Distributed Function Secret Sharing and Applications

Function Secret Sharing (FSS) has emerged as a pivotal cryptographic tool for secure computation, delivering exceptional online efficiency with constant interaction rounds. However, the reliance on a trusted third party for key generation in existing FSS works compromises both security and practical deployment. In this paper, we introduce efficient distributed key generation schemes for FSS-based distributed point function and distributed comparison function, supporting both input and output to be arithmetic-shared. We further design crucial FSSbased components optimized for online efficiency, serving as the building blocks for advanced protocols. Finally, we propose an efficient framework for evaluating complex trigonometric functions, ubiquitous in scientific computations. Our framework leverages the periodic property of trigonometric functions, which reduces the bit length of input during FSS evaluation. This mitigates the potential performance bottleneck for FSS-based protocols incurred by bit length. Extensive empirical evaluations on real-world applications demonstrate a latency reduction of up to 14.73× and a communication cost decrease ranging from 27.67 ∼ 184.42× over the state-of-the-art work.