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In this work, we exploit a multi-antenna cooperative jammer to enable secure short packet communications in Internet of Things (IoT) networks. Specifically, we propose three jamming schemes to combat eavesdropping, i.e., the zero forcing beamforming (ZFB) scheme, null-space artificial noise (NAN) scheme, and transmit antenna selection (TAS) scheme. Assuming Rayleigh fading, we derive new closed-form approximations for the secrecy throughput with finite blocklength coding. To gain further insights, we also analyze the asymptotic performance of the secrecy throughput in the case of infinite blocklength. Furthermore, we investigate the optimization problem in terms of maximizing the secrecy throughput with the latency and reliability constraints to determine the optimal blocklength. Simulation results validate the accuracy of the approximations and evaluate the impact of key parameters such as the jamming power and the number of antennas at the jammer on the secrecy throughput.