Abstract
Homomorphic encryption allows to perform various calculations on encrypted data without decryption. In this paper, we propose an efficient method for secure multiple matrix multiplications over the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan. Our method is a generalization of Duong et al.’s method, which computes only one multiplication between two matrices. In order to minimize both the ciphertext size and the computation cost, our method packs every matrix into a single ciphertext so that it enables efficient matrix multiplications over the packed ciphertexts. We also propose several modifications to obtain practical performance of secure multiplications among matrices with larger size and entries. We show implementation results of our packing method with modifications for secure multiplications among two and three matrices with \(32 \times 32\) and \(64 \times 64\) sizes and entries from 16-bit to 64-bit.
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Acknowledgments
This work was supported by JST CREST Grant Number JPMJCR14D6, Japan. This work was also supported by JSPS KAKENHI Grant Numbers 16K17644 and 16H02830.
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Mishra, P.K., Duong, D.H., Yasuda, M. (2017). Enhancement for Secure Multiple Matrix Multiplications over Ring-LWE Homomorphic Encryption. In: Liu, J., Samarati, P. (eds) Information Security Practice and Experience. ISPEC 2017. Lecture Notes in Computer Science(), vol 10701. Springer, Cham. https://doi.org/10.1007/978-3-319-72359-4_18
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DOI: https://doi.org/10.1007/978-3-319-72359-4_18
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