Secure publicly verifiable and proactive secret sharing schemes with general access structure

A publicly verifiable secret sharing allows anyone to detect the cheating of dealer or participants only from the public information. In this paper, by using bilinear pairings and monotone span programs we propose two practical publicly verifiable secret sharing schemes with general access structure. The first scheme has provable security in the standard model. The other scheme is proactive, robust and secure against mobile attack. These schemes tolerate active and adaptive adversaries and provide great capabilities for many applications.