A Toy MPC Protocol

Abstract

In this chapter, we discuss a simple MPC protocol, which allows a set of n mutually-distrusting parties to compute the sum of their private bits “securely”, without revealing anything beyond the sum. This is a simple case study for a specific function before we plunge into the more involved general case. We will also introduce a powerful proof mechanism based on the simulation-paradigm, which is used extensively throughout this book. We conclude with a few possible breaks for the MPC protocol in the face of stronger adversarial setting, including malicious adversaries. Consider a set of n mutually-distrusting parties $\mathcal {P}= \{P_1, \ldots , P_n \}$, where each party $P_i$ has a private bit $b_i \in \{ 0, 1\}$. The parties are interested to learn the sum $S {\mathop {=}\limits ^{def}}b_1 + \cdots + b_n$ and nothing beyond. Specifically, each $P_i$ should learn only S and whatever it can infer about the inputs of the other parties from its own input $b_i$ and the sum S. For instance, once S is learnt by $P_i$, an obvious inference that $P_i$ can make is that the sum of the remaining inputs, namely $b_1 + \cdots + b_{i - 1} + b_{i + 1} + \cdots + b_n$, is $S - b_i$. Such an inference is allowed and is not considered as a “breach” of privacy.