divergentdave
commented
1 month ago I looked at the distribution of $Lap\mathbb{Z}(t)+Lap\mathbb{Z}(t)$ a couple ways, and I wind up with either an infinite sum or an integral that seems hard to put in closed form. It should be possible to use numerical approximations to the PDF or CDF instead, and that'll be good enough for test purposes.
Currently, the integration tests exercising DP just confirm that any noise was added to the aggregate result. We could strengthen this by performing a statistical test to evaluate whether the observed noise is a likely output of sampling the desired distribution, and failing if they are too different. As an example, libprio-rs currently uses a chi-squared test on a histogram produced from the discrete Gaussian sampler. (there may be other appropriate tests as well)