An Efficient Proxy Re-Signature Over Lattices

  • Mingming Jiang
  • Jinqiu Hou
  • Yuyan GuoEmail author
  • Yan Wang
  • Shimin Wei
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1105)


In 2008, Libert and Vergnaud constructed the first multi-use unidirectional proxy re-signature scheme. In this scheme, the proxy can translate the signatures several times but only in one direction. Thus, two problems remain open. That is, to construct a multi-use unidirectional proxy re-signature scheme based on classical hardness assumptions, and to design a multi-use unidirectional proxy re-signature scheme with the size of signatures and the verification cost growing sub-linearly with the number of translations. This paper solves the first problem and sharply reduces the verification costs. We use the preimage sampleable algorithm to develop a multi-use unidirectional proxy re-signature scheme based on lattices, namely, the hardness of the Small Integer Solution (SIS) problem. The verification cost does not grow with the number of translations and the size of signatures grows linearly with the number of translations in this scheme. Furthermore, the proposal is secure in quantum environment.


Lattice cryptography Proxy re-signature scheme Small Integer Solution (SIS) problem Gaussian Sample Multi-use 



We are thankful to anonymous referees for their helpful comments. This paper is supported by the National Natural Science Foundation of China under Grant No. 61902140, No. 60573026, the Anhui Provincial Natural Science Foundation under Grant No. 1708085QF154, No. 1908085QF288, NO. 1808085QF181, the Nature Science Foundation of Anhui Higher Education Institutions under Grant No. KJ2019A0605, No. KJ2018A0398, No. KJ2019B018.


  1. 1.
    Blaze, M., Bleumer, G., Strauss, M.: Divertible protocols and atomic proxy cryptography. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 127–144. Springer, Heidelberg (1998). Scholar
  2. 2.
    Ateniese, G., Hohenberger, S.: Proxy re-signatures: new definitions, algorithms, and applications. In: CCS Proceedings of the 15th ACM Conference on Computer and Communications Security, Alexandria, VA, USA, March 2005, pp. 310–319 (2005).
  3. 3.
    Libert, B., Vergnaud, D.: Multi-use unidirectional proxy re-signatures. In: CCS Proceedings of the 15th ACM Conference on Computer and Communications Security, Alexandria, VA, USA, October 2008, pp. 511–520 (2008)Google Scholar
  4. 4.
    Sunitha, N.R., Amberker, B.B.: Multi-use unidirectional forward-secure proxy re-signature scheme. In: Proceedings of the 3rd IEEE International Conference on Internet Multimedia Services Architecture and Applications, Bangalore, India, December 2009, pp. 223–228 (2009)Google Scholar
  5. 5.
    Sunitha, N.R.: Proxy re-signature schemes: multi-use, unidirectional and translations. J. Adv. Inf. Technol. 2(3), 165–176 (2011)Google Scholar
  6. 6.
    Shao, J., Cao, Z., Wang, L., Liang, X.: Proxy re-signature schemes without random oracles. In: Srinathan, K., Rangan, C.P., Yung, M. (eds.) INDOCRYPT 2007. LNCS, vol. 4859, pp. 197–209. Springer, Heidelberg (2007). Scholar
  7. 7.
    Shao, J., Wei, G.Y., Ling, Y., Xie, M.D.: Unidirectional identity-based proxy re-signature. In: Proceedings of the IEEE Communications Society, Hangzhou, China, June 2011, pp. 1–5 (2011)Google Scholar
  8. 8.
    Shao, J., Feng, M., Zhu, B., Cao, Z., Liu, P.: The security model of unidirectional proxy re-signature with private re-signature key. In: Steinfeld, R., Hawkes, P. (eds.) ACISP 2010. LNCS, vol. 6168, pp. 216–232. Springer, Heidelberg (2010). Scholar
  9. 9.
    Yang, P.Y., Cao, Z.F., Dong, X.L.: Threshold proxy re-signature. J. Syst. Sci. Complex 2011(24), 816–824 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: How to use a short basis: trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the STOC 2008, Victoria, Canada, May 2008, pp. 197–206 (2008)Google Scholar
  11. 11.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), Article 34 (2009)Google Scholar
  12. 12.
    Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). Scholar
  13. 13.
    Lindner, R., Peikert, C.: Better key sizes (and attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319–339. Springer, Heidelberg (2011). Scholar
  14. 14.
    Stehlé, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: Paterson, Kenneth G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 27–47. Springer, Heidelberg (2011). Scholar
  15. 15.
    Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010). Scholar
  16. 16.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010). Scholar
  17. 17.
    Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98–115. Springer, Heidelberg (2010). Scholar
  18. 18.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the STOC 2009, Bethesda, Maryland, USA, May 2009, pp. 169–178 (2009)Google Scholar
  19. 19.
    Gentry, C.: Toward basing fully homomorphic encryption on worst-case hardness. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 116–137. Springer, Heidelberg (2010). Scholar
  20. 20.
    Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011). Scholar
  21. 21.
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Proceedings of the FOCS 2011, Palm Springs, CA, USA, October 2011, pp. 97–106 (2011)Google Scholar
  22. 22.
    Lyubashevsky, V.: lattice signatures without trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012). Scholar
  23. 23.
    Gordon, S.D., Katz, J., Vaikuntanathan, V.: A group signature scheme from lattice assumptions. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 395–412. Springer, Heidelberg (2010). Scholar
  24. 24.
    Rückert, M.: Lattice-based blind signatures. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 413–430. Springer, Heidelberg (2010). Scholar
  25. 25.
    Rückert, M.: Strongly unforgeable signatures and hierarchical identity-based signatures from lattices without random oracles. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 182–200. Springer, Heidelberg (2010). Scholar
  26. 26.
    Alwen, J., Peiker, C.: Generating shorter bases for hard random lattices. In: Proceedings of the STACS 2009, Freiburg, Germany, February 2009, pp. 75–86 (2009)Google Scholar
  27. 27.
    Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011). Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Mingming Jiang
    • 1
  • Jinqiu Hou
    • 1
  • Yuyan Guo
    • 1
    Email author
  • Yan Wang
    • 2
  • Shimin Wei
    • 1
  1. 1.School of Computer Science and TechnologyHuaibei Normal UniversityHuaibeiChina
  2. 2.School of Mathematics ScienceHuaibei Normal UniversityHuaibeiChina

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