International Association
for Cryptologic Research

Computing the maximum from a list of secret inputs is a widely-used functionality that is employed ei- ther indirectly as a building block in secure computation frameworks, such as ABY (NDSS’15) or directly used in multiple applications that solve optimisation problems, such as secure machine learning or secure aggregation statistics. Incremental distributed point function (I-DPF) is a powerful primitive (IEEE S&P’21) that significantly reduces the client- to-server communication and are employed to efficiently and securely compute aggregation statistics. In this paper, we investigate whether I-DPF can be used to improve the efficiency of secure two-party computation (2PC) with an emphasis on computing the maximum value and the k-th (with k unknown to the computing parties) ranked value from a list of secret inputs. Our answer is affir- mative, and we propose novel secure 2PC protocols that use I-DPF as a building block, resulting in significant efficiency gains compared to the state-of-the-art. More precisely, our contributions are: (i) We present two new secure computa- tion frameworks that efficiently compute secure aggregation statistics bit-wisely or batch-wisely; (ii) we propose novel protocols to compute the maximum value, the k-th ranked value from a list of secret inputs; (iii) we provide variations of the proposed protocols that can perform batch computations and thus provide further efficiency improvements; and (iv) we provide an extensive performance evaluation for all proposed protocols. Our protocols have a communication complexity that is independent of the number of secret inputs and linear to the length of the secret input domain. Our experimental re- sults show enhanced efficiency over state-of-the-art solutions, particularly notable when handling large-scale inputs. For instance, in scenarios involving an input set of five million elements with an input domain size of 31 bits, our protocol ΠMax achieves an 18% reduction in online execution time and a 67% decrease in communication volume compared to the most efficient existing solution.