Paper 2023/631

Optimization of Functional Bootstrap with Large LUT and Packing Key Switching

Abstract

Homomorphic encryption can perform calculations on encrypted data, which can protect the privacy of data during the usage of data. Functional Bootstraps algorithm proposed by I. Chillotti et al. can compute arbitrary functions represented as lookup table whilst bootstrapping, but the computational efficiency of F unctional Bootstraps with large lookup table or highly precise functions is not high enough. To tackle this issue, we propose a new Tree-BML algorithm. Our Tree-BML algorithm accelerates the computation of F unctional Bootstraps with large LUT by compressing more LWE ciphertexts to a TRLWE ciphertext and utilizing the PBSmanyLUT algorithm which was proposed by I. Chillotti et al. in 2021. The Tree-BML algorithm reduces the running time of LUT computation by 72.09% compared to Tree-based method(Antonio Guimarães et al., 2021). Additionally, we introduce a new TLWE-to-TRLWE Packing Key Switching algorithm which reduces the storage space required and communication overhead of homomorphic encryption algorithm by only generating one of those key-switching key ciphertexts of polynomials with the same non-zero coefficient values but only those values located in different slots. Our algorithm reduces the key-switching key size by 75% compared to Base-aware TLWE-to-TRLWE Key Switching algorithm. Finally, we obtained that our algorithms does not introduce new output error through theoretical and experiment result.