Achieving average consensus without disclosing sensitive initial states is important for secure multi-agent coordination. This work lifts each vector-valued agent state into a higher-dimensional space and designs dynamic, low-rank, positive-semidefinite matrix-valued inter-agent couplings. The resulting fully distributed algorithm conceals the original states while preserving exact average consensus. Its convergence analysis is reduced to an average-consensus problem on switching matrix-weighted networks, and privacy is guaranteed when each agent has at least one legitimate neighbor. Because the method relies on basic matrix operations rather than cryptographic procedures, it is suitable for efficient distributed control and optimization.