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In this letter, we consider downlink transmission of a multiuser multiple-input multiple-output (MU-MIMO) system with zero-forcing (ZF) precoders in the presence of multiple attackers. We propose a cooperative pilot spoofing attack (CPSA), where the attackers collaboratively impair the channel estimations in the uplink channel training phase, aiming at deteriorating the downlink throughput of the whole cell. We first evaluate the impacts of CPSA on the channel estimation and the downlink ZF precoding design, and then we derive an analytical expression for the achievable downlink sum-rate. Furthermore, we investigate the optimal attack strategy to minimize the achievable downlink sum-rate. We show that the optimization problem under consideration is a convex one so the global optimum could be obtained conveniently. Numerical results show that the CPSA attack results in a severe performance deterioration with the increase in the attacking power and the number of attackers.