability at least 1 - δ . We discuss our bounds in relation to other known results, relate CDSS with non-malleable secret sharing, and suggest directions for future work.