  We consider the estimation of the cumulative hazard function, and
equivalently the distribution function, with censored data under a setup that
preserves the privacy of the survival database. This is done through a
$\alpha$-locally differentially private mechanism for the failure indicators
and by proposing a non-parametric kernel estimator for the cumulative hazard
function that remains consistent under the privatization. Under mild
conditions, we also prove lowers bounds for the minimax rates of convergence
and show that estimator is minimax optimal under a well-chosen bandwidth.
