A server-aided secure interval test and comparison protocol with OPRF

Abstract

As mobile and edge devices become more prevalent, applications handling sensitive data, such as health monitoring, age verification for online services, and vulnerability scanning tools, are becoming increasingly common. The comparison of critical data (e.g., health metrics, ages, or software versions) is essential for informed decision-making. However, securely processing this sensitive information in resource-limited environments presents significant challenges. To address these challenges, we propose a server-aided secure interval test and comparison protocol based on point and range encoding. The proposed protocol allows two parties to verify if a value belongs to an interval or is less than another value without revealing their private inputs. To handle the set membership problem in the encoding, we introduce an innovative oblivious updatable key pseudorandom function. Leveraging this function, our protocol achieves efficient delegation to a cloud server, ensures that online costs grow linearly with input length, and maintains exceptionally low amortized preprocessing costs. We formally prove the semi-honest security of our protocol and compare it to the other semi-honest protocols. On the client side, our protocol requires only tens of microseconds for computational time and less than 1 KB for communication cost for inputs up to 40 bits. Compared to the other secure interval test protocols, it significantly reduces both computational and communication costs, especially for larger inputs. Moreover, it achieves the lowest computation costs while maintaining similar communication costs to the other secure comparison protocols.