MTER: An Efficient Multi-User Threshold Equality Retrieval for Double Auction in Smart Grid Market

With the increasing electricity consumption and the wide application of renewable energy sources, energy auction attracts a lot of attention due to its economic benefits. In recent years, much research employs double auction mechanisms to design a market model for smart grid and shows its paramount importance for energy trading. However, few of them are able to quickly and securely identify the potential winner or winners from all sealed bids and asks throughout the auction process. In this paper, we propose an efficient multi-user threshold equality retrieval (MTER) by a novel non-interactive threshold public key encryption with equality test (T-PKEET) as a building block for bid-ask filtering to help different double auction mechanisms be implemented effectively in the smart grid. In this new T-PKEET primitive, the key used to authorize the equality test is shared among n servers so that at least k servers are collaborated to compute the test function: a combiner who has a user U ’s ciphertext C and another user Û’s ciphertext Ĉ wishes to carry out the equality test on ciphertexts C and Ĉ Preferably, T-PKEET solves a challenge problem of resisting against message recovery attack in PKEET system. We construct a concrete T-PKEET scheme with flexible authorization by issuing tag-based test key shares and ciphertext-based test key shares and prove it to achieve st-IND-CCA2 security against insider adversary in the standard model. The experimental results show that the Trapdoor and Test algorithms of T-PKEET scheme have significant efficiency, whose cost is only 8.46% and 17.78% that of the work closest to ours. Therefore, our construction can effectively facilitate demand responses of the filtering on sealed bids and asks for double auction in smart grid.