A Survey on Implementations of Homomorphic Encryption Schemes

Abstract

With the increased need for data confidentiality in various applications of our daily life, homomorphic encryption (HE) has emerged as a promising cryptographic topic. HE enables to perform computations directly on encrypted data (ciphertexts) without decryption in advance. Since the results of calculations remain encrypted and can only be decrypted by the data owner, confidentiality is guaranteed and any third party can operate on ciphertexts without access to decrypted data (plaintexts). Applying a homomorphic cryptosystem in a real-world application depends on its resource efficiency. Several works compared different HE schemes and gave the stakes of this research field. However, the existing works either do not deal with recently proposed HE schemes (such as CKKS) or focus only on one type of HE. In this paper, we conduct an extensive comparison and evaluation of homomorphic cryptosystems’ performance based on their experimental results. The study covers all three families of HE, including several notable schemes such as BFV, BGV, CKKS, RSA, El-Gamal, and Paillier, as well as their implementation specification in widely used HE libraries, namely Microsoft SEAL, PALISADE, and HElib. In addition, we also discuss the resilience of HE schemes to different kind of attacks such as Indistinguishability under chosen-plaintext attack and integer factorization attacks on classical and quantum computers.

A Blockchain-Based End-to-End Data Protection Model for Personal Health Records Sharing: A Fully Homomorphic Encryption Approach

“…BFV also has better performance when compared to Paillier. We considered a 128-bit security level parameter, as stated in [ 54 ], to compare both aforesaid algorithms, then we extrapolated it to our database to obtain a metric and compare the models. We show the result in Figure 6 .…”

HEProfiler: An In-Depth Profiler of Approximate Homomorphic Encryption Libraries

“…Most relevant to our work, they conclude that CKKS homomorphic multiplication is best implemented by PALISADE at smaller parameters, but that SEAL performs better at larger parameters. Doan et al [9] survey many different fully and partially homomorphic encryption schemes. Their survey covers many aspects, such as theoretical capabilities and limits, security differences, and performance comparison.…”

“…This approach to parameter selection allows us to fairly evaluate library performance in a wide range of circumstances without the tedious manual selection of parameters. Other works [8,9] assign CKKS parameters (e.g., N , |q|) directly and force the libraries to adhere to these; we instead allow libraries to select their own parameters. We give the parameters for leveled CKKS that each library chooses in Table 2.…”

“…Many other works similarly profile FHE performance [8][9][10][11][12][13][14]. In our work, in order to give a fair comparison, we faced the challenge of finding equitable ways to compare libraries while allowing each library the freedom to exercise its parameter selection strategies.…”

“…(For example: HEAAN allows the user to choose from a small set of precomputed parameter settings based on the computation's multiplicative depth, while HElib asks the user to directly choose many parameters of the underlying ring polynomials used in CKKS.) In contrast, many other works simply mandate parameters for all profiled libraries [8,9], depriving the libraries of the opportunity to use their own unique strategies for selecting the best parameters for good performance. Our review and profiling was advised by lead contributors of each of these libraries, allowing us to very thoroughly perform a fair comparison without disadvantaging any library.…”