Investigate what parts of Li-Yamana 2023 can be incorporated into HEIR

Privacy Preserving Function Evaluation using Lookup Tables with Word-Wise FHE
Ruixiao LI and Hayato YAMANA

https://www.jstage.jst.go.jp/article/transfun/advpub/0/advpub_2023EAP1114/_pdf/-char/ja

> This paper proposes a novel LUT-based privacy-preserving function evaluation method to handle multi-input functions while reducing the latency by adopting word-wise HE. Our optimization strategy adjusts table sizes to minimize the latency while preserving function output accuracy, especially for common machine-learning functions. Through our experimental evaluation utilizing the BFV scheme of the Microsoft SEAL library, we confirmed the runtime of arbitrary functions whose LUTs consist of all input-output combinations represented by given input bits: 1) single-input 12-bit functions in 0.14 s, 2) single-input 18-bit functions in 2.53 s, 3) two-input 6-bit functions in 0.17 s, and 4) three-input 4-bit functions in 0.20 s, employing four threads. Besides, we confirmed that our proposed table size optimization strategy worked well, achieving 1.2 times speed up with the same absolute error of order 10−4 for Swish and 1.9 times speed up for ReLU while decreasing the absolute error from order 10−2 to 10−4 compared to the baseline, i.e., polynomial approximation.