A Group-Oriented Cryptosystem (GOC) allows a sender to encrypt a message sent to a group of users so only the specified sets of users in that group can cooperatively decrypt the message. Recently, Li et al. pointed out unauthorized sets in the receiving group can recover the encrypted messages in Yang et al.'s GOC; and they further repaired this security flaw. However, the improved GOC contains inexact security analysis. Further, conversion of the scheme into a threshold cryptosystem results in inefficiency. This study enhances Li et al.'s GOC, both in that it achieves the requirements of GOC but also that it can be efficiently converted into a threshold cryptosystem. Under the decisional Diffie–Hellman problem assumption, the proposed scheme is demonstrated to be provably secure against chosen plaintext attacks.