• Corpus ID: 1467571

Somewhat Practical Fully Homomorphic Encryption

@article{Fan2012SomewhatPF,
  title={Somewhat Practical Fully Homomorphic Encryption},
  author={Junfeng Fan and Frederik Vercauteren},
  journal={IACR Cryptol. ePrint Arch.},
  year={2012},
  volume={2012},
  pages={144}
}
In this paper we port Brakerski’s fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. [...] Key Method We provide a detailed, but simple analysis of the various homomorphic operations, such as multiplication, relinearisation and bootstrapping, and derive tight worst case bounds on the noise caused by these operations. The analysis of the bootstrapping step is greatly simplified by using a modulus switching trick. Finally, we derive concrete parameters for which the…Expand
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717 Citations
Highly Influential Citations
135
Background Citations
240
Methods Citations
302
Results Citations
4

717 Citations

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Citation Type

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References

SHOWING 1-10 OF 23 REFERENCES
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 over the Integers
TLDR
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.
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.
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.
(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 without Modulus Switching from Classical GapSVP
TLDR
A new tensoring technique for LWE-based fully homomorphic encryption that uses the same modulus throughout the evaluation process no need for "modulus switching", and this modulus can take arbitrary form.
Implementing Gentry's Fully-Homomorphic Encryption Scheme
TLDR
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
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.
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.
Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits
  • Craig Gentry, S. Halevi
  • Computer Science, Mathematics
    2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
  • 2011
TLDR
A new blueprint for FHE is described, showing how to eliminate the squashing step, and thereby eliminate the need to assume that the sparse subset sum problem (SSSP) is hard, as all previous leveled FHE schemes have done.
...
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