Verifiable Additive Homomorphic Secret Sharing with Dynamic Aggregation Support

Abstract

(n,m,t)-Homomorphic Secret Sharing (HSS) allows n clients to share data secretly to m servers, which compute a function f homomorphically on the received secretly shared data while restricting the input data acquired by a collection of t servers to private ones. In Verifiable Homomorphic Secret Sharing (VHSS), if there are partially colluding malicious servers submitting erroneous computation results to the client, such erroneous computation results will be rejected by the client. In traditional static homomorphic secret sharing schemes, once a secret share of raw data is assigned to a group of servers, then all servers in the group must participate in the computation, which means that the computation has to be restarted once some servers fail to perform the task. In order to solve the above problem, we propose the first dynamic homomorphic secret sharing scheme for additive computation in this paper. In our scheme, once some servers fail, there is no need to recalculate the secret sharing but only the need to reissue the index set of servers that perform the computation, Our structure assigns more computation to the servers, which is very useful in real scenarios. In addition, we propose dynamic verifiable homomorphic secret sharing schemes based on the above schemes, which have less computational overhead compared to the existing schemes, although we sacrifice the public verifiability property. Finally, we give a detailed correctness, security, and verifiability analysis of the two proposed schemes and provide the theoretical and experimental evaluation results of the computational overhead.