Survival function estimation is used in many disciplines, but it is most common in medicalanalytics in the form of the Kaplan-Meier estimator. Sensitive data (patient records) isused in the estimation without any explicit control on the information leakage, which is asignificant privacy concern. We propose a first differentially private estimator of the survivalfunction and show that it can be easily extended to provide differentially private confidenceintervals and test statistics without spending any extra privacy budget. We further provideextensions for differentially private estimation of the competing risk cumulative incidencefunction, Nelson-Aalen’s estimator for the hazard function, etc. Using eleven real-life clinicaldatasets, we provide empirical evidence that our proposed method provides good utilitywhile simultaneously providing strong privacy guarantees.