Improved Secure Integer Comparison via Homomorphic Encryption

Bourse, Florian; Sanders, Olivier; Traoré, Jacques

doi:10.1007/978-3-030-40186-3_17

Cited by 29 publications

(31 citation statements)

References 40 publications

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“…Table 5 compares them with the integer comparison implemented by Zhou et al [ZLPL20] using logic gates. We calculated the speedups using as reference the slowest implementation, which, in this case, is the second implementation of Bourse et al [BST20]. However, adjusting the speedups to consider the difference in speed between machines, we can see that the implementation of Zhou et al [ZLPL20] using logic gates is up to 1.75 times slower than the one of Bourse et al [BST20] and up to 5.6 times slower than ours.…”

Section: -Bit Integer Comparisonmentioning

confidence: 79%

“…We calculated the speedups using as reference the slowest implementation, which, in this case, is the second implementation of Bourse et al [BST20]. However, adjusting the speedups to consider the difference in speed between machines, we can see that the implementation of Zhou et al [ZLPL20] using logic gates is up to 1.75 times slower than the one of Bourse et al [BST20] and up to 5.6 times slower than ours. The chaining and tree-based methods perform the same number of bootstraps and should present a very a Execution time provided by the authors, who executed experiments on a machine 3.67 times slower than ours.…”

Section: -Bit Integer Comparisonmentioning

confidence: 79%

“…This second method is a generalized version of the integer comparison algorithm of Bourse et al [BST20]. It is much more functionally restricted than the first method, but it usually presents a smaller error growth.…”

Section: Chaining Methodsmentioning

confidence: 99%

“…To represent unbounded integers, we decompose them in digits of the base B and encrypt each digit in a TLWE sample. This approach is more common for applications using binary digits, but it has also been used with arbitrary bases [BST20].…”

Section: Functional Bootstrap In Tfhementioning

confidence: 99%

“…Integer comparison is an extremely useful function in computing, but it presents some challenges to be implemented in homomorphic circuits, especially for unbounded integers. Bourse et al [BST20] presented a very efficient implementation using the functional bootstrap of TFHE. The chaining method we presented in Section 3.2 is a generalization of their technique.…”

Section: -Bit Integer Comparisonmentioning

confidence: 99%

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Revisiting the functional bootstrap in TFHE

Guimarães

Borin

Aranha

2021

TCHES

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The FHEW cryptosystem introduced the idea that an arbitrary function can be evaluated within the bootstrap procedure as a table lookup. The faster bootstraps of TFHE strengthened this approach, which was later named Functional Bootstrap (Boura et al., CSCML’19). From then on, little effort has been made towards defining efficient ways of using it to implement functions with high precision. In this paper, we introduce two methods to combine multiple functional bootstraps to accelerate the evaluation of reasonably large look-up tables and highly precise functions. We thoroughly analyze and experimentally validate the error propagation in both methods, as well as in the functional bootstrap itself. We leverage the multi-value bootstrap of Carpov et al. (CT-RSA’19) to accelerate (single) lookup table evaluation, and we improve it by lowering the complexity of its error variance growth from quadratic to linear in the value of the output base. Compared to previous literature using TFHE’s functional bootstrap, our methods are up to 2.49 times faster than the lookup table evaluation of Carpov et al. (CT-RSA’19) and up to 3.19 times faster than the 32-bit integer comparison of Bourse et al. (CT-RSA’20). Compared to works using logic gates, we achieved speedups of up to 6.98, 8.74, and 3.55 times over 8-bit implementations of the functions ReLU, Addition, and Maximum, respectively.

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Section: -Bit Integer Comparisonmentioning

confidence: 79%

Section: -Bit Integer Comparisonmentioning

confidence: 79%

Section: Chaining Methodsmentioning

confidence: 99%

Section: Functional Bootstrap In Tfhementioning

confidence: 99%

Section: -Bit Integer Comparisonmentioning

confidence: 99%

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Revisiting the functional bootstrap in TFHE

Guimarães

Borin

Aranha

2021

TCHES

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Privacy-Preserving Machine Learning Using Cryptography

Rechberger

Walch

2022

Security and Artificial Intelligence

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Discretization Error Reduction for High Precision Torus Fully Homomorphic Encryption

Lee

Yoon

2023

Lecture Notes in Computer Science

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In recent history of fully homomorphic encryption, bootstrapping has been actively studied throughout many HE schemes. As bootstrapping is an essential process to transform somewhat homomorphic encryption schemes into fully homomorphic, enhancing its performance is one of the key factors of improving the utility of homomorphic encryption.In this paper, we propose an extended bootstrapping for TFHE, which we name it by EBS. One of the main drawback of TFHE bootstrapping was that the precision of bootstrapping is mainly decided by the polynomial dimension N . Thus if one wants to bootstrap with high precision, one must enlarge N , or take alternative method. Our EBS enables to use small N for parameter selection, but to bootstrap in higher dimension to keep high precision. Moreover, it can be easily parallelized for faster computation. Also, the EBS can be easily adapted to other known variants of TFHE bootstrappings based on the original bootstrapping algorithm.We implement our EBS along with the full domain bootstrapping methods known (FDFB, TOTA, Comp), and show how much our EBS can improve the precision for those bootstrapping methods. We provide experimental results and thorough analysis with our EBS, and show that EBS is capable of bootstrapping with high precision even with small N , thus small key size, and small complexity than selecting large N by birth.

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Improved Secure Integer Comparison via Homomorphic Encryption

Cited by 29 publications

References 40 publications

Revisiting the functional bootstrap in TFHE

Revisiting the functional bootstrap in TFHE

Privacy-Preserving Machine Learning Using Cryptography

Discretization Error Reduction for High Precision Torus Fully Homomorphic Encryption

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