Techniques for efficient, accurate, and secure computation of a differentially private median of the union of two large confidential datasets are disclosed. In some example embodiments, a computer-implemented method comprises obtaining secret shares of a first dataset of a first entity, secret shares of a second dataset of a second entity, secret shares of gap values for the first dataset, secret shares of gap values for the second dataset, secret shares of probability mass values for the first dataset, and secret shares of probability mass values for the second dataset. The probability mass values may be computed via an exponential mechanism. In some example embodiments, the computer-implemented method further comprises determining a median of a union of the first dataset and the second dataset using an inverse transform sampling algorithm based on the obtained secret shares, and then performing a function of a networked computer system using the determined median.