Breaking the circuit-size barrier in secret sharing

Abstract

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. Keywords: Information-theoretic techniques; Security and privacy; Cryptography; Theory of computation; Computational complexity and cryptography; Circuit complexity; Communication complexity; Cryptographic protocols