Faster Fully Homomorphic Encryption

@inproceedings{Stehl2010FasterFH,
  title={Faster Fully Homomorphic Encryption},
  author={Damien Stehl{\'e} and Ron Steinfeld},
  booktitle={ASIACRYPT},
  year={2010}
}
We describe two improvements to Gentry’s fully homomorphic scheme based on ideal lattices and its analysis: we provide a more aggressive analysis of one of the hardness assumptions (the one related to the Sparse Subset Sum Problem) and we introduce a probabilistic decryption algorithm that can be implemented with an algebraic circuit of low multiplicative degree. Combined together, these improvements lead to a faster fully homomorphic scheme, with a O(λ 3.5) bit complexity per elementary binary… 

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...

References

SHOWING 1-10 OF 39 REFERENCES

Fully Homomorphic Encryption over the Integers

A fully homomorphic encryption scheme, using only elementary modular arithmetic, that reduces the security of the scheme to finding an approximate integer gcd, and investigates the hardness of this task, building on earlier work of Howgrave-Graham.

Implementing Gentry's Fully-Homomorphic Encryption Scheme

A working implementation of a variant of Gentry's fully homomorphic encryption scheme, similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010), with a number of optimizations that allow it to implement all aspects of the scheme, including the bootstrapping functionality.

Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes

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.

Toward Basing Fully Homomorphic Encryption on Worst-Case Hardness

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 using ideal lattices

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.

A fully homomorphic encryption scheme

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.

A Faster Lattice Reduction Method Using Quantum Search

This work proposes a new lattice reduction method that approximates shortest lattice vectors up to a factor ≤ (k/6) n/2k and makes use of Grover’s quantum search algorithm, demonstrating that the availability of quantum computers will affect not only the security of cryptosystems based on integer factorization or discrete logarithms, but also of lattice based cryptosSystems.

Computing arbitrary functions of encrypted data

It is shown that this separation is possible: a "fully homomorphic" encryption scheme is described that keeps data private, but that allows a worker that does not have the secret decryption key to compute any (still encrypted) result of the data, even when the function of theData is very complex.

On the Insecurity of a Server-Aided RSA Protocol

A new lattice-based provable passive attack on RSA-S1 which recovers the factorization of the RSA modulus when a very small public exponent is used, for many choices of the parameters.

Predicting Lattice Reduction

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.