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In mobile ad hoc networks (MANETs), a single certificate authority (CA) node could be a security bottleneck. Multiple replica of CA is fault tolerant, but the network is as vulnerable as single CA or even worse since breaking one of the CAs means breaking all of them. Many distributed CA models based on the secret sharing scheme are proposed. In this paper, the suitable construction of the distributed CA is discussed based on the optimization theory. By the analyzing of the characters of the distributed CA in MANETs and the processes of the secure services provided, the optimization model is built. The mean response time of the applications is the optimization goal and the service success probability, system security probability and the loss probability of applications are the constraints in the optimization model. A classic resolving process of the optimization model is given, which is instructional for designing the construction of distributed CA applied in MANETs.