• Department of Respiratory and Critical Care Medicine, Affiliated Nanjing Gaochun People's Hospital, Jiangsu University, Nanjing, 210000, Jiangsu, China.
• Department of Respiratory and Critical Care Medicine, Affiliated Nanjing Gaochun People's Hospital, Jiangsu University, Nanjing, 210000, Jiangsu, China. zhaomingming10086@outlook.com.

In the age of big data, privacy, particularly medical data privacy, is becoming increasingly important. Differential privacy (DP) has emerged as a key method for safeguarding privacy during data analysis and publishing. Cancer identification and classification play a vital role in early detection and treatment. This paper introduces a novel algorithm, DPFCM_GK, which combines differential privacy with fuzzy c-means (FCM) clustering using a Gaussian kernel function. The algorithm enhances cancer detection while ensuring data privacy. Three publicly available lung cancer datasets, along with a dataset from our hospital, are used to test and demonstrate the effectiveness of DPFCM_GK. The experimental results show that DPFCM_GK achieves high clustering accuracy and enhanced privacy as the privacy budget (ε) increases. For the UCIML, NLST, and NSCLC datasets, it reaches optimal results at lower ε (1.52, 1.24, and 2.32) compared to DPFCM. In the lung cancer dataset, DPFCM_GK outperforms DPFCM within, 0.05 ≤ ε ≤ 2.5, with significant differences (χ² = 4.54 ∼ 29.12; P < 0.05), and both methods converge to an accuracy of 94.5% as ε increases. Although differential privacy initially increases iteration counts, DPFCM_GK demonstrates faster convergence and fewer iterations compared to DPFCM, with significant reductions (T= 23.08, 43.47, and 48.93; P<0.05). For the UCIML dataset, DPFCM_GK significantly reduces runtime compared to other models (DPFCM, LDP-SGD, LDP-Fed, LDP-FedSGD, MGM-DPL, LDP-FL) under the same privacy budget. The runtime reduction is statistically significant with T-values of (T = 21.08, 316.24, 102.35, 222.37, 162.23, 159.25; P < 0.05). DPFCM_GK still maintains excellent time efficiency when applied to the NLST and NSCLC datasets(P < 0.05). For the LLCS dataset, For the LLCS dataset, the DPFCM_GK demonstrates significant improvement as the privacy budget increases, especially in low-budget scenarios, where the performance gap is most pronounced (T=4.20, 8.44, 10.92, 3.95, 7.16, 8.51, P < 0.05). These results confirm DPFCM_GK as a practical solution for medical data analysis, balancing accuracy, privacy, and efficiency.