The outsourcing of genomic data into public cloud computing settings raises concerns over privacy and security. Significant advancements in secure computation methods have emerged over the past several years, but such techniques need to be rigorously evaluated for their ability to support the analysis of human genomic data in an efficient and cost-effective manner. With respect to public cloud environments, there are concerns about the inadvertent exposure of human genomic data to unauthorized users. In analyses involving multiple institutions, there is additional concern about data being used beyond agreed research scope and being prcoessed in untrused computational environments, which may not satisfy institutional policies. To systematically investigate these issues, the NIH-funded National Center for Biomedical Computing iDASH (integrating Data for Analysis, 'anonymization' and SHaring) hosted the second Critical Assessment of Data Privacy and Protection competition to assess the capacity of cryptographic technologies for protecting computation over human genomes in the cloud and promoting cross-institutional collaboration. Data scientists were challenged to design and engineer practical algorithms for secure outsourcing of genome computation tasks in working software, whereby analyses are performed only on encrypted data. They were also challenged to develop approaches to enable secure collaboration on data from genomic studies generated by multiple organizations (e.g., medical centers) to jointly compute aggregate statistics without sharing individual-level records. The results of the competition indicated that secure computation techniques can enable comparative analysis of human genomes, but greater efficiency (in terms of compute time and memory utilization) are needed before they are sufficiently practical for real world environments.