Secure Computation Schemes for Mahalanobis Distance Between Sample Vectors in Combating Malicious Deception

In the context of rapid advancements in big data and artificial intelligence, similarity measurement methods between samples have been widely applied in data mining, pattern recognition, medical diagnosis, financial risk control, and other fields. The Mahalanobis distance, due to its effectiveness in capturing correlations within high-dimensional data, has become a crucial tool in many practical scenarios. However, sample data often contains sensitive privacy information, making it essential to achieve secure and privacy-preserving computation of Mahalanobis distance. This paper proposes a secure Mahalanobis distance calculation scheme tailored for sample vectors that effectively resists malicious cheating behaviors. The designed multi-party computation algorithms ensure privacy protection while maintaining computational efficiency and minimizing communication overhead. The experimental results compare three algorithms in terms of execution time and communication delay across varying sample sizes and vector dimensions. The results demonstrate that our proposed scheme achieves a favorable balance between security and performance. This research provides a practical and robust solution for similarity measurement under privacy constraints and lays a theoretical and practical foundation for secure data collaboration in multi-party computing environments, offering significant application potential.