# Implementing Gentry's Fully-Homomorphic Encryption Scheme

@inproceedings{Gentry2011ImplementingGF, title={Implementing Gentry's Fully-Homomorphic Encryption Scheme}, author={Craig Gentry and Shai Halevi}, booktitle={International Conference on the Theory and Application of Cryptographic Techniques}, year={2011} }

We describe a working implementation of a variant of Gentry's fully homomorphic encryption scheme (STOC 2009), similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010. [] Key MethodOur main optimization is a key-generation method for the underlying somewhat homomorphic encryption, that does not require full polynomial inversion.

## 944 Citations

### Better Bootstrapping in Fully Homomorphic Encryption

- Computer Science, MathematicsPublic Key Cryptography
- 2012

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, and allows to store the encryption of the secret key as a single ciphertext, thus reducing the size of the public key.

### Fully Homomorphic Encryption over the Integers with Shorter Public Keys

- Mathematics, Computer ScienceIACR Cryptol. ePrint Arch.
- 2011

It is shown that fully homomorphic encryption can be implemented using simple arithmetic operations, and some optimizations from the recent Gentry-Halevi implementation of Gentry's scheme are obtained, roughly the same level of efficiency.

### Public Key Compression and Modulus Switching for Fully Homomorphic Encryption over the Integers

- Mathematics, Computer ScienceEUROCRYPT
- 2012

A compression technique that reduces the public key size of van Dijk, Gentry, Halevi and Vaikuntanathan's (DGHV) fully homomorphic scheme over the integers from O(Î»7) to O( Î»5) remains semantically secure, but in the random oracle model.

### Fully Homomorphic Encryption in JCrypTool Coen Ramaekers c

- Computer Science, Mathematics
- 2011

This thesis provides an overview of the recent achievements on Fully Homomorphic Encyrption (FHE) schemes and also provides a tool demonstrating that FHE allows computations with ciphertexts whileâ€¦

### Exploring the Feasibility of Fully Homomorphic Encryption

- Computer Science, MathematicsIEEE Transactions on Computers
- 2015

Two optimizations coupled with a novel precomputation technique are introduced drastically reducing the computation latency for all FHE primitives and the GH FHE scheme on two GPUs is implemented to further speedup the operations.

### Fully Homomorphic Encryption without Bootstrapping

- Computer Science, MathematicsIACR Cryptol. ePrint Arch.
- 2011

A new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), without Gentryâ€™s bootstrapping procedure is presented, which dramatically improves performance and bases security on weaker assumptions.

### Fully homomorphic SIMD operations

- Computer Science, MathematicsDes. Codes Cryptogr.
- 2014

It is shown that the SIMD operations can be used to perform the recrypt procedure in parallel, resulting in a substantial speed-up, and this somewhat homomorphic scheme can be made fully homomorphic in a naive way by recrypting all data elements separately.

### Practical Bootstrapping in Quasilinear Time

- Computer Science, MathematicsCRYPTO
- 2013

The current state of the art, due to Gentry, Halevi, and Smart, is able to bootstrap â€śpackedâ€ť ciphertexts in time only quasilinear O(Î») = Î» Â· logO(1) Î» in the security parameter.

### (Leveled) fully homomorphic encryption without bootstrapping

- Computer Science, MathematicsITCS '12
- 2012

A novel approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions, using some new techniques recently introduced by Brakerski and Vaikuntanathan (FOCS 2011).

### Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages

- Computer Science, MathematicsCRYPTO
- 2011

A somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security reduces to the worst-case hardness of problems on ideal lattices using the RLWE assumption, which allows us to completely abstract out the lattice interpretation.

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We describe a working implementation of a variant of Gentryâ€™s fully homomorphic encryption scheme (STOC 2009), similar to the variant used in an earlier implementation effort by Smart and Vercauterenâ€¦

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