Implementing Gentry's Fully-Homomorphic Encryption Scheme

@inproceedings{Gentry2011ImplementingGF,
  title={Implementing Gentry's Fully-Homomorphic Encryption Scheme},
  author={Craig Gentry and Shai Halevi},
  booktitle={EUROCRYPT},
  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.

Fully Homomorphic Encryption over the Integers with Shorter Public Keys

TLDR
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

TLDR
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(λ7) to O( λ5) remains semantically secure, but in the random oracle model.

Fully Homomorphic Encryption in JCrypTool Coen Ramaekers c

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 while

Exploring the Feasibility of Fully Homomorphic Encryption

TLDR
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.

The Analysis of Constructing Fully Homomorphic Encryption over Integers

TLDR
A new modulus switching technique for the D GHV scheme that enables to use the new FHE framework without bootstrapping from Brakerski, Gentry and Vaikuntanathan with theDGHV scheme.

Fully Homomorphic Encryption without Bootstrapping

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

Fully homomorphic SIMD operations

TLDR
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

TLDR
The current state of the art, due to Gentry, Halevi, and Smart, is able to bootstrap “packed” ciphertexts in time only quasilinear O(λ) = λ · logO(1) λ in the security parameter.

(Leveled) fully homomorphic encryption without bootstrapping

TLDR
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

TLDR
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.
...

References

SHOWING 1-10 OF 20 REFERENCES

Implementing Gentry ’ s Fully-Homomorphic Encryption Scheme Preliminary Report

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

Faster Fully Homomorphic Encryption

TLDR
Two improvements to Gentry’s fully homomorphic scheme based on ideal lattices are described: a more aggressive analysis of one of the hardness assumptions and a probabilistic decryption algorithm that can be implemented with an algebraic circuit of low multiplicative degree.

Fully homomorphic encryption using ideal lattices

TLDR
This work proposes a fully homomorphic encryption scheme that allows one to evaluate circuits over encrypted data without being able to decrypt, and describes a public key encryption scheme using ideal lattices that is almost bootstrappable.

An Improvement of Key Generation Algorithm for Gentry's Homomorphic Encryption Scheme

TLDR
A key generation algorithm is proposed for Gentry's homomorphic encryption scheme that controls the bound of the circuit depth by using the relation between the circuit Depth and the eigenvalues of a basis of a lattice.

A fully homomorphic encryption scheme

TLDR
This work designs a somewhat homomorphic "boostrappable" encryption scheme that works when the function f is the scheme's own decryption function, and shows how, through recursive self-embedding, bootstrappable encryption gives fully homomorphic encryption.

Toward Basing Fully Homomorphic Encryption on Worst-Case Hardness

TLDR
A worst-case / average-case connection is proved that bases Gentry's scheme (in part) on the quantum hardness of the shortest independent vector problem (SIVP) over ideal lattices in the worst- case.

Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes

TLDR
This work presents a fully homomorphic encryption scheme which has both relatively small key and ciphertext size and allows efficient fully homomorphism over any field of characteristic two.

On the sparse subset sum problem from Gentry-Halevi's implementation of fully homomorphic encryption

  • M. Lee
  • Computer Science, Mathematics
    IACR Cryptol. ePrint Arch.
  • 2011
TLDR
The experiment shows that even their large instance of a sparse subset sum problem could be solved within two days with probability of about 44% and a more conservative parameter choice can easily avoid the attack.

Public-Key Cryptosystems from Lattice Reduction Problems

TLDR
A new proposal for a trapdoor one-way function, from which the security of the new construction is based on the conjectured computational difficulty of lattice-reduction problems, providing a possible alternative to existing public-key encryption algorithms and digital signatures such as RSA and DSS.

Predicting Lattice Reduction

TLDR
The goal of this paper is to provide an assessment of lattice reduction algorithms' behaviour based on extensive experiments performed with the NTL library, and to suggest several conjectures on the worst case and the actual behaviour of lattICE reduction algorithms.