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Consider a ppt two-party protocol \(\varPi = (\mathsf {A} ,\mathsf {B} )\) in which the parties get no private inputs and obtain outputs \(O^{\mathsf {A} },O^{\mathsf {B} }\in \left\{ 0,1\right\} \), and let \(V^\mathsf {A} \) and \(V^\mathsf {B} \) denote the parties’ individual views. Protocol \(\varPi \) has \(\alpha \)-agreement if \(\Pr [O^{\mathsf {A} }=O^{\mathsf {B} }] = \tfrac{1}{2}+\alpha \). The leakage of \(\varPi \) is the amount of information a party obtains about the event \(\left\{ O^{\mathsf {A} }=O^{\mathsf {B} }\right\} \); that is, the leakage \(\epsilon \) is the maximum, over \(\mathsf {P} \in \left\{ \mathsf {A} ,\mathsf {B} \right\} \), of the distance between \(V^\mathsf {P} |_{O^{\mathsf {A} }= O^{\mathsf {B} }}\) and \(V^\mathsf {P} |_{O^{\mathsf {A} }\ne O^{\mathsf {B} }}\). 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 \(\epsilon \ll \alpha \) then the protocol can be transformed into an OT protocol.

Channels of Small Log-Ratio Leakage and Characterization of Two-Party Differentially Private Computation