Academic
Publications
Fully Homomorphic Encryption over the Integers

Fully Homomorphic Encryption over the Integers,10.1007/978-3-642-13190-5_2,Marten van Dijk,Craig Gentry,Shai Halevi,Vinod Vaikuntanathan

Fully Homomorphic Encryption over the Integers   (Citations: 29)
BibTex | RIS | RefWorks Download
We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry's technique to construct fully homomorphic scheme from a \boot- strappable" somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappable encryption scheme merely uses addition and multiplication over the integers. The main appeal of our scheme is the conceptual simplicity. We reduce the security of our scheme to flnding an approximate integer gcd { i.e., given a list of integers that are near-multiples of a hidden integer, output that hidden integer. We investigate the hardness of this task, building on earlier work of Howgrave-Graham.
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...While various forms of homomorphic encryption can provide data secrecy [8, 32], we demonstrate that we can efficiently verify the results of arbitrary tasks (abstracted as function evaluations) on a computational service (e.g., in the cloud) without trusting any hardware or software on that system [7, 22]...

    Bryan Parno. Trust extension for commodity computers

    • ...While recent groundbreaking work has shown how to compute arbitrary functions on encrypted data [17, 33, 12], far less is known about computing functions on signed data...

    Dan Bonehandet al. Homomorphic Signatures for Polynomial Functions

    • ... cryptosystem [OU98]; Paillier cryptosystem [Pai99] and its generalization by Damg˚ ard and Jurik [DJ01]; Regev’s LWE based cryptosystem [Reg05]; the scheme of Damg˚ ard, Geisler and Krøigaard [DGK09] based on a subgroup-decision problem; the subset-sum based scheme by Lyubashevsky, Palacio and Segev [LPS10]; Gentry, Halevi and Vaikuntanathan’s scheme [GHV10] based on LWE, and van Dijk, Gentry, Halevi and Vaikuntanathan’s scheme ...

    Rikke Bendlinet al. Semi-homomorphic Encryption and Multiparty Computation

    • ...In fact, this transformation was used by Barak [1] in his exposition of the work of van Dijk et al. [3]...
    • ...encryption. One application of this methodology, which actually motivated this work, is to simplify the presentation of the DGHV fully-homomorphic encryption scheme [3]...
    • ...Building on the work of Gentry [6], van Dijk et al. [3], proposed a simpler fully-homomorphic public-key scheme...
    • ...Although the somewhat homomorphic public-key scheme constructed by our transformation is slightly different from the one of [3], the final steps of bootstrapping (see [6]) and reducing the (multiplicative) depth of the decryption circuit can still be applied to both of our constructions...
    • ...Public-Key Scheme By modification [3] or generically by Theorem 2 [6] + [3]...
    • ...Public-Key Scheme By modification [3] or generically by Theorem 2 [6] + [3]...

    Ron Rothblum. Homomorphic Encryption: From Private-Key to Public-Key

    • ...In light of the small number of FHE candidates [20,17], and our little understanding of this notion, one may ask whether it is possible to relax this requirement and achieve full-KDM security under weaker assumptions...

    Benny Applebaum. Key-Dependent Message Security: Generic Amplification and Completeness

Sort by: