The paper introduces a novel backdoor attack method called Full Combination Backdoor Attack (FCBA) in federated learning (FL). Traditional backdoor attacks in FL are often diluted by subsequent benign updates, leading to a significant reduction in attack success rates over iterations. To address this issue, FCBA employs combinatorics to generate more comprehensive and resilient backdoor patterns in the global model. The method involves dividing a global trigger into multiple local triggers, each embedded by separate adversaries, and then aggregating these decentralized responses. This approach enhances the global model's ability to recognize and respond to the backdoor, making it more resistant to benign updates and achieving higher attack success rates on the test set. The paper evaluates FCBA on three datasets (MNIST, CIFAR-10, and GTSRB) using two models across various settings. The results show that FCBA outperforms state-of-the-art (SOTA) backdoor attacks in terms of attack persistence, with a 56.8% increase in attack success rate after 120 rounds compared to the baseline. The core code for FCBA is available at https://github.com/PhD-TaoLiu/FCBA. The introduction highlights the challenges of backdoor attacks in FL, such as the dilution effect of benign updates and the limited persistence of traditional attacks. The paper also discusses existing defense methods and their limitations, emphasizing the need for more robust solutions. The experimental setup, evaluation metrics, and analysis of crucial factors influencing FCBA's performance are detailed, demonstrating its effectiveness and robustness against various defense mechanisms.The paper introduces a novel backdoor attack method called Full Combination Backdoor Attack (FCBA) in federated learning (FL). Traditional backdoor attacks in FL are often diluted by subsequent benign updates, leading to a significant reduction in attack success rates over iterations. To address this issue, FCBA employs combinatorics to generate more comprehensive and resilient backdoor patterns in the global model. The method involves dividing a global trigger into multiple local triggers, each embedded by separate adversaries, and then aggregating these decentralized responses. This approach enhances the global model's ability to recognize and respond to the backdoor, making it more resistant to benign updates and achieving higher attack success rates on the test set. The paper evaluates FCBA on three datasets (MNIST, CIFAR-10, and GTSRB) using two models across various settings. The results show that FCBA outperforms state-of-the-art (SOTA) backdoor attacks in terms of attack persistence, with a 56.8% increase in attack success rate after 120 rounds compared to the baseline. The core code for FCBA is available at https://github.com/PhD-TaoLiu/FCBA. The introduction highlights the challenges of backdoor attacks in FL, such as the dilution effect of benign updates and the limited persistence of traditional attacks. The paper also discusses existing defense methods and their limitations, emphasizing the need for more robust solutions. The experimental setup, evaluation metrics, and analysis of crucial factors influencing FCBA's performance are detailed, demonstrating its effectiveness and robustness against various defense mechanisms.