We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform the tests. Under the notion of local differential privacy, we propose simple, sample-optimal, and communication-efficient protocols for these two questions in the noninteractive setting, where in addition users may or may not share a common random seed. In particular, we show that the availability of shared (public) randomness greatly reduces the sample complexity. Underlying our public-coin protocols are privacy-preserving mappings which, when applied to the samples, minimally contract the distance between their respective probability distributions.

翻译：我们研究在样本分布于多个用户的环境下对离散分布进行良好和独立的测试。用户希望保护其数据的隐私,同时使中央服务器能够进行测试。根据地方差异隐私的概念,我们提议在非互动环境中为这两个问题制定简单、最优化的样本和通信效率高的规程,除此之外,用户可能分享或可能不分享普通随机种子。特别是,我们表明共享(公共)随机性可大大降低样本的复杂性。我们的公用coin协议的基础是隐私保护图,在对样本应用时,将各自概率分布之间的距离减到最小。