An efficient secure interval test protocol for small integers

The interval test problem is a variant of Yao’s millionaires’ problem to check whether a value $x$ belongs to an interval $R$. Existing solutions to the interval test problem prioritize generic protocols but encounter efficiency challenges. There is a growing interest in developing efficient and secure multi-party computation protocols tailored to specific applications. In this paper, we propose a secure and simplified protocol for solving the interval test problem. This protocol exhibits high generality, as it only requires invocations of the private set intersection cardinality (PSI-CA) subprotocol. Furthermore, we modify it to construct a more efficient protocol for small integers by introducing oblivious transfer (OT) to reduce the times of homomorphic encryption. Our protocols provide privacy protection for both clients and servers in the semi-honest security model. We evaluate the computational and communication overhead of our protocols. Our OT-based secure interval test (OT-SIT) protocol is seven times faster than existing protocols for 18-bit integers. When the bit length is 4, it reduces communication overhead by approximately 97%. The upstream overhead is as low as 500 B. However, it uses binary tree structures, so the advantages in computation and communication quickly diminish as the bit length increase.