Journal of the ACM (JACM)
Computer Architecture, Fourth Edition: A Quantitative Approach
Computer Architecture, Fourth Edition: A Quantitative Approach
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
A fast parallel algorithm for routing in permutation networks
IEEE Transactions on Computers
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
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
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
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
Perfectly secure multiparty computation and the computational overhead of cryptography
EUROCRYPT'10 Proceedings of the 29th 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
Shift-type homomorphic encryption and its application to fully homomorphic encryption
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Towards an interpreter for efficient encrypted computation
Proceedings of the 2012 ACM Workshop on Cloud computing security workshop
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
A fully homomorphic cryptosystem with approximate perfect secrecy
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
When homomorphism becomes a liability
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Constant-Overhead secure computation of boolean circuits using preprocessing
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Reusable garbled circuits and succinct functional encryption
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Secure pattern matching using somewhat homomorphic encryption
Proceedings of the 2013 ACM workshop on Cloud computing security workshop
Lessons learned with PCF: scaling secure computation
Proceedings of the First ACM workshop on Language support for privacy-enhancing technologies
Private database queries using somewhat homomorphic encryption
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Cryptanalysis of Brenner et al.'s somewhat homomorphic encryption scheme
AISC '13 Proceedings of the Eleventh Australasian Information Security Conference - Volume 138
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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We show that homomorphic evaluation of (wide enough) arithmetic circuits can be accomplished with only polylogarithmic overhead. Namely, we present a construction of fully homomorphic encryption (FHE) schemes that for security parameter λ can evaluate any width-Ω(λ) circuit with t gates in time t· polylog(λ). To get low overhead, we use the recent batch homomorphic evaluation techniques of Smart-Vercauteren and Brakerski-Gentry-Vaikuntanathan, who showed that homomorphic operations can be applied to "packed" ciphertexts that encrypt vectors of plaintext elements. In this work, we introduce permuting/routing techniques to move plaintext elements across these vectors efficiently. Hence, we are able to implement general arithmetic circuit in a batched fashion without ever needing to "unpack" the plaintext vectors. We also introduce some other optimizations that can speed up homomorphic evaluation in certain cases. For example, we show how to use the Frobenius map to raise plaintext elements to powers of p at the "cost" of a linear operation.