Correction to: Nature Communications https://doi.org/10.1038/s41467-021-25972-y, published online 11 October 2021.

The original version of this Article omitted a reference to previous work in ‘Blatt, M., Gusev, A., Polyakov, Y. & Goldwasser, S. Secure large-scale genome-wide association studies using homomorphic encryption. Proc. Natl. Acad. Sci. USA 117, 11608–11613 (2020)’. This has been added as reference 25 at the fifth paragraph of the Introduction, second line: ‘More sophisticated solutions for FA, which aim to provide end-to-end privacy protection, including for the shared intermediate data, have been proposed15–25.’. This has been corrected in the PDF and HTML versions of the Article.