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In 2009, Jeong et al. suggested a secret broadcast scheme in broadcasting networks using binding encryption. With a binding encryption scheme, a ciphertext is made for a group of receivers, and we can assure that all of the receivers will extract the exact same plaintext from the ciphertext. However, Wu et al. pointed out that Jeong et al.'s binding encryption scheme provides only weak decryption consistency. In this paper, we suggest a binding encryption scheme that provides strong decryption consistency without random oracles. Our binding encryption scheme uses the unique properties of lattices to provide strong decryption consistency.