Given that distributed systems face adversarial behaviors such as eavesdropping and cyberattacks, how to ensure the evidence fusion result is credible becomes a must-be-addressed topic. Different from traditional research that assumes nodes are cooperative, we focus on three requirements for evidence fusion, i.e., preserving evidence's privacy, identifying attackers and excluding their evidence, and dissipating high-conflicting among evidence caused by random noise and interference. To this end, this paper proposes an algorithm for credible evidence fusion against cyberattacks. Firstly, the fusion strategy is constructed based on conditionalized credibility to avoid counterintuitive fusion results caused by high-conflicting. Under this strategy, distributed evidence fusion is transformed into the average consensus problem for the weighted average value by conditional credibility of multi-source evidence (WAVCCME), which implies a more concise consensus process and lower computational complexity than existing algorithms. Secondly, a state decomposition and reconstruction strategy with weight encryption is designed, and its effectiveness for privacy-preserving under directed graphs is guaranteed: decomposing states into different random sub-states for different neighbors to defend against internal eavesdroppers, and encrypting the sub-states' weight in the reconstruction to guard against out-of-system eavesdroppers. Finally, the identities and types of attackers are identified by inter-neighbor broadcasting and comparison of nodes' states, and the proposed update rule with state corrections is used to achieve the consensus of the WAVCCME. The states of normal nodes are shown to converge to their WAVCCME, while the attacker's evidence is excluded from the fusion, as verified by the simulation on a distributed unmanned reconnaissance swarm.