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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 Ω(2d/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 demon- strating that our results are tight up to poly(d) factors.
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