Breaking the circuit-size barrier in secret sharing
Tianren Liu, Vinod Vaikuntanathan · 2018
We study secret sharing schemes for general (non-threshold) access structures. A general secret sharing scheme for n parties is associated to a monotone function F:{0,1}n→{0,1}. In such a scheme, a dealer distributes shares of a secret s among n parties. Any subset of parties T ⊆ [n] should be able to put together their shares and reconstruct the secret s if F(T)=1, and should have no information about s if F(T)=0. One of the major long-standing questions in information-theoretic cryptography is to minimize the (total) size of the shares in a secret-sharing scheme for arbitrary monotone functions F.