An Empirical Study on Privacy and Secure Multi-party Computation Using Exponentiation

Protocols for secure multi-party computation allow participants to share a computation while each party learns only what can be inferred from their own inputs and the output of the computation. However, the execution time of a secure protocol may be too high therefore it is not practical unless some tradeoffs are made between data access and confidentiality. This paper aims to provide some empirical basis for making such tradeoffs in computing exponentiation. We have designed exponentiation protocols for secure two-party computation using scalar products as the basic building blocks. A detailed performance evaluation was carried out by taking advantage of the compositional nature of our protocols. We have come up with a time function which provides good prediction of the execution time of the proposed exponentiation protocols based on the execution time of scalar products. Using the time function, we have obtained several interesting tradeoffs between execution time and privacy. In particular, compromising some private information enables a reduction in the execution time from years, if not centuries, to days or even minutes. Based on our results, we argue that there are indeed reasonable tradeoffs between privacy and execution time. Furthermore, our study indicates that a system intelligently offering users possible tradeoff options will make secure multi-party computation a more attractive approach to enhancing privacy in practice.