The growing number of health-data breaches, the use of genomic databases for law enforcement purposes and the lack of transparency of personal genomics companies are raising unprecedented privacy concerns. To enable a secure exploration of genomic datasets with controlled and transparent data access, we propose a citizen-centric approach that combines cryptographic privacy-preserving technologies, such as homomorphic encryption and secure multi-party computation, with the auditability of blockchains. Our open-source implementation supports queries on the encrypted genomic data of hundreds of thousands of individuals, with minimal overhead. We show that real-world adoption of our system alleviates widespread privacy concerns and encourages data access sharing with researchers.