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

## TL;DR

This paper develops a scalable method to quantify information flow in secure three-party affine computations using min-entropy, enabling practical privacy analysis in large input scenarios.

## Contribution

It derives a closed-form formula for min-entropy in three-party affine computations, scalable to large inputs, and provides bounds for non-uniform priors.

## Key findings

- Explicit formula for min-entropy under uniform priors
- Constant-time computation relative to input size
- Logarithmic complexity in affine coefficients

## Abstract

Elaborate protocols in Secure Multi-party Computation enable several participants to compute a public function of their own private inputs while ensuring that no undesired information leaks about the private inputs, and without resorting to any trusted third party. However, the public output of the computation inevitably leaks some information about the private inputs. Recent works have introduced a framework and proposed some techniques for quantifying such information flow. Yet, owing to their complexity, those methods do not scale to practical situations that may involve large input spaces. The main contribution of the work reported here is to formally investigate the information flow captured by the min-entropy in the particular case of secure three-party computations of affine functions in order to make its quantification scalable to realistic scenarios. To this end, we mathematically derive an explicit formula for this entropy under uniform prior beliefs about the inputs. We show that this closed-form expression can be computed in time constant in the inputs sizes and logarithmic in the coefficients of the affine function. Finally, we formulate some theoretical bounds for this privacy leak in the presence of non-uniform prior beliefs.