An Efficient and Scalable FHE-Based PDQ Scheme: Utilizing FFT to Design a Low Multiplication Depth Large-Integer Comparison Algorithm

The growing number of data privacy breaches and associated financial losses have driven the demand for private database queries. Clients typically submit queries that involve both search and computation operations, such as counting students under a certain age or calculating the BMI of employees above a specific age. Existing protocols often face limitations due to reliance on specific-purpose encryption schemes or multiple communication rounds between clients and servers. In this work, we present a unified framework utilizing fully homomorphic encryption techniques to efficiently and privately process queries with search and computation operations. Our contributions include a homomorphic encryption-based private comparison algorithm, called the layered comparison algorithm, which achieves a 2.6-6.6X performance improvement compared to algorithms from prior work; a fast Fourier transform-based preprocessing method enabling accurate large integer arithmetic operations in the encrypted domain; and a scalable database encoding method. Evaluation results demonstrate the practicality of our system, as it processes an aggregated query for a 1k-row encrypted database in approximately 4.53 seconds.