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Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement

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Abstract

Wang et al. introduced a new variant of small integer solution (SIS), namely, bilateral inhomogeneous small integer solution (Bi-ISIS) which is based on lattice cryptography, and constructed a Bi-ISIS-based key exchange (KE) protocol. In this paper, we indicate that Wang et al.’s Bi-ISIS-based KE protocol is not secure because a common shared key can be recovered directly by using linear algebraic methods. Furthermore, we analysis two simple variants of the Bi-ISIS-based KE and show that they are also insecure. To avoid the shared key attack, we present an improvement of the Bi-ISIS-based KE, whose security is reduced to the learning with error problem over modules (M-LWE).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61672270 and No. 61602216), the Research Foundation for Humanities and Social Sciences of Ministry of Education, China (No. 14YJAZH023 and No. 15YJCZH129), the Project of Changzhou Province Science-Based Application (No. 2016365).

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Authors and Affiliations

  1. School of Computer Engineering, Jiangsu University of Technology, Changzhou, 213001, China

    Zhengjun Jing, Chunsheng Gu, Zhimin Yu & Peizhong Shi

  2. School of Computer Science and Educational Software, Guangzhou University, Guangzhou, 510006, China

    Chongzhi Gao

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  1. Zhengjun Jing
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  2. Chunsheng Gu
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  3. Zhimin Yu
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  4. Peizhong Shi
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Correspondence to Zhengjun Jing.

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Jing, Z., Gu, C., Yu, Z. et al. Cryptanalysis of lattice-based key exchange on small integer solution problem and its improvement. Cluster Comput 22 (Suppl 1), 1717–1727 (2019). https://doi.org/10.1007/s10586-018-2293-x

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