Computationally-efficient techniques facilitate secure crowdsourcing of genomic and phenotypic data, e.g., for large-scale association studies. In one embodiment, a method begins by receiving, via a secret sharing protocol, genomic and phenotypic data of individual study participants. Another data set, comprising results of pre-computation over random number data, e.g., mutually independent and uniformly-distributed random numbers and results of calculations over those random numbers, is also received via secret sharing. A secure computation then is executed against the secretly-shared genomic and phenotypic data, using the secretly-shared results of the pre-computation over random number data, to generate a set of genome-wide association study (GWAS) statistics. For increased computational efficiency, at least a part of the computation is executed over dimensionality-reduced genomic data. The resulting GWAS statistics are then used to identify genetic variants that are statistically-correlated with a phenotype of interest.