Journal of the ACM (JACM)
Replication is not needed: single database, computationally-private information retrieval
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Secure Two-Party Computation Is Practical
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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 from ring-LWE and security for key dependent messages
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Can homomorphic encryption be practical?
Proceedings of the 3rd ACM workshop on Cloud computing security workshop
(Leveled) fully homomorphic encryption without bootstrapping
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
FC'10 Proceedings of the 14th international conference on Financial Cryptography and Data Security
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
Birthday paradox for multi-collisions
ICISC'06 Proceedings of the 9th international conference on Information Security and Cryptology
Improved key generation for gentry's fully homomorphic encryption scheme
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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
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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At PKC 2010 Smart and Vercauteren presented a variant of Gentry's fully homomorphic public key encryption scheme and mentioned that the scheme could support SIMD style operations. The slow key generation process of the Smart---Vercauteren system was then addressed in a paper by Gentry and Halevi, but their key generation method appears to exclude the SIMD style operation alluded to by Smart and Vercauteren. In this paper, we show how to select parameters to enable such SIMD operations. As such, we obtain a somewhat homomorphic scheme supporting both SIMD operations and operations on large finite fields of characteristic two. This somewhat homomorphic scheme can be made fully homomorphic in a naive way by recrypting all data elements separately. However, we show that the SIMD operations can be used to perform the recrypt procedure in parallel, resulting in a substantial speed-up. Finally, we demonstrate how such SIMD operations can be used to perform various tasks by studying two use cases: implementing AES homomorphically and encrypted database lookup.