Distributed data sharing in dynamic networks is ubiquitous. It raises the concern that the private information of dynamic networks could be leaked when data receivers are malicious or communication channels are insecure. In this paper, we propose to intentionally perturb the inputs and outputs of a linear dynamic system to protect the privacy of target initial states and inputs from released outputs. We formulate the problem of perturbation design as an optimization problem which minimizes the cost caused by the added perturbations while maintaining system controllability and ensuring the privacy. We analyze the computational complexity of the formulated optimization problem. To minimize the ℓ ₀ and ℓ ₂ norms of the added perturbations, we derive their convex relaxations which can be efficiently solved. The efficacy of the proposed techniques is verified by a case study on a heating, ventilation, and air conditioning system.