Privacy Implications of Shuffling

LDP deployments are vulnerable to inference attacks as an adversary can link the noisy responses to their identity and subsequently, auxiliary information using the order of the data. An alternative model, shuffle DP, prevents this by shuffling the noisy responses uniformly at random. However, this limits the data learnability -only symmetric functions (input order agnostic) can be learned. In this paper, we strike a balance and show that systematic shuffling of the noisy responses can thwart specific inference attacks while retaining some meaningful data learnability. To this end, we propose a novel privacy guarantee, d σ -privacy, that captures the privacy of the order of a data sequence. d σ -privacy allows tuning the granularity at which the ordinal information is maintained, which formalizes the degree the resistance to inference attacks trading it off with data learnability. Additionally, we propose a novel shuffling mechanism that can achieve d σ -privacy and demonstrate the practicality of our mechanism via evaluation on real-world datasets. 1 The analyst and the adversary could be same, we refer to them separately for the ease of understanding.