Genome-wide association studies (GWAS), especially on rare diseases, may necessitate exchange of sensitive genomic data between multiple institutions. Since genomic data sharing is often infeasible due to privacy concerns, cryptographic methods, such as secure multiparty computation (SMC) protocols, have been developed with the aim of offering privacy-preserving collaborative GWAS. Unfortunately, the computational overhead of these methods remain prohibitive for human-genome-scale data. Here we introduce SkSES (https://github.com/ndokmai/sgx-genome-variants-search), a hardware-software hybrid approach for privacy-preserving collaborative GWAS, which improves the running time of the most advanced cryptographic protocols by two orders of magnitude. The SkSES approach is based on trusted execution environments (TEEs) offered by current-generation microprocessors-in particular, Intel's SGX. To overcome the severe memory limitation of the TEEs, SkSES employs novel 'sketching' algorithms that maintain essential statistical information on genomic variants in input VCF files. By additionally incorporating efficient data compression and population stratification reduction methods, SkSES identifies the top k genomic variants in a cohort quickly, accurately and in a privacy-preserving manner.