Client-Aided Two-Party Secure Interval Test Protocol

Secure interval test protocol checks if an integer is within some interval in a privacy-preserving manner. A natural application is geological location hiding, where we can check whether a person is in a certain territory without revealing any information. In addition, secure interval test protocol enables us to do arithmetic over private values with rounding errors. Therefore, it allows servers to obtain an approximation of a complicated function.In this work, we present an efficient secure interval test protocol that checks whether a shared value is within the range of two plain values. We also show that the interval test protocol can be used as a building block to construct protocols with richer functionality such as the approximation of exponential functions or logarithmic functions.Our protocol is constructed in the client-aided model, which is briefly mentioned in some previous work on constructing practical MPC frameworks such as SecureML (S&P'17), in which any number of clients can not only create shares of their inputs but also generate some necessary correlated randomness used in the online phase and distribute them to servers. Such correlated randomness generated by clients serves efficient protocols since servers don't have to jointly generate randomness by themselves, which can avoid costly computation/communication.In this paper, we improve the state-of-the-art secure interval test protocol by Nishide and Ohta (PKC'07) based on a secret sharing scheme. We use the client-aided model and tree-based techniques, which contribute to reducing communication rounds. Our proposed protocol has only 4 communication rounds regardless of the bit length of inputs. This is about 3 times fewer rounds than existing protocols. Using the proposed protocol, we further introduce a secure look-up table technique that can be utilized to securely compute some richer functions.