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Elaborate protocols in Secure Multi-party Computation enable severalparticipants to compute a public function of their own private inputs whileensuring that no undesired information leaks about the private inputs, andwithout resorting to any trusted third party. However, the public output of thecomputation inevitably leaks some information about the private inputs. Recentworks have introduced a framework and proposed some techniques for quantifyingsuch information flow. Yet, owing to their complexity, those methods do notscale to practical situations that may involve large input spaces. The maincontribution of the work reported here is to formally investigate theinformation flow captured by the min-entropy in the particular case of securethree-party computations of affine functions in order to make itsquantification scalable to realistic scenarios. To this end, we mathematicallyderive an explicit formula for this entropy under uniform prior beliefs aboutthe inputs. We show that this closed-form expression can be computed in timeconstant in the inputs sizes and logarithmic in the coefficients of the affinefunction. Finally, we formulate some theoretical bounds for this privacy leakin the presence of non-uniform prior beliefs.

Scalable Information-Flow Analysis of Secure Three-Party Affine Computations