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Efficient Linear Homomorphic Encryption from LWE Over Rings

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Abstract

As the basis for secure public-key encryption under various cases, the learning with errors (LWE) problem has proved to be versatile for encryption schemes. Unfortunately, it tends not to be efficient enough for practical applications. For improving the efficiency issues and quickening the practical applications of the lattice-based public-key cryptosystems, an efficient homomorphic encryption scheme is presented in this paper, which is based on the learning with errors over rings (R-LWE) assumption, and its security is reducible to the hardness of the shortest vector problem in the worst case on ideal lattices. Furthermore, the scheme possesses homomorphism feature that encryption operations are consistent with message operations. The security analysis shows that the proposed encryption scheme is secure against chosen-plaintext attacks in the standard model. At the same time, the efficiency analysis and simulation results indicate that the scheme is much more efficient than previous lattice-based cryptosystems.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (61171072, 61001058), the Key Program for Technology & Innovation of College in Guangdong Province (CXZD1143) and the Science & Technology Projects of Shenzhen (CXB201104210002A).

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Authors and Affiliations

  1. ATR Key Laboratory of National Defense Technology, Shenzhen University, Shenzhen, 518060, China

    Ting Wang, Jianping Yu, Peng Zhang & Xuan Xie

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  1. Ting Wang
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  2. Jianping Yu
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  3. Peng Zhang
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  4. Xuan Xie
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Correspondence to Ting Wang.

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Wang, T., Yu, J., Zhang, P. et al. Efficient Linear Homomorphic Encryption from LWE Over Rings. Wireless Pers Commun 74, 1005–1016 (2014). https://doi.org/10.1007/s11277-013-1335-1

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