Secure multi-party computation has seen substantial performance improvements in recent years and is being increasingly used in commercial products. While a significant amount of work was dedicated to improving its efficiency under standard security models, the threat models do not account for information leakage from the output of secure function evaluation. Quantifying information disclosure about private inputs from observing the function outcome is the subject of this work. Motivated by the City of Boston gender pay gap studies, in this work we focus on the computation of the average of salaries and quantify information disclosure about private inputs of one or more participants (the target) to an adversary via information-theoretic techniques. We study a number of distributions including log-normal, which is typically used for modeling salaries. We consequently evaluate information disclosure after repeated evaluation of the average function on overlapping inputs, as was done in the Boston gender pay study that ran multiple times, and provide recommendations for using the sum and average functions in secure computation applications. Our goal is to develop mechanisms that lower information disclosure about participants' inputs to a desired level and provide guidelines for setting up real-world secure evaluation of this function.

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