Comparison of FHE Schemes and Libraries for Efficient Cryptographic Processing

In recent years, opportunities to collect and analyze big data in the cloud have increased. Cryptographic processing is imperative for protecting data on cloud servers, and homomorphic encryption, which can perform calculations in an encrypted state, is highly expected for this purpose. Fully Homomorphic Encryption (FHE) is an encryption scheme that allows for addition and multiplication operations any number of times in an encrypted state. In the pursuit of practical applications of FHE, multiple encryption schemes have been proposed, and several libraries are available for executing these schemes. In this study, we first conducted a comparison to help select the appropriate FHE encryption scheme and library based on the execution environment and processing requirements of the application. Specifically, we organize the time-space complexity and compatible operations for BFV, BGV, CKKS, and Zama's variant of TFHE schemes implemented in OpenFHE, Lattigo, and TFHEpp libraries. For achieving 128-bit security, it was found that BGV, BFV, and CKKS, in that order, are the fastest. Additionally, the memory usage varied depending on the library, with OpenFHE requiring less memory than Lattigo. It is worth noting the differences in the encryption processes of BFV, BGV and CKKS schemes compared with Zama's variant of TFHE scheme. In the comparison between CKKS and Zama's variant of TFHE, Zama's variant of TFHE was more compatible with multiplications between arbitrary values, but CKKS was more compatible with vector inner products. A common challenge for all FHE encryption schemes is their immense time-space complexity. Therefore, as a second consideration, we compared the execution times and Solid State Drive (SSD) bandwidths between OpenFHE and TFHEpp for Zama's variant of TFHE in environments with limited DRAM, such as in the cloud. It was found that TFHEpp is faster when DRAM is limited. This is because the gate key generation time in OpenFHE significantly increases owing to a lack of memory required for arithmetic processing.