  Conditional independence (CI) tests are widely used in statistical data
analysis, e.g., they are the building block of many algorithms for causal graph
discovery. The goal of a CI test is to accept or reject the null hypothesis
that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in
\mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional
independence testing under the constraint of differential privacy. We design
two private CI testing procedures: one based on the generalized covariance
measure of Shah and Peters (2020) and another based on the conditional
randomization test of Cand\`es et al. (2016) (under the model-X assumption). We
provide theoretical guarantees on the performance of our tests and validate
them empirically. These are the first private CI tests with rigorous
theoretical guarantees that work for the general case when $Z$ is continuous.
