Computing the maximum from a list of secret inputs is a widely-used functionality that is employed either 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 affirmative, 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 computation 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 results 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$\Pi_{\text{Max}}$achieves an 18% reduction in online execution time and a 67% decrease in communication volume compared to the most efficient existing solution.

Privacy is a major concern in large-scale digital applications, such as cloud-computing, machine learning services, and access control. Users want to protect not only their plain data but also their associated attributes (e.g., age, location, etc). Functional encryption (FE) is a cryptographic tool that allows fine-grained access control over encrypted data. However, existing FE fall short as they are either inefficient and far from reality or they leak sensitive user-specific information. We propose SACfe, a novel attribute-based FE scheme that provides secure, fine-grained access control and hides both the user's attributes and the function applied to the data, while preserving the data's confidentiality. Moreover, it enables users to encrypt unbounded-length messages along with an arbitrary number of hidden attributes into ciphertexts. We design SACfe, a protocol for performing linear computation on encrypted data while enforcing access control based on inner product predicates. We show how SACfe can be used for online biometric authentication for privacy-preserving access control. As an additional contribution, we introduce an attribute-based linear FE for unbounded length of messages and functions where access control is realized by monotone span programs. We implement our protocols using the CiFEr cryptographic library and show its efficiency for practical settings.