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Towards Security Authentication for IoT Devices with Lattice-Based ZK

  • Jie Cai
  • Han JiangEmail author
  • Qiuliang Xu
  • Guangshi Lv
  • Minghao Zhao
  • Hao Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11058)

Abstract

In recent years, IoT devices have been widely used in the newly-emerging technologized such as crowd-censoring and smart city. Authentication among each IoT node plays a central role in secure communications. Generally, zero-knowledge identification scheme enables one party to authenticate himself without disclosing any additional information. However, a zero-knowledge based protocol normally involves heavily computational or interactive overhead, which is unaffordable for lightweight IoT devices. In this paper, we propose a modified zero-knowledge identification scheme based on that of Silva, Cayrel and Lindner (SCL, for short). The security of our scheme relies on the existence of a commitment scheme and on the hardness of ISIS problem (i.e., a hardness assumption that can be reduced to worst-case lattice problems). We present the detail construction and security proof in this paper.

Keywords

Lattice-based cryptography Identification Hash function SIS problem Zero-knowledge 

Notes

Acknowledgement

This work is supported by the National Natural Science Foundation of China under grant No. 61572294, 61602287 and 11771252, Natural Science Foundation of Shandong Province under grant No. ZR2017MF021, State Key Program of National Natural Science of China under grant No. 61632020, the Fundamental Research Funds of Shandong University under grant No. 2017JC019 and 2016JC029, and the Primary Research & Development Plan of Shandong Province under grant No. 2018GGX101037. We thank the reviewers for their constructive suggestions. Special thanks for Chuan Zhao at University of Jinan for his generous help and discussion.

References

  1. 1.
    Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987).  https://doi.org/10.1007/3-540-47721-7_12CrossRefGoogle Scholar
  2. 2.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: ACM Symposium on Theory of Computing, pp. 197–206 (2008).  https://doi.org/10.1145/1374376.1374407
  3. 3.
    Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. J. Comput. 18(1), 186–208 (1989).  https://doi.org/10.1137/0218012MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lyubashevsky, V.: Lattice-based identification schemes secure under active attacks. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 162–179. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78440-1_10CrossRefGoogle Scholar
  5. 5.
    Lyubashevsky, V., Micciancio, D.: Generalized compact knapsacks are collision resistant. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 144–155. Springer, Heidelberg (2006).  https://doi.org/10.1007/11787006_13CrossRefGoogle Scholar
  6. 6.
    Lyubashevsky, V., Micciancio, D.: Asymptotically efficient lattice-based digital signatures. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 37–54. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78524-8_3CrossRefGoogle Scholar
  7. 7.
    Micciancio, D., Peikert, C.: Hardness of SIS and LWE with small parameters. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 21–39. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40041-4_2CrossRefGoogle Scholar
  8. 8.
    Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. In: IEEE Symposium on Foundations of Computer Science, pp. 372–381, October 2004.  https://doi.org/10.1109/FOCS.2004.72
  9. 9.
    Miklós, A.: Generating hard instances of lattice problems. Electron. Colloq. Comput. Complex. 3(7) (1996). http://eccc.hpi-web.de/eccc-reports/1996/TR96-007/index.html
  10. 10.
    Véron, P.: Cryptanalysis of harari’s identification scheme. In: Boyd, C. (ed.) Cryptography and Coding 1995. LNCS, vol. 1025, pp. 264–269. Springer, Heidelberg (1995).  https://doi.org/10.1007/3-540-60693-9_28CrossRefGoogle Scholar
  11. 11.
    Peikert, C.: A decade of lattice cryptography. Found. Trends Theor. Comput. Sci. 10(4), 283–424 (2016).  https://doi.org/10.1561/0400000074MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Cayrel, P.-L., Lindner, R., Rückert, M., Silva, R.: Improved zero-knowledge identification with lattices. In: Heng, S.-H., Kurosawa, K. (eds.) ProvSec 2010. LNCS, vol. 6402, pp. 1–17. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-16280-0_1CrossRefGoogle Scholar
  13. 13.
    Rosemberg, S., Pierre-Louis, C., Richard, L.: Zero-knowledge identification based on lattices with low communication costs. XI Simpósio Brasileiro de Segurança da Informaçao e de Sistemas Computacionais 8, 95–107 (2011)Google Scholar
  14. 14.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999).  https://doi.org/10.1137/S0036144598347011MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Uriel, F., Amos, F., Adi, S.: Zero-knowledge proofs of identity. J. Cryptol. 1(2), 77–94 (1988).  https://doi.org/10.1007/BF02351717MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jie Cai
    • 1
  • Han Jiang
    • 2
    Email author
  • Qiuliang Xu
    • 2
  • Guangshi Lv
    • 1
  • Minghao Zhao
    • 3
  • Hao Wang
    • 4
  1. 1.School of MathematicsShandong UniversityJi’nanChina
  2. 2.Software CollegeShandong UniversityJi’nanChina
  3. 3.School of SoftwareTsinghua UniversityBeijingChina
  4. 4.School of Information Science and EngineeringShandong Normal UniversityJi’nanChina

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