Efficient FHEW Bootstrapping with Small Evaluation Keys, and Applications to Threshold Homomorphic Encryption

Lee, Yongwoo; Micciancio, Daniele; Kim, Andrey; Choi, Rakyong; Deryabin, Maxim; Eom, Jieun; Yoo, Dong-Hoon

doi:10.1007/978-3-031-30620-4_8

Cited by 22 publications

(18 citation statements)

References 38 publications

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“…The enhancements in the usage of FHEW/TFHE itself has also been studied throughout many works, including the extension of binary keys to general keys (ternary, Gaussian, etc.) [20,32], or improved FHEW bootstrapping with ring automorphisms [28]. When it come to high precision TFHE, most of the works select decomposition of plaintext message [15,19,22,29,34], with low precision TFHE bootstrapping, and no algorithm was known to bootstrap a single ciphertext with large precision except using large N .…”

Section: Related Workmentioning

confidence: 99%

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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Section: Related Workmentioning

confidence: 99%

Discretization Error Reduction for High Precision Torus Fully Homomorphic Encryption

Lee

Yoon

2023

Lecture Notes in Computer Science

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“…Recently, many efficient implementations of NTT and NTT-based polynomial multiplication have been proposed in the literature, which makes NTT-based polynomial multiplication the core arithmetic operation in the majority of homomorphic encryption implementations. In addition, there have been some recent studies that improve the efficiency of bootstrapping by optimizing the blind rotation algorithm [8,9].…”

Section: Introduction 1motivationmentioning

confidence: 99%

Parallel Accelerating Number Theoretic Transform for Bootstrapping on a Graphics Processing Unit

Li,

Pan,

et al. 2024

Mathematics

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The bootstrapping procedure has become the main bottleneck affecting the efficiency of all known fully homomorphic encryption (FHE) schemes. The state-of-the-art scheme for efficient bootstrapping, which is called fully homomorphic encryption over the torus (TFHE), accelerates polynomial multiplication by leveraging number theoretic transform (NTT) and implementing NTT in parallel on a GPU. Unfortunately, almost none of the recent advancements in NTT take full advantage of a GPU, leading to the need for more time. With this in mind, in this work, a novel faster number theoretic transform based on a GPU is proposed, in which matrix multiplication is used to implement a decomposed small-point NTT. When implementing matrix multiplication, we introduce a merging preprocessing method to merge multiple inputs of the small-point NTT, aiming to effectively minimize the count of modulo operations. Subsequently, when the merged result is multiplied by rotation factors, we use logical left shift rather than arithmetic multiplication to improve the computational efficiency. Our scheme can easily be used to realize a 1024-point NTT and the results of the experiments show that the speedup ratio of our method over the butterfly algorithm is about 2.49.

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“…Recently, Lee et al [12] briefly introduced (a theoretical version of) a MPHE protocol based on TFHE. They first design a single key TFHE with larger coefficients for the secret key and then, they naturally extend it to the MPHE version, introducing a simple (global) bootstrapping key generation algorithm which requires all parties' local bootstrapping keys.…”

Section: Introductionmentioning

confidence: 99%

“…We observe that their technique requires only k multiplications in the FFT domain among bootstrapping keys in the main loop of the boostrapping algorithm. Whereas Lee et al [12] makes use of key switching including two FFT conversions and an external product, which is more expensive than the k FFT multiplications in every loop. However, a detailed comparison of both techniques, even in the single key setting, has not appeared in the literature just yet.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, we compare the complexity of the bootstrapping technique of [12] with our extension of [13] and we show which scheme performs better in what parameter sets, based on our noise analysis. We provide a prototype implementation of our key generation algorithm using the Concrete library [14] with exact parameters yielding at least 110 bits security.…”

Section: Introductionmentioning

confidence: 99%

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Efficient TFHE Bootstrapping in the Multiparty Setting

Park,

Rovira

2023

IEEE Access

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TFHE is a practical fully homomorphic encryption scheme (FHE) capable of computing any boolean gate or non-linear function. The scheme was originally designed to work for the single key setting. To implement realistic application scenarios, it is necessary to extend it to handle multiple users. In this paper, we introduce a new approach to generate TFHE bootstrapping keys for (predefined) multiple users. Hence, a fixed number of users can enjoy the same level of efficiency as in the single key setting, keeping their individual input privacy. Our construction relies on a novel algorithm called homomorphic indicator, which can be of independent interest. We provide a detailed analysis of the noise growth and a set of secure parameters suitable to be used in practice. Moreover, we compare the complexity of our technique with other state-of-the-art constructions and show which method performs better depending on the parameter sets. We also provide a prototype implementation of our technique. To the best of our knowledge, this is the first implementation of TFHE in the multiparty setting.

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Efficient FHEW Bootstrapping with Small Evaluation Keys, and Applications to Threshold Homomorphic Encryption

Cited by 22 publications

References 38 publications

Discretization Error Reduction for High Precision Torus Fully Homomorphic Encryption

Discretization Error Reduction for High Precision Torus Fully Homomorphic Encryption

Parallel Accelerating Number Theoretic Transform for Bootstrapping on a Graphics Processing Unit

Efficient TFHE Bootstrapping in the Multiparty Setting

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