Cryptanalysis of a lattice based key exchange protocol



2014年, WANG等人提出了一个基于格的密钥交换协议。原方案研究中首先在小整数解问题(SIS)基础上他们提出了两个新的困难问题, 并基于新困难问题设计了格密钥交换协议。本文提出了一个可以在多项式时间内恢复共享密钥的高效攻击算法, 并通过理论分析和实验验证严格论证攻击算法的正确性与高效性。由于最小整数解问题在格密码设计中有很广泛的研究, 因此该方法的研究可以进行进一步推广。

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  1. 1

    Zhang H G, Han W B, Lai X J, et al. Survey on cyberspace security. Sci China Inf Sci, 2015, 58: 110101

    Google Scholar 

  2. 2

    Ajtai M, Dwork C. A public-key cryptosystem with worst-case/average-case equivalence. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing. New York: ACM, 1997. 284–293

    Google Scholar 

  3. 3

    Arbitman Y, Dogon G, Lyubashevsky V, et al. SWIFFTX: a proposal for the SHA-3 standard. 2008

  4. 4

    Ducas L, Durmus A, Lepoint T, et al. Lattice signatures and bimodal gaussians. In: Advances in Cryptology—CRYPTO 2013. Berlin: Springer, 2013. 40–56

    Google Scholar 

  5. 5

    Lindner R, Peikert C. Better key sizes (and attacks) for LWE-based encryption. In: Proceedings of the 11th International Conference on Topics in Cryptology: CT-RSA, San Francisco, 2011. 319–339

    Google Scholar 

  6. 6

    Ducas L, Lyubashevsky V, Prest T. Efficient identitybased encryption over NTRU lattices. In: Advances in Cryptology—ASIACRYPT 2014. Berlin: Springer, 2014. 22–41

    Google Scholar 

  7. 7

    Micciancio D, Regev O. Worst-case to average-case reductions based on Gaussian measures. SIAM J Comput, 2007, 37: 267–302

    Article  MATH  Google Scholar 

  8. 8

    Wang S B, Zhu Y, Ma D, et al. Lattice-based key exchange on small integer solution problem. Sci China Inf Sci, 2014, 57: 112111

    Google Scholar 

  9. 9

    Gupta D S, Biswas G P. Cryptanalysis of Wang et al.’s lattice-based key exchange protocol. Perspect Sci, 2016, 8: 228–230

    Article  Google Scholar 

Download references


This work was supported by National Natural Science Foundation of China (Grant Nos. 61303212, 61202385, 61202386, 61303024, 61170080), State Key Program of National Natural Science of China (Grant Nos. 61332019, U1135004), National Basic Research Program of China (Grant No. 2014CB340600), Foundation of Science and Technology on Information Assurance Laboratory (Grant No. KJ-14-002), and Open Project of Beijing Key Lab of Trusted Computing (BJUT).

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Correspondence to Houzhen Wang.

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The authors declare that they have no conflict of interest.

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Mao, S., Zhang, P., Wang, H. et al. Cryptanalysis of a lattice based key exchange protocol. Sci. China Inf. Sci. 60, 028101 (2017).

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  • 公钥密码
  • 格密码
  • 密钥交换协议
  • 密码分析