Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Making NTRU as secure as worst-case problems over ideal lattices
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
New algorithms for learning in presence of errors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Fully homomorphic encryption from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Efficient Fully Homomorphic Encryption from (Standard) LWE
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
On ideal lattices and learning with errors over rings
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Fully homomorphic encryption with polylog overhead
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Trapdoors for lattices: simpler, tighter, faster, smaller
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Pseudorandom functions and lattices
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lattice signatures without trapdoors
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Ring switching in BGV-Style homomorphic encryption
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
Field switching in BGV-style homomorphic encryption
Journal of Computer Security - Advances in Security for Communication Networks
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The Ring-LWE problem, introduced by Lyubashevsky, Peikert, and Regev (Eurocrypt 2010), has been steadily finding many uses in numerous cryptographic applications. Still, the Ring-LWE problem defined in [LPR10] involves the fractional ideal R ∨, the dual of the ring R , which is the source of many theoretical and implementation technicalities. Until now, getting rid of R ∨, required some relatively complex transformation that substantially increase the magnitude of the error polynomial and the practical complexity to sample it. It is only for rings R =ℤ[X ]/(X n +1) where n a power of 2, that this transformation is simple and benign. In this work we show that by applying a different, and much simpler transformation, one can transfer the results from [LPR10] into an "easy-to-use" Ring-LWE setting (i.e. without the dual ring R ∨), with only a very slight increase in the magnitude of the noise coefficients. Additionally, we show that creating the correct noise distribution can also be simplified by generating a Gaussian distribution over a particular extension ring of R , and then performing a reduction modulo f (X ). In essence, our results show that one does not need to resort to using any algebraic structure that is more complicated than polynomial rings in order to fully utilize the hardness of the Ring-LWE problem as a building block for cryptographic applications.