Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Coron, Jean-Sébastien; Mandal, Avradip; Naccache, David; Tibouchi, Mehdi

doi:10.1007/978-3-642-22792-9_28

Cited by 312 publications

(261 citation statements)

References 14 publications

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“…To this end, we prove that n-MPACD is hard if PACD [26,15,16,8] is also hard. The reduction is provided in Appendix B.…”

Section: Masked Partial Approximate Common Divisorsmentioning

confidence: 98%

“…Asymptotic Parameters: When we consider algorithms for n-MPACD, we basically assume that parameters are set to thwart various lattice-based attacks and factoring algorithms; that is, γ (x 0 's bit size) must be large enough to prevent lattice-based attacks, so that γ = ω(η 2 log λ) [34,15,12] and η = ω(λ 2 ), to prevent an efficient factorization algorithm such as ECM from having sub-exponential complexity in the size of factors. In this paper, we focus on the size of errors r ij ∈ (−2 ρ , 2 ρ ) and the complexities of all algorithms associated with ρ.…”

Section: Masked Partial Approximate Common Divisorsmentioning

confidence: 99%

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Security Analysis of Multilinear Maps over the Integers

Lee

Seo

2014

Advances in Cryptology – CRYPTO 2014

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Abstract. At Crypto 2013, Coron, Lepoint, and Tibouchi (CLT) proposed a practical Graded Encoding Scheme (GES) over the integers, which has very similar cryptographic features to ideal multilinear maps. In fact, the scheme of Coron et al. is the second proposal of a secure GES, and has advantages over the first scheme of Garg, Gentry, and Halevi (GGH). For example, unlike the GGH construction, the subgroup decision assumption holds in the CLT construction. Immediately following the elegant innovations of the GES, numerous GES-based cryptographic applications were proposed. Although these applications rely on the security of the underlying GES, the security of the GES has not been analyzed in detail, aside from the original papers produced by Garg et al. and Coron et al. We present an attack algorithm against the system parameters of the CLT GES. The proposed algorithm's complexityÕ(2 ρ/2 ) is exponentially smaller thanÕ(2 ρ ) of the previous best attack of Coron et al., where ρ is a function of the security parameter. Furthermore, we identify a flaw in the generation of the zero-testing parameter of the CLT GES, which drastically reduces the running time of the proposed algorithm. The experimental results demonstrate the practicality of our attack.

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“…To this end, we prove that n-MPACD is hard if PACD [26,15,16,8] is also hard. The reduction is provided in Appendix B.…”

Section: Masked Partial Approximate Common Divisorsmentioning

confidence: 98%

Section: Masked Partial Approximate Common Divisorsmentioning

confidence: 99%

Security Analysis of Multilinear Maps over the Integers

Lee

Seo

2014

Advances in Cryptology – CRYPTO 2014

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“…2 can be expressed as polynomial equation as in (16). Such a polynomial equation can be efficiently implemented using our HE scheme.…”

Section: Binary Decision Treesmentioning

confidence: 99%

“…Starting with Gentry's mathematical breakthrough constructing the first plausible FHE scheme [22], [23], we have seen rapid development in the theory and implementation of homomorphic encryption (HE) schemes. HE schemes can now be based on a variety of cryptographic assumptions -approximate greatest common divisors [16], [18], learning with errors (LWE) [9], [10], [12], [25], and Ring-LWE (RLWE) [11], [24], [32].…”

Section: Introductionmentioning

confidence: 99%

SHIELD: Scalable Homomorphic Implementation of Encrypted Data-Classifiers

Khedr

Gulak

Vaikuntanathan

2016

IEEE Trans. Comput.

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Abstract-Homomorphic encryption (HE) systems enable computations on encrypted data, without decrypting and without knowledge of the secret key. In this work, we describe an optimized Ring Learning With Errors (RLWE) based implementation of a variant of the HE system recently proposed by Gentry, Sahai and Waters (GSW). Although this system was widely believed to be less efficient than its contemporaries, we demonstrate quite the opposite behavior for a large class of applications. We first highlight and carefully exploit the algebraic features of the system to achieve significant speedup over the state-of-the-art HE implementation, namely the IBM homomorphic encryption library (HElib). We introduce several optimizations on top of our HE implementation, and use the resulting scheme to construct a homomorphic Bayesian spam filter, secure multiple keyword search, and a homomorphic evaluator for binary decision trees. Our results show a factor of 10× improvement in performance (under the same security settings and CPU platforms) compared to IBM HElib for these applications. Our system is built to be easily portable to GPUs (unlike IBM HElib) which results in an additional speedup of up to a factor of 103.5× to offer an overall speedup of 1035×.

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“…Since then, candidate schemes have been based on a variety of computational assumptions (see, for example: [4,5,6,7]) including the decision learning with errors (DLWE ) assumption [8,9,10,1]. The latest DLWE -based work is due to Gentry, Sahai, and Waters (GSW) [1], and it is this work we focus most closely on in our paper.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Leakage Resilient Fully Homomorphic Encryption

Berkoff

Liu

2014

Theory of Cryptography

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Abstract. We construct the first leakage resilient variants of fully homomorphic encryption (FHE) schemes. Our leakage model is bounded adaptive leakage resilience. We first construct a leakage-resilient leveled FHE scheme, meaning the scheme is homomorphic for all circuits of depth less than some pre-established maximum set at key generation. We do so by applying ideas from recent works analyzing the leakage resilience of public key encryption schemes based on the decision learning with errors (DLWE ) assumption to the Gentry, Sahai and Waters ([1]) leveled FHE scheme. We then move beyond simply leveled FHE, removing the need for an a priori maximum circuit depth, by presenting a novel way to combine schemes. We show that by combining leakage resilient leveled FHE with multi-key FHE, it is possible to create a leakage resilient scheme capable of homomorphically evaluating circuits of arbitrary depth, with a bounded number of distinct input ciphertexts.

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Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Cited by 312 publications

References 14 publications

Security Analysis of Multilinear Maps over the Integers

Security Analysis of Multilinear Maps over the Integers

SHIELD: Scalable Homomorphic Implementation of Encrypted Data-Classifiers

Leakage Resilient Fully Homomorphic Encryption

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