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Federated learning (FL) enables multiple parties to collaboratively train machine learning models while preserving data privacy. However, securing communication within FL frameworks remains a significant challenge due to potential vulnerabilities to data breaches and integrity attacks. This paper proposes a novel approach using Dilithium, a robust digital signature framework, to enhance data security in FL. By integrating Dilithium into FL protocols, this study demonstrates robust communication security, preventing data tampering and unauthorized access, thereby promoting safer and more efficient collaborative model training across distributed networks. Furthermore, our approach incorporates an optimized client selection algorithm and a parallelized GPU-based training process that reduces latency and ensures seamless synchronization among participants. Experimental results demonstrate that our system achieves a total processing time of 6.891 seconds, significantly outperforming the 10.24 seconds of normal FL and 12.32 seconds of FL-Dilithium systems on the same computing platforms. Additionally, the proposed model achieves an accuracy of 94%, surpassing the 93% of the normal FL.