Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Better key sizes (and attacks) for LWE-based encryption
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
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
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
On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Fully homomorphic encryption with polylog overhead
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Better bootstrapping in fully homomorphic encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Ring switching in BGV-Style homomorphic encryption
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
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The security of contemporary homomorphic encryption schemes over cyclotomic number field relies on fields of very large dimension. This large dimension is needed because of the large modulus-to-noise ratio in the key-switching matrices that are used for the top few levels of the evaluated circuit. However, a smaller modulus-to-noise ratio is used in lower levels of the circuit, so from a security standpoint it is permissible to switch to lower-dimension fields, thus speeding up the homomorphic operations for the lower levels of the circuit. However, implementing such field-switching is nontrivial, since these schemes rely on the field algebraic structure for their homomorphic properties.A basic ring-switching operation was used by Brakerski, Gentry and Vaikuntanathan, over rings of the form Z[X]/(X2n+1), in the context of bootstrapping. In this work we generalize and extend this technique to work over any cyclotomic number field, and show how it can be used not only for bootstrapping but also during the computation itself in conjunction with the “packed ciphertext” techniques of Gentry, Halevi and Smart.