A fully homomorphic encryption scheme with better key size

Chen, Zhigang; Wang, Jian; Zhang, Zengnian; Song, Xiangfei

doi:10.1109/cc.2014.6969773

Cited by 16 publications

(6 citation statements)

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“…Suppose ciphertext c i under the secret key S L is a fresh ciphertext for i∈{1,2}, namely, c i ←FHE.Enc(pk 1 , m i ). According to the analysis in [20]- [23], we get e mult 1 ∞ < 5(n 2 + t)BE, e mult 2 ∞ < (1/2)(n 2 + t) 2 B 2 and e t ∞ < (n 2 +t) 2 B+(1/2)n 2 B. Putting these together, we get the bound of noise magnitude after once homomorphic multiplication between two fresh ciphertexts such as…”

Section: Noise Analysismentioning

confidence: 96%

A Multi-Bit Fully Homomorphic Encryption With Shorter Public Key From LWE

Song

Chen

2019

IEEE Access

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There has been a great deal of work on improving the efficiency of fully homomorphic encryption (FHE) scheme. Our approach, in this regard, is to use the idea of packed ciphertexts to construct a multi-bit FHE with a short public key on the basis of the learning with errors (LWE) problem. More specifically, our FHE scheme builds on a basic encryption scheme that chooses LWE samples from the Gaussian distribution and adds Gaussian error to it. This results in decreasing the number of LWE samples from 2nlogq to n + 1. We prove that our FHE scheme is pragmatically feasible and its security relies on the hardness of the LWE problem. In addition, we form a new process of key switching for multi-bit FHE based on the ideas adopted by Brakerski et al. for optimizing the process of key switching. Finally, we analyze and compare the concrete parameters between our FHE scheme and BGH13 scheme. The result shows that compared with the BGH13 scheme, our scheme has a smaller public key by a factor about logq.INDEX TERMS Fully homomorphic encryption, public key encryption, multi-bit plaintext, concrete security parameters.

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Section: Noise Analysismentioning

confidence: 96%

A Multi-Bit Fully Homomorphic Encryption With Shorter Public Key From LWE

Song

Chen

2019

IEEE Access

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“…Approximate eigenvector DGHV10 [26] CMNT11 [27] CNT12 [28] CCKM+13 [29] CLT14 [30] CS15 [31] BBL17 [32] BV11 [33] BGV12 [20] CWZS14 [35] CSZ16 [37] BLLN13 [38] CZ17 [42] CKKS17 [45] CHKK+18 [46] GSW13 [48] AP14 [49] DM15 [51] CGGI16 [52] KGV16 [53] BL14 [50] LGM16 [54] LMW17 [55] Bra12 [36] CCS19 [47] CH18 [44] Approximate greatest common divisor Figure 2. The development of fully homomorphic encryption.…”

Section: Relinearizationmentioning

confidence: 99%

“…It could execute one homomorphic multiplication without increasing the ciphertext size. Based on the assumption of binary LWE [ 34 ], Chen et al [ 35 ] proposed the CWZS14 FHE scheme, the concrete parameters of which are analyzed as follows. In this scheme, the secret key is generated from

randomly, where l is the dimension.…”

Section: Homomorphic Encryptionmentioning

confidence: 99%

“…Compared with Brakerski’s FHE scheme [ 36 ], in Chen’s scheme, the sizes of the public key and secret key are

times smaller, the size of tensor ciphertext is

times smaller and the key switching matrix is

times smaller, where q is the modulus. In [ 37 ], Chen’s scheme [ 35 ] was extended to the batch CSZ16 FHE scheme. Compared with the LWE assumption, the assumption of learning with errors over rings (RLWE) has the advantage that its polynomial multiplication can be implemented by the technique of the fast Fourier transform.…”

Section: Homomorphic Encryptionmentioning

confidence: 99%

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A Survey on Secure Computation Based on Homomorphic Encryption in Vehicular Ad Hoc Networks

Sun

Zhang

et al. 2020

Sensors

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In vehicular ad hoc networks (VANETs), the security and privacy of vehicle data are core issues. In order to analyze vehicle data, they need to be computed. Encryption is a common method to guarantee the security of vehicle data in the process of data dissemination and computation. However, encrypted vehicle data cannot be analyzed easily and flexibly. Because homomorphic encryption supports computations of the ciphertext, it can completely solve this problem. In this paper, we provide a comprehensive survey of secure computation based on homomorphic encryption in VANETs. We first describe the related definitions and the current state of homomorphic encryption. Next, we present the framework, communication domains, wireless access technologies and cyber-security issues of VANETs. Then, we describe the state of the art of secure basic operations, data aggregation, data query and other data computation in VANETs. Finally, several challenges and open issues are discussed for future research.

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“…Then some FHE schemes were proposed based on different mathematical hard problem. For example, the scheme is based on prime ideal [3], the schemes are based on integer [4][5][6] and the schemes are based on Learning with errors (LWE) or its ring variant (RLWE) [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

A General Design Method of Constructing Fully Homomorphic Encryption with Ciphertext Matrix

2019

KSII TIIS

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It is important to construct fully homomorphic encryption with ciphertext matrix that makes fully homomorphic encryption become very nature and simple. We present a general design method of constructing fully homomorphic encryption whose ciphertext is matrix. By using this design method, we can deduce a fully homomorphic encryption scheme step by step based on a basic encryption scheme. The process of deduction is similar to solving equation and the final output result is a fully homomorphic encryption scheme with ciphertext matrix. The idea of constructing ciphertext matrix is ciphertexts stack, which don't simply stack ciphertexts together but is to obtain the desired homomorphic property. We use decryption structure as tool to analyze homomorphic property and noise growth during homomorphic evaluation. By using this design method, we obtain three corresponding fully homomorphic encryption schemes. Our obtained fully homomorphic encryption schemes are more efficient.

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A fully homomorphic encryption scheme with better key size

Cited by 16 publications

References 0 publications

A Multi-Bit Fully Homomorphic Encryption With Shorter Public Key From LWE

A Multi-Bit Fully Homomorphic Encryption With Shorter Public Key From LWE

A Survey on Secure Computation Based on Homomorphic Encryption in Vehicular Ad Hoc Networks

A General Design Method of Constructing Fully Homomorphic Encryption with Ciphertext Matrix

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