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• W3159225770 abstract "Consider a PPT two-party protocol $pi=(A,B)$ in which the parties get no private inputs and obtain outputs $O^A,O^Bin {0,1}$, and let $V^A$ and $V^B$ denote the parties' individual views. Protocol $pi$ has $alpha$-agreement if $Pr[O^A=O^B]=1/2+alpha$. The leakage of $pi$ is the amount of information a party obtains about the event ${O^A=O^B}$; that is, the leakage $epsilon$ is the maximum, over $Pin{A,B}$, of the distance between $V^P|OA=OB$ and $V^P|OAneq OB$. Typically, this distance is measured in statistical distance, or, in the computational setting, in computational indistinguishability. For this choice, Wullschleger [TCC 09] showed that if $alpha>>epsilon$ then the protocol can be transformed into an OT protocol. We consider measuring the protocol leakage by the log-ratio distance (which was popularized by its use in the differential privacy framework). The log-ratio distance between X,Y over domain Omega is the minimal $epsilon>0$ for which, for every $vinOmega$, $log(Pr[X=v]/Pr[Y=v])in [-epsilon,epsilon]$. In the computational setting, we use computational indistinguishability from having log-ratio distance $epsilon$. We show that a protocol with (noticeable) accuracy $alphainOmega(epsilon^2)$ can be transformed into an OT protocol (note that this allows $epsilon>>alpha$). We complete the picture, in this respect, showing that a protocol with $alphain o(epsilon^2)$ does not necessarily imply OT. Our results hold for both the information theoretic and the computational settings, and can be viewed as a fine grained approach to weak OT amplification. We then use the above result to fully characterize the complexity of differentially private two-party computation for the XOR function, answering the open question put by Goyal, Khurana, Mironov, Pandey, and Sahai [ICALP 16] and Haitner, Nissim, Omri, Shaltiel, and Silbak [FOCS 18]." @default.
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• W3159225770 date "2021-05-03" @default.
• W3159225770 modified "2023-09-27" @default.
• W3159225770 title "Channels of Small Log-Ratio Leakage and Characterization of Two-Party Differentially Private Computation" @default.
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