# Fully Homomorphic Encryption over the Integers with Shorter Public Keys

@article{Coron2011FullyHE, title={Fully Homomorphic Encryption over the Integers with Shorter Public Keys}, author={Jean-S{\'e}bastien Coron and Avradip Mandal and David Naccache and Mehdi Tibouchi}, journal={IACR Cryptol. ePrint Arch.}, year={2011}, volume={2011}, pages={441} }

At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme over the integers. [] Key Method We prove that the scheme remains semantically secure, based on a stronger variant of the approximate-GCD problem, already considered by van Dijk et al.
We alsodescribe the first implementation of the resulting fully homomorphic scheme. Borrowing some optimizations from the recent Gentry-Halevi implementation of Gentry's scheme, we obtain roughly the same level of efficiency. This shows that…

## 448 Citations

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