Improved Programmable Bootstrapping with Larger Precision and Efficient Arithmetic Circuits for TFHE

Chillotti, Ilaria; Ligier, Damien; Orfila, Jean-Baptiste; Tap, Samuel

doi:10.1007/978-3-030-92078-4_23

Cited by 60 publications

(63 citation statements)

References 22 publications

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“…Among them, the comparison operation proposed in [9] has the best performance, and we improve the performance of [9]. Another comparison operation method on the CKKS scheme that uses FHEW/TFHE bootstrapping was recently studied [23]- [26]. Although this approach uses FHEW/TFHE bootstrapping, users can still use efficient word-wise operations in the CKKS scheme with this approach, and when a comparison operation is required, users switch the ciphertexts to FHEW/TFHE ciphertexts and perform the comparison operation using FHEW/TFHE bootstrapping.…”

Section: A Our Contributionsmentioning

confidence: 99%

Optimization of Homomorphic Comparison Algorithm on RNS-CKKS Scheme

Lee

Kim

et al. 2022

IEEE Access

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Since the sign function can be used to implement the comparison operation, max function, and rectified linear unit (ReLU) function, several studies have been conducted to efficiently evaluate the sign function in the Cheon-Kim-Kim-Song (CKKS) scheme, one of the most promising fully homomorphic encryption schemes. Recently, Lee et al. (IEEE Trans. Depend. Sec. Comp.) proposed a practically optimal approximation method of sign function on the CKKS scheme using a composition of minimax approximate polynomials. In addition, Lee et al. proposed a polynomial-time algorithm that finds degrees of component polynomials minimizing the number of non-scalar multiplications for homomorphic comparison/max/ReLU functions. However, homomorphic comparison/max/ReLU functions using Lee et al.'s approximation method have not been successfully implemented on the residue number system variant CKKS (RNS-CKKS) scheme. In addition, the degrees of component polynomials found by Lee et al.'s algorithm are not optimized for the RNS-CKKS scheme because the algorithm does not consider that the running time of non-scalar multiplication depends much on the ciphertext level in the RNS-CKKS scheme. In this paper, we propose a fast algorithm for inverse minimax approximation error, a subroutine required to find the optimal set of degrees of component polynomials. This proposed algorithm makes it possible to find the optimal set of degrees of component polynomials with higher degrees than the previous study. In addition, we propose a method to find the degrees of component polynomials optimized for the RNS-CKKS scheme using the proposed algorithm for inverse minimax approximation error. We successfully implement the homomorphic comparison, max function, and ReLU function algorithms on the RNS-CKKS scheme with a low comparison failure rate (< 2 −15 ) and provide the various parameter sets according to the precision parameter α. We reduce the depth consumption of the homomorphic comparison, max function, and ReLU function algorithms by one depth for several α. In addition, the numerical analysis demonstrates that the homomorphic comparison, max function, and ReLU function algorithms using the degrees of component polynomials found by the proposed algorithm reduce running time by 6%, 7%, and 6% on average compared with those using the degrees of component polynomials found by Lee et al.'s algorithm, respectively.INDEX TERMS Cheon-Kim-Kim-Song (CKKS) scheme, fully homomorphic encryption (FHE), homomorphic comparison operation, minimax approximate polynomial, Remez algorithm, residue number system variant CKKS (RNS-CKKS) scheme.

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Section: A Our Contributionsmentioning

confidence: 99%

Optimization of Homomorphic Comparison Algorithm on RNS-CKKS Scheme

Lee

Kim

et al. 2022

IEEE Access

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“…In a recent paper [11], authors identify altogether eight limitations of TFHE, among them is the limited message space size (point B in [11]). To overcome this limitation, several authors suggest to split a long input into smaller chunks and then evaluate a series of LUTs: either using the binary message space for arbitrary functions [9], or using a multivalue message space for the comparison of unbounded integers [5], for integer addition [24,28], or for arbitrary functions [19,11]. Another limitation of TFHE, which is not fully addressed yet, is the fact that the bootstrapping operation is not multi-thread friendly (point C in [11]; resolved to certain extent).…”

Section: Problem Statementmentioning

confidence: 99%

“…To overcome this limitation, several authors suggest to split a long input into smaller chunks and then evaluate a series of LUTs: either using the binary message space for arbitrary functions [9], or using a multivalue message space for the comparison of unbounded integers [5], for integer addition [24,28], or for arbitrary functions [19,11]. Another limitation of TFHE, which is not fully addressed yet, is the fact that the bootstrapping operation is not multi-thread friendly (point C in [11]; resolved to certain extent).…”

Section: Problem Statementmentioning

confidence: 99%

Parallel Operations over TFHE-Encrypted Multi-Digit Integers

Klemsa

Önen

2022

Proceedings of the Twelfth ACM Conference on Data and Application Security and Privacy

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Recent advances in Fully Homomorphic Encryption (FHE) allow for a practical evaluation of non-trivial functions over encrypted data. In particular, novel approaches for combining ciphertexts broadened the scope of prospective applications. However, for arithmetic circuits, the overall complexity grows with the desired precision and there is only a limited space for parallelization.In this paper, we put forward several methods for fully parallel addition of multi-digit integers encrypted with the TFHE scheme. Since these methods handle integers in a special representation, we also revisit the signum function, firstly addressed by Bourse et al., and we propose a method for the maximum of two numbers; both with particular respect to parallelization. On top of that, we outline an approach for multiplication by a known integer.According to our experiments, the fastest approach for parallel addition of 31-bit encrypted integers in an idealized setting with 32 threads is estimated to be more than 6× faster than the fastest sequential approach. Finally, we demonstrate our algorithms on an evaluation of a practical neural network.

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“…with binary coefficients (in a recent work [121], the authors used Z q instead of a torus). Then, the TRLWE scheme is constructed as follows:…”

Section: Scheme V3: Trlwe Scheme [14]mentioning

confidence: 99%

“…A relevant feature of the TFHE scheme is that the bootstrapping technique enables an univariate function to be evaluated simultaneously to the noise reduction operation [121]. This is normally referred to as programmable bootstrapping (PBS).…”

Section: Scheme V3: Trlwe Scheme [14]mentioning

confidence: 99%

Survey on Fully Homomorphic Encryption, Theory and Applications

Marcolla¹,

Sucasas²,

Manzano³

et al. 2022

Preprint

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This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption FHE. It consequently covers design fundamentals and security properties of FHE, and describes the main FHE schemes based on various mathematical problems. On a more practical level, the paper presents a view on privacy-preserving Machine Learning using homomorphic encryption, then surveys FHE at length from an engineering angle, covering the potential application of FHE in fog computing, and cloud computing services. It also provides a comprehensive analysis of existing state-of-the-art FHE libraries and tools, implemented in software and hardware, and the performance thereof.

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Improved Programmable Bootstrapping with Larger Precision and Efficient Arithmetic Circuits for TFHE

Cited by 60 publications

References 22 publications

Optimization of Homomorphic Comparison Algorithm on RNS-CKKS Scheme

Optimization of Homomorphic Comparison Algorithm on RNS-CKKS Scheme

Parallel Operations over TFHE-Encrypted Multi-Digit Integers

Survey on Fully Homomorphic Encryption, Theory and Applications

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