Two-operation homomorphic perfect sharing schemes over rings

Two-operation homomorphic sharing schemes were introduced by Frankel and Desmedt. They have proved that if the set of keys is a Boolean algebra or a finite field, then there does not exist a two-operation homomorphic sharing scheme. In this paper it is proved that there do not exist perfect two-operation homomorphic sharing schemes over finite rings with identities. A necessary condition for the existence of perfect two-operation sharing schemes over finite rings without identities is given. This subject was supported by NSF of Zhejiang Province