Due to the wide application of average consensus algorithm, its security and privacy problems have attracted great attention. In this paper, we consider the system threatened by a set of unknown agents that are both malicious and curious, who add additional input signals to the system in order to perturb the final consensus value or prevent consensus, and try to infer the initial state of other agents. At the same time, we design a privacy-preserving average consensus algorithm equipped with an attack detector with a time-varying exponentially decreasing threshold for every benign agent, which can guarantee the initial state privacy of every benign agent, under mild conditions. The attack detector will trigger an alarm if it detects the presence of malicious attackers. An upper bound of false alarm rate in the absence of malicious attackers and the necessary and sufficient condition for there is no undetectable input by the attack detector in the system are given. Specifically, we show that under this condition, the system can achieve asymptotic consensus almost surely when no alarm is triggered from beginning to end, and an upper bound of convergence rate and some quantitative estimates about the error of final consensus value are given. Finally, numerical case is used to illustrate the effectiveness of some theoretical results.
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