Fully Homomorphic Encryption over the Integers

@inproceedings{Dijk2010FullyHE,
  title={Fully Homomorphic Encryption over the Integers},
  author={Marten van Dijk and Craig Gentry and Shai Halevi and Vinod Vaikuntanathan},
  booktitle={International Conference on the Theory and Application of Cryptographic Techniques},
  year={2010}
}
We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct a fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappable encryption scheme merely uses addition and multiplication over the integers. The main appeal of our scheme is the conceptual simplicity. We reduce the security of our scheme to finding an… 

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