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Keywords
(3)
Homomorphic Encryption
Modular Arithmetic
Polynomial Ring
Related Publications
(1)
Fully homomorphic encryption using ideal lattices
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Fully Homomorphic Encryption over the Integers
Fully Homomorphic Encryption over the Integers,10.1007/9783642131905_2,Marten van Dijk,Craig Gentry,Shai Halevi,Vinod Vaikuntanathan
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Fully Homomorphic Encryption over the Integers
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Citations: 29
)
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Marten van Dijk
,
Craig Gentry
,
Shai Halevi
,
Vinod Vaikuntanathan
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 nearmultiples of a hidden integer, output that hidden integer. We investigate the hardness of this task, building on earlier work of HowgraveGraham.
Conference:
Theory and Application of Cryptographic Techniques  EUROCRYPT
, pp. 2443, 2010
DOI:
10.1007/9783642131905_2
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Citation Context
(26)
...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 Bonehand
,
et 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 subgroupdecision problem; the subsetsum 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 Bendlin
,
et al.
Semihomomorphic 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 fullyhomomorphic encryption scheme [
3
]...
...Building on the work of Gentry [6], van Dijk et al. [
3
], proposed a simpler fullyhomomorphic publickey scheme...
...Although the somewhat homomorphic publickey 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...
...PublicKey Scheme By modification [
3
] or generically by Theorem 2 [6] + [3]...
...PublicKey Scheme By modification [3] or generically by Theorem 2 [6] + [
3
]...
Ron Rothblum
.
Homomorphic Encryption: From PrivateKey to PublicKey
...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 fullKDM security under weaker assumptions...
Benny Applebaum
.
KeyDependent Message Security: Generic Amplification and Completeness
References
(28)
Probabilistic encryption
(
Citations: 1567
)
Shafi Goldwasser
,
Silvio Micali
Journal:
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, vol. 28, no. 2, pp. 270299, 1984
Approximate Integer Common Divisors
(
Citations: 25
)
Nick Howgravegraham
Conference:
Cryptography and Lattices  CaLC
, pp. 5166, 2001
Evaluating Branching Programs on Encrypted Data
(
Citations: 26
)
Yuval Ishai
,
Anat Paskin
Conference:
Theory of Cryptography
, pp. 575594, 2007
A survey of parallel algorithms for shared memory machines
(
Citations: 242
)
R. Karp
,
V. Ramachandran
Published in 1990.
The Computational Complexity of Simultaneous Diophantine Approximation Problems
(
Citations: 60
)
J. C. Lagarias
Conference:
IEEE Symposium on Foundations of Computer Science  FOCS
, pp. 3239, 1982
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Citations
(29)
Trust extension for commodity computers
Bryan Parno
Journal:
Communications of The ACM  CACM
, pp. 7685, 2012
Homomorphic Signatures for Polynomial Functions
(
Citations: 3
)
Dan Bonehand
,
David Mandell Freeman
Conference:
Theory and Application of Cryptographic Techniques  EUROCRYPT
, pp. 149168, 2011
Semihomomorphic Encryption and Multiparty Computation
(
Citations: 2
)
Rikke Bendlin
,
Ivan Damgård
,
Claudio Orlandi
,
Sarah Zakarias
Conference:
Theory and Application of Cryptographic Techniques  EUROCRYPT
, pp. 169188, 2011
Homomorphic Encryption: From PrivateKey to PublicKey
(
Citations: 1
)
Ron Rothblum
Conference:
Theory of Cryptography
, pp. 219234, 2011
KeyDependent Message Security: Generic Amplification and Completeness
(
Citations: 2
)
Benny Applebaum
Conference:
Theory and Application of Cryptographic Techniques  EUROCRYPT
, pp. 527546, 2011