Computer Architecture
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Fairplay—a secure two-party computation system
SSYM'04 Proceedings of the 13th conference on USENIX Security Symposium - Volume 13
How to generate and exchange secrets
SFCS '86 Proceedings of the 27th 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
A fully homomorphic encryption scheme
A fully homomorphic encryption scheme
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
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 over the integers with shorter public keys
CRYPTO'11 Proceedings of the 31st annual conference on 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
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
(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
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
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Fully homomorphic encryption (FHE) techniques are capable of performing encrypted computation on Boolean circuits, i.e., the user specifies encrypted inputs to the program, and the server computes on the encrypted inputs. Applying these techniques to general programs with recursive procedures and data-dependent loops has not been a focus of attention. In this paper, we take a first step toward building an interpreter that, given programs with complex control flow, schedules efficient code suitable for the application of FHE schemes. We first describe how programs written in a small Turing-complete instruction set can be executed with encrypted data and point out inefficiencies in this methodology. We then provide examples of scheduling (a) the greatest common divisor (GCD) problem using Euclid's algorithm and (b) the 3-Satisfiability (3SAT) problem using a recursive backtracking algorithm into path-levelized FHE computations. We describe how path levelization reduces control flow ambiguity and improves encrypted computation efficiency. Using these techniques and data-dependent loops as a starting point, we then build support for hierarchical programs made up of phases, where each phase corresponds to a fixed point computation that can be used to further improve the efficiency of encrypted computation. In our setting, the adversary learns an estimate of the number of steps required to complete the computation, which we show is the least amount of leakage possible.