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One of the most used types of auctions in the smart grid is the double auction, in which both buyers and sellers can respectively submit their bids and asks to participate in the auction. In recent years, many schemes have been designed to propose a double auction mechanism for the smart grids; however, few of these schemes consider the information security aspects and users' privacy. In this paper, we propose a protocol that helps different double auction mechanisms be implemented securely in the smart grids. This protocol not only can satisfy the security requirements of a double auction scheme but is also compatible with the smart grid technologies. In this scheme, in order to preserve the users' anonymity and privacy, a pseudo-identity is assigned to each participant, and the bids/asks are encrypted using the Paillier cryptosystem. By virtue of the Pedersen commitment scheme used in this paper, the participants can be verified as having correctly and honestly followed the auction protocol. Moreover, the theoretical analysis and implementation results show that the proposed scheme can be considered as an efficient scheme for the smart grid entities involved in the auction process. [ABSTRACT FROM AUTHOR]