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首页> 外文期刊>Information Theory, IEEE Transactions on >Private Interactive Communication Across an Adversarial Channel
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Private Interactive Communication Across an Adversarial Channel

机译：对抗渠道上的私人互动交流

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摘要

Consider two parties, Alice and Bob, who hold private inputs and , and wish to compute a function privately in the information theoretic sense; that is, each party should learn nothing beyond . However, the communication channel available to them is noisy. This means that the channel can introduce errors in the transmission between the two parties. Moreover, the channel is adversarial in the sense that it knows the protocol that Alice and Bob are running, and maliciously introduces errors to disrupt the communication, subject to some bound on the total number of errors. A fundamental question in this setting is to design a protocol that remains private in the presence of large number of errors. If Alice and Bob are only interested in computing correctly, and not privately, then quite robust protocols are known that can tolerate a constant fraction of errors. However, none of these solutions is applicable in the setting of privacy, as they inherently leak information about the parties’ inputs. This leads to the question whether we can simultaneously achieve privacy and error-resilience against a constant fraction of errors. We show that privacy and error-resilience are contradictory goals. In particular, we show that for every constant , there exists a function which is privately computable in the error-less setting, but for which no private and correct protocol is resilient against a -fraction of errors.
机译：考虑两方，爱丽丝和鲍勃，他们拥有私人输入和，并希望从信息理论的角度私下计算函数。也就是说，每一方都不应学到其他东西。但是，他们可用的通信通道很嘈杂。这意味着通道可能会在双方之间的传输中引入错误。此外，从某种意义上说，该通道是对抗性的，因为它知道Alice和Bob正在运行的协议，并且恶意地引入错误来破坏通信，这取决于错误总数。在这种情况下，一个基本问题是设计一种在存在大量错误的情况下仍保持私有的协议。如果Alice和Bob仅对正确计算感兴趣，而对私有计算不感兴趣，那么已知相当健壮的协议可以容忍一定比例的错误。但是，这些解决方案均不适用于隐私设置，因为它们会固有地泄露有关各方输入的信息。这就提出了一个问题，我们是否可以同时针对一定比例的错误实现隐私和错误恢复能力。我们表明，隐私和容错能力是相互矛盾的目标。特别是，我们表明，对于每个常量，都存在一个在无错误设置中可以私有计算的函数，但是对于该函数而言，没有专用且正确的协议可以抵抗少量错误。

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