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A New Design of Online/Offline Signatures Based on Lattice

  • Mingmei Zheng
  • Shao-Jun Yang
  • Wei Wu
  • Jun Shao
  • Xinyi Huang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11125)

Abstract

With the rapid development of mobile internet, a large number of lightweight devices are widely used. Therefore, lightweight cryptographic primitives are urgently demanded. Among these primitives, online/offline signatures are one of the most promising one. Motivated by this situation, we propose a lattice-based online/offline signature scheme by using the hash-sign-switch paradigm, which was introduced by Shamir and Tauman in 2001. Our scheme not only has the advantages of online/offline signatures, but also can resist quantum computer attacks. The scheme we propose is built on several techniques, such as cover-free sets and programmable hash functions. Furthermore, we design a specific chameleon hash function, which plays an important role in the hash-sign-switch paradigm. Under the Inhomogeneous Small Integer Solution (ISIS) assumption, we prove that our proposed chameleon hash function is collision-resistant, which makes a direct application of this new design. In particular, our method satisfies existential unforgeability against adaptive chosen message attacks in the standard model.

Keywords

Online/offline signature Lattice Chameleon hash function The Inhomogeneous Small Integer Solution (ISIS) assumption 

Notes

Acknowledgements

The authors would like to thank anonymous reviewers for their helpful comments. This work is supported by National Natural Science Foundation of China (61472083, 61771140, 11701089, 61472364), Distinguished Young Scholars Fund of Fujian (2016J06013), Fujian Normal University Innovative Research Team (NO. IRTL1207), Fujian Province Department of Education Project (JOPX 15066), and Zhejiang Provincial Natural Science Foundation (NO. LZ18F020003).

References

  1. 1.
    Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, Pennsylvania, USA, 22–24 May 1996, pp. 99–108 (1996).  https://doi.org/10.1145/237814.237838
  2. 2.
    Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1–9. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-48523-6_1CrossRefGoogle Scholar
  3. 3.
    Boyen, X.: Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13013-7_29CrossRefGoogle Scholar
  4. 4.
    Crutchfield, C., Molnar, D., Turner, D., Wagner, D.: Generic on-line/off-line threshold signatures. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 58–74. Springer, Heidelberg (2006).  https://doi.org/10.1007/11745853_5CrossRefGoogle Scholar
  5. 5.
    Deiseroth, B., Fehr, V., Fischlin, M., Maasz, M., Reimers, N.F., Stein, R.: Computing on authenticated data for adjustable predicates. In: Jacobson, M., Locasto, M., Mohassel, P., Safavi-Naini, R. (eds.) ACNS 2013. LNCS, vol. 7954, pp. 53–68. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-38980-1_4CrossRefGoogle Scholar
  6. 6.
    Ducas, L., Micciancio, D.: Improved short lattice signatures in the standard model. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 335–352. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44371-2_19CrossRefzbMATHGoogle Scholar
  7. 7.
    Erdös, P., Frankl, P., Füredi, Z.: Families of finite sets in which no set is covered by the union of r others. Isr. J. Math. 51(1–2), 79–89 (1985)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Even, S., Goldreich, O., Micali, S.: On-line/off-line digital signatures. J. Cryptol. 9(1), 35–67 (1996).  https://doi.org/10.1007/BF02254791MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, 17–20 May 2008, pp. 197–206 (2008).  https://doi.org/10.1145/1374376.1374407
  10. 10.
    Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988).  https://doi.org/10.1137/0217017MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 21–38. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85174-5_2CrossRefGoogle Scholar
  12. 12.
    Krawczyk, H., Rabin, T.: Chameleon hashing and signatures. IACR Cryptology ePrint Archive 1998/10 (1998). http://eprint.iacr.org/1998/010
  13. 13.
    Kumar, R., Rajagopalan, S., Sahai, A.: Coding constructions for blacklisting problems without computational assumptions. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 609–623. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-48405-1_38CrossRefGoogle Scholar
  14. 14.
    Liu, J.K., Baek, J., Zhou, J.Y., Yang, Y.J., Wong, J.W.: Efficient online/offline identity-based signature for wireless sensor network. Int. J. Inf. Sec. 9(4), 287–296 (2010).  https://doi.org/10.1007/s10207-010-0109-yCrossRefGoogle Scholar
  15. 15.
    Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29011-4_41CrossRefGoogle Scholar
  16. 16.
    Shamir, A., Tauman, Y.: Improved online/offline signature schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 355–367. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-44647-8_21CrossRefGoogle Scholar
  17. 17.
    Vershynin, R.: Introduction to the non-asymptotic analysis of random matrices. CoRR abs/1011.3027 (2010). http://arxiv.org/abs/1011.3027
  18. 18.
    Xiang, X.Y.: Online/offline signature scheme based on ideal lattices (in Chinese). J. Cryptologic Res. 4(3), 253–261 (2017)Google Scholar
  19. 19.
    Xiang, X.Y., Li, H.: Lattice-based online/offline signature scheme (in Chinese). J. Beijing Univ. Posts Telecommun. 38(3), 117–120, 134 (2015)Google Scholar
  20. 20.
    Zhang, J., Chen, Y., Zhang, Z.: Programmable hash functions from lattices: short signatures and ibes with small key sizes. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 303–332. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53015-3_11CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mingmei Zheng
    • 1
  • Shao-Jun Yang
    • 1
  • Wei Wu
    • 1
  • Jun Shao
    • 2
  • Xinyi Huang
    • 1
  1. 1.Fujian Provincial Key Laboratory of Network Security and Cryptology, School of Mathematics and InformaticsFujian Normal UniversityFuzhouChina
  2. 2.School of Computer and Information EngineeringZhejiang Gongshang UniversityHangzhouChina

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