Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
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 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
Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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
Fully homomorphic encryption with polylog overhead
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 4th conference on Innovations in Theoretical Computer Science
ML confidential: machine learning on encrypted data
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Enabling secure query processing in the cloud using fully homomorphic encryption
Proceedings of the Second Workshop on Data Analytics in the Cloud
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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Gentry's bootstrapping technique is currently the only known method of obtaining a "pure" fully homomorphic encryption (FHE) schemes, and it may offers performance advantages even in cases that do not require pure FHE (e.g., when using the noise-control technique of Brakerski-Gentry-Vaikuntanathan). The main bottleneck in bootstrapping is the need to evaluate homomorphically the reduction of one integer modulo another. This is typically done by emulating a binary modular reduction circuit, using bit operations on binary representation of integers. We present a simpler approach that bypasses the homomorphic modular-reduction bottleneck to some extent, by working with a modulus very close to a power of two. Our method is easier to describe and implement than the generic binary circuit approach, and we expect it to be faster in practice (although we did not implement it yet). In some cases it also allows us to store the encryption of the secret key as a single ciphertext, thus reducing the size of the public key. We also show how to combine our new method with the SIMD homomorphic computation techniques of Smart-Vercauteren and Gentry-Halevi-Smart, to get a bootstrapping method that works in time quasi-linear in the security parameter. This last part requires extending the techniques from prior work to handle arithmetic not only over fields, but also over some rings. (Specifically, our method uses arithmetic modulo a power of two, rather than over characteristic-two fields.)