<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Homomorphic encryption enables various calculations while preserving the data confidentiality. In this paper, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011) to secure matrix multiplication between two matrices. To reduce both the ciphertext size and the computation cost, we propose a new method to pack a matrix into a single ciphertexts so that it also enables efficient matrix multiplication over the packed ciphertexts. Our packing method generalizes Yasuda et al.’s methods (Security Comm. Networks 2015 and ACISP 2015), which are for secure inner product. We also implement our methods and give a comparison with previous packing methods.</p></abstract>

Homomorphic encryption enables various calculations while preserving the data confidentiality. In this paper, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011) to secure matrix multiplication between two matrices. To reduce both the ciphertext size and the computation cost, we propose a new method to pack a matrix into a single ciphertexts so that it also enables efficient matrix multiplication over the packed ciphertexts. Our packing method generalizes Yasuda et al.’s methods (Security Comm. Networks 2015 and ACISP 2015), which are for secure inner product. We also implement our methods and give a comparison with previous packing methods.

Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption

Institute of Mathematics for Industry and Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption"}

Homomorphic encryption enables various calculations while preserving the data confidentiality. In this paper, we apply the somewhat homomorphic encryption...

Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption

Published Online: Feb 25, 2017

Page range: 69 - 83

Received: Sep 20, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0031

Keywords
somewhat homomorphic encryption, packing methods, secure inner product, secure matrix multiplication

© 2016 Dung Hoang Duong et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption

Published Online: Feb 25, 2017

Page range: 69 - 83

Received: Sep 20, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0031

Keywordssomewhat homomorphic encryption, packing methods, secure inner product, secure matrix multiplication

© 2016 Dung Hoang Duong et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
somewhat homomorphic encryption, packing methods, secure inner product, secure matrix multiplication