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Patient genomes are interpretable only in the context of other genomes; however, genome sharing enables discrimination. Thousands of monogenic diseases have yielded definitive genomic diagnoses and potential gene therapy targets. Here we show how to provide such diagnoses while preserving participant privacy through the use of secure multiparty computation. In multiple real scenarios (small patient cohorts, trio analysis, two-hospital collaboration), we used our methods to identify the causal variant and discover previously unrecognized disease genes and variants while keeping up to 99.7% of all participants’ most sensitive genomic information private.