**Integer Matrices Homomorphic Encryption and Its application**

*Yanan Bai and Jingwei Chen and Yong Feng and Wenyuan Wu*

**Abstract: **We construct an integer matrices encryption scheme based on binary matrices encryption scheme proposed in Hiromasa et al.(PKC 2015). Our scheme supports homomorphic addition and multiplication operations, we prove the correctness and analyze the security. Besides, we implement four encryption schemes including public-key and symmetric-key binary matrices encryption schemes from Hiromasa et al.(PKC 2015), and public-key and symmetric-key integer matrices encryption schemes from this work. The experimental results show that the running time of homomorphic multiplycation just costs 3.03sec for integer matrix with $60\times 60$ entry size. It provides a promising prospect for applications. Finally, we apply integer matrices encryption to homomorphiclly solve a problem that computes the number of length-$k$ walks between any two vertices of a graph. The implement of the algorithm shows the effectiveness.

**Category / Keywords: **Homomorphic Encryption;LWE;Integer Matrices Homomorphic Encryption

**Date: **received 22 Oct 2018, last revised 23 Nov 2018

**Contact author: **baiyanan at cigit ac cn

**Available format(s): **PDF | BibTeX Citation

**Note: **This is the revised version.

**Version: **20181123:081052 (All versions of this report)

**Short URL: **ia.cr/2018/1025

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