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Time synchronization is crucial to Wireless Sensor Networks (WSNs) due to the requirement of coordination between sensor nodes. Existing secure time synchronization protocols of WSNs introduce high overhead when used for global time synchronization. In this paper, we propose a lightweight secure global time synchronization protocol for WSNs. In the proposed protocol, a broadcast synchronization packet makes all sensor nodes in the network synchronize with the trusted source. The synchronization packet is protected by a proposed broadcast authentication algorithm, which introduces asymmetry by transmitting hash values of secret keys in advance. It achieves immediate authentication and does not require the loose time synchronization. To defend the pulse-delay attacks, the arrival time of the synchronization packet is checked according to the estimated arrival time interval. The upper bound on the skew of the proposed protocol is proved. The message complexity in one period of the proposed protocol is O(n) where n represents the number of sensor nodes. The simulation results show that the maximum skew is within tens of milliseconds.