{"id":340817,"date":"2016-12-23T11:49:08","date_gmt":"2016-12-23T19:49:08","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&#038;p=340817"},"modified":"2018-10-16T20:44:27","modified_gmt":"2018-10-17T03:44:27","slug":"distributed-differentially-private-protocols-require-oblivious-transfer","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/distributed-differentially-private-protocols-require-oblivious-transfer\/","title":{"rendered":"Do Distributed Differentially-Private Protocols Require Oblivious Transfer?"},"content":{"rendered":"<div>We study the cryptographic complexity of two-party differentially-private protocols for a large natural class of boolean functionalities. Information theoretically, McGregor et al. [FOCS 2010] and Goyal et al. [Crypto 2013] demonstrated several functionalities for which the maximal possible accuracy in the distributed setting is significantly lower than that in the client-server setting. Goyal et al. [Crypto 2013] further showed that &#8220;highly accurate&#8221; protocols in the distributed setting for any non-trivial functionality in fact imply the existence of one-way functions. However, it has remained an open problem to characterize the exact cryptographic complexity of this class. In particular, we know that semi-honest oblivious transfer helps obtain optimally accurate distributed differential privacy. But we do not know whether the reverse is true. We study the following question: Does the existence of optimally accurate distributed differentially private protocols for any class of functionalities imply the existence of oblivious transfer (or equivalently secure multi-party computation)? We resolve this question in the affirmative for the class of boolean functionalities that contain an XOR embedded on adjacent inputs. We give a reduction from oblivious transfer to: &#8211; Any distributed optimally accurate epsilon-differentially private protocol with epsilon > 0 computing a functionality with a boolean XOR embedded on adjacent inputs. &#8211; Any distributed non-optimally accurate epsilon-differentially private protocol with epsilon > 0, for a constant range of non-optimal accuracies and constant range of values of epsilon, computing a functionality with a boolean XOR embedded on adjacent inputs. Enroute to proving these results, we demonstrate a connection between optimally-accurate twoparty differentially-private protocols for functions with a boolean XOR embedded on adjacent inputs, and noisy channels, which were shown by Cr\u00e9peau and Kilian [FOCS 1988] to be sufficient for oblivious transfer.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>We study the cryptographic complexity of two-party differentially-private protocols for a large natural class of boolean functionalities. Information theoretically, McGregor et al. [FOCS 2010] and Goyal et al. [Crypto 2013] demonstrated several functionalities for which the maximal possible accuracy in the distributed setting is significantly lower than that in the client-server setting. Goyal et al. 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