Fully Homomorphic Encryption over the Integers

Dijk, Marten van; Gentry, Craig; Halevi, Shai; Vaikuntanathan, Vinod

doi:10.1007/978-3-642-13190-5_2

Cited by 1,198 publications

(772 citation statements)

References 24 publications

Supporting

Mentioning

690

Contrasting

Unclassified

Order By: Relevance

“…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%

Security Analysis of Multilinear Maps over the Integers

Lee

Seo

2014

Advances in Cryptology – CRYPTO 2014

View full text Add to dashboard Cite

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.

show abstract

Section: Masked Partial Approximate Common Divisorsmentioning

confidence: 99%

Security Analysis of Multilinear Maps over the Integers

Lee

Seo

2014

Advances in Cryptology – CRYPTO 2014

View full text Add to dashboard Cite

show abstract

“…They allow to outsource specific computations, e.g., encryption and signatures [18], to untrusted workers, but require interaction to compute arbitrary functions. Recently, Fully HE (FHE) schemes have been proposed for arbitrary computations on encrypted data [11,38,41]. When combined with GCs for verifiability (cf.…”

Section: Secure Computationmentioning

confidence: 99%

Twin Clouds: Secure Cloud Computing with Low Latency

Bugiel

Nürnberger

Sadeghi

et al. 2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Cloud computing promises a cost effective enabling technology to outsource storage and massively parallel computations. However, existing approaches for provably secure outsourcing of data and arbitrary computations are either based on tamper-proof hardware or fully homomorphic encryption. The former approaches are not scaleable, while the latter ones are currently not efficient enough to be used in practice.We propose an architecture and protocols that accumulate slow secure computations over time and provide the possibility to query them in parallel on demand by leveraging the benefits of cloud computing. In our approach, the user communicates with a resource-constrained Trusted Cloud (either a private cloud or built from multiple secure hardware modules) which encrypts algorithms and data to be stored and later on queried in the powerful but untrusted Commodity Cloud. We split our protocols such that the Trusted Cloud performs security-critical precomputations in the setup phase, while the Commodity Cloud computes the time-critical query in parallel under encryption in the query phase.

show abstract

“…The Paillier cryptosystem [20,21] is additively homomorphic; the El Gamal [5] cryptosystem is multiplicatively homomorphic; and the Boneh-Goh-Nissim cryptosystem approach [2] supports one multiplication between unlimited number of additions. A more recent approach provides full support of both addition and multiplication at higher computation costs [6,25]. We omit further mathematical details in this paper, since they are out of our scope.…”

Section: Cryptographic Primitivesmentioning

confidence: 99%

Privacy Preserving Group Linkage

Chen

Luo

et al. 2011

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. The problem of privacy-preserving record linkage is to find the intersection of records from two parties, while not revealing any private records to each other. Recently, group linkage has been introduced to measure the similarity of groups of records [19]. When we extend the traditional privacy-preserving record linkage methods to group linkage measurement, group membership privacy becomes vulnerable -record identity could be discovered from unlinked groups. In this paper, we introduce threshold privacy-preserving group linkage (TPPGL) schemes, in which both parties only learn whether or not the groups are linked. Therefore, our approach is secure under group membership inference attacks. In experiments, we show that using the proposed TPPGL schemes, group membership privacy is well protected against inference attacks with a reasonable overhead.

show abstract

Fully Homomorphic Encryption over the Integers

Cited by 1,198 publications

References 24 publications

Security Analysis of Multilinear Maps over the Integers

Security Analysis of Multilinear Maps over the Integers

Twin Clouds: Secure Cloud Computing with Low Latency

Privacy Preserving Group Linkage

Contact Info

Product

Resources

About