Secure Division Protocol and Applications to Privacy-preserving Chi-squared Tests

We present a new secure integer division protocol with private divisor. Our protocol is based loosely on the Bogdanov et al. (Int. J. Inf. Secur.'12) protocol, which securely computes the classical Goldschmidt's division algorithm. While the Bogdanov et al. scheme was designed specifically to work only on a 3-out-of-3 secret sharing scheme, our scheme works on a 2-out-of-2 secret sharing scheme. This has an advantage since the latter setting is more widely used in the literature of secure computation, and our protocol can thus be used as an efficient building block in this setting. We implement our protocol in Python and provide its benchmark. As a main application of our division protocol, we implement a secure protocol for privacy-preserving chi-squared tests on genomic data. This demonstrates that the proposed protocol is suitable for the statistical analysis on sensitive data.