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
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
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Fully homomorphic SIMD operations
Designs, Codes and Cryptography
Field switching in BGV-style homomorphic encryption
Journal of Computer Security - Advances in Security for Communication Networks
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The security of BGV-style homomorphic encryption schemes over polynomial rings relies on rings 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, larger noise (and hence 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 rings, thus speeding up the homomorphic operations for the lower levels of the circuit. However, implementing such ring-switching is nontrivial, since these schemes rely on the ring algebraic structure for their homomorphic properties. A basic ring-switching operation was used by Brakerski, Gentry and Vaikuntanathan, over polynomial rings of the form $\mathbb{Z}[X]/(X^{2^n}+1)$, in the context of bootstrapping. In this work we generalize and extend this technique to work over any cyclotomic ring 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).