Conventional distributed formation control of multiple vehicle systems (MVSs) has two drawbacks: inflexible formation changes and explicit-value exchanges of vehicles' information such as position and velocity among all vehicles. Since formation changes are needed, each vehicle is required to update its relative position which is quite difficult in large spatial applications. Firstly, the explicit-value exchanges possibly result in two critical issues. When each vehicle policy needs to keep its information confidential from another unexpected listener, the explicit-value exchanges are invalid for the privacy policies. Additionally, the explicit-value storing or exchanging signals or parameters are much more vulnerable and dangerous to security threats. This work proposes an approach to overcome the above challenges by taking advantage of model predictive control-consensus algorithms to achieve desired formations. We will also allow the computation to be effectively distributed among the vehicle agents according to their computational capabilities. Secondly, we use the highly secure encryption scheme that empowers all computations carried out in encrypted forms, including system parameters and signals. Our results are verified by the formation control of multiple vehicles working in large-scale environments where a ground station does not touch all vehicles due to limited communication ranges and security problems. Compared to cutting-edge studies, the formation of vehicles is still able to be changed securely by the ground station without updating new formations to all vehicles. Besides, the data privacy of each vehicle is preserved by encrypting all physical signals.