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Exploring the Feasibility of Fully Homomorphic Encryption

Wei Wang, Yin Hu, Lianmu Chen, Xinming Huang, Berk Sunar
Worcester Polytechnic Institute
Worcester Polytechnic Institute, 2012
@article{wang2012exploring,

   title={Exploring the Feasibility of Fully Homomorphic Encryption},

   author={Wang, W. and Hu, Y. and Chen, L. and Huang, X. and Sunar, B.},

   year={2012}

}

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In a major breakthrough, Gentry introduced the first plausible construction of a fully homomorphic encryption (FHE) scheme in 2009. FHE allows the evaluation of arbitrary functions directly on encrypted data on untrusted servers. Later, in 2010 Gentry-Halevi presented the first FHE implementation. However, even for the small setting with 2,048 dimensions, the authors reported a performance of 1.8 seconds for a single bit encryption and 32 seconds for recryption on a high end server. Much of the latency is due to computationally intensive multi-million-bit modular multiplications. In this paper, we adopt Strassen’s FFT-based algorithm for large number multiplication and employ a novel precomputation technique along with delayed modular reductions which allows us to carry out the bulk of computations in the frequency domain. We manage to eliminate all FFT conversion except the final inverse transformation drastically reducing the computation latency for all FHE primitives. In addition, we realize the FHE scheme on a GPU to further speed up the operations. Our experimental results with small parameter setting show speedups of 174, 7.6 and 13.5 times for encryption, decryption and recryption, respectively, when compared to the Gentry-Halevi implementation.
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