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Lattice-based key exchange on small integer solution problem

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Abstract

In this paper, we propose a new hard problem, called bilateral inhomogeneous small integer solution (Bi-ISIS), which can be seen as an extension of the small integer solution problem on lattices. The main idea is that, instead of choosing a rectangle matrix, we choose a square matrix with small rank to generate Bi-ISIS problem without affecting the hardness of the underlying SIS problem. Based on this new problem, we present two new hardness problems: computational Bi-ISIS and decisional problems. As a direct application of these problems, we construct a new lattice-based key exchange (KE) protocol, which is analogous to the classic Diffie-Hellman KE protocol. We prove the security of this protocol and show that it provides better security in case of worst-case hardness of lattice problems, relatively efficient implementations, and great simplicity.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    ShanBiao Wang & RongQuan Feng

  2. School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Yan Zhu

  3. Department of Computer and Information Science, University of Michigan-Dearborn, Dearborn, MI, 48128, USA

    Di Ma

Authors
  1. ShanBiao Wang
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  2. Yan Zhu
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  3. Di Ma
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  4. RongQuan Feng
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Correspondence to Yan Zhu.

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Wang, S., Zhu, Y., Ma, D. et al. Lattice-based key exchange on small integer solution problem. Sci. China Inf. Sci. 57, 1–12 (2014). https://doi.org/10.1007/s11432-014-5147-z

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  • DOI: https://doi.org/10.1007/s11432-014-5147-z

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