How to generate factored random numbers
SIAM Journal on Computing - Special issue on cryptography
On the multiplicative complexity of Boolean functions over the basis ∧,⊕,1
Theoretical Computer Science - Selected papers in honor of Manuel Blum
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
A fully homomorphic encryption scheme
A fully homomorphic encryption scheme
Implementing Gentry's fully-homomorphic encryption scheme
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Fully homomorphic encryption with relatively small key and ciphertext sizes
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Fully homomorphic encryption over the integers
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
The geometry of lattice cryptography
Foundations of security analysis and design VI
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Breaking fully-homomorphic-encryption challenges
CANS'11 Proceedings of the 10th international conference on Cryptology and Network Security
On the CCA-1 security of somewhat homomorphic encryption over the integers
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
Public key compression and modulus switching for fully homomorphic encryption over the integers
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Towards an interpreter for efficient encrypted computation
Proceedings of the 2012 ACM Workshop on Cloud computing security workshop
On optimal bounds of small inverse problems and approximate GCD problems with higher degree
ISC'12 Proceedings of the 15th international conference on Information Security
Secure pattern matching using somewhat homomorphic encryption
Proceedings of the 2013 ACM workshop on Cloud computing security workshop
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At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme over the integers. The main appeal of this scheme (compared to Gentry's) is its conceptual simplicity. This simplicity comes at the expense of a public key size in Õ(λ10) which is too large for any practical system. In this paper we reduce the public key size to Õ(λ7) by encrypting with a quadratic form in the public key elements, instead of a linear form. We prove that the scheme remains semantically secure, based on a stronger variant of the approximate-GCD problem, already considered by van Dijk et al. We alsodescribe the first implementation of the resulting fully homomorphic scheme. Borrowing some optimizations from the recent Gentry-Halevi implementation of Gentry's scheme, we obtain roughly the same level of efficiency. This shows that fully homomorphic encryption can be implemented using simple arithmetic operations.