Abstract
With Fully Homomorphic Encryption (FHE), it is possible to produce encryptions of the addition and multiplication of encrypted values without access to the private-key. Since homomorphic multiplication is the most burdensome operation of FHE, every possible improvement to it has a significant impact on the performance of the homomorphic evaluation of arbitrary functions. In this paper, we propose an optimized homomorphic multiplication algorithm and apply it to the NTT-based Fast Lattice library (NFLlib), which is a library designed for the implementation of Lattice-based Cryptography (LBC). When implemented with AVX2 Single Instruction Multiple Data (SIMD) extensions on a i7-4770k CPU, the proposed algorithm produces a normalized speed-up of 1.93 when compared with the fastest AVX2 implementation of the state of the art. Furthermore, when extended to decryption, the new method achieves a normalized speed-up of 2.0 when compared with related art.
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Notes
- 1.
\({:=}\) is used to denote imperative assignment.
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Acknowledgments
This work was partially supported by the ARTEMIS Joint Undertaking under grant agreement nr. 621429 and by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013, and through the PhD grant with reference SFRH/BD/103791/2014.
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Martins, P., Sousa, L. (2017). Enhancing Data Parallelism of Fully Homomorphic Encryption. In: Hong, S., Park, J. (eds) Information Security and Cryptology – ICISC 2016. ICISC 2016. Lecture Notes in Computer Science(), vol 10157. Springer, Cham. https://doi.org/10.1007/978-3-319-53177-9_10
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