  We provide a lowerbound on the sample complexity of distribution-free parity
learning in the realizable case in the shuffle model of differential privacy.
Namely, we show that the sample complexity of learning $d$-bit parity functions
is $\Omega(2^{d/2})$. Our result extends a recent similar lowerbound on the
sample complexity of private agnostic learning of parity functions in the
shuffle model by Cheu and Ullman. We also sketch a simple shuffle model
protocol demonstrating that our results are tight up to $poly(d)$ factors.
