Proxy Re-encryption from Lattices

  • Elena Kirshanova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8383)


We propose a new unidirectional proxy re-encryption scheme based on the hardness of the LWE problem. Our construction is collusionsafe and does not require any trusted authority for the re-encryption key generation. We extend a recent trapdoor definition for a lattice of Micciancio and Peikert. Our proxy re-encryption scheme is provably CCA-1 secure in the selective model under the LWE assumption.


Proxy re-encryption lattices learning with errors 


  1. 1.
    Ajtai, M.: Generating hard instances of lattice problems. In: Proceedings of STOC, pp. 99–108 (1996)Google Scholar
  2. 2.
    Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. Theory of Computing Systems 48(3), 535–553 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ateniese, G., Fu, K., Green, M., Hohenberger, S.: Improved proxy re-encryption schemes with applications to secure distributed storage. In: NDSS, pp. 29–43 (2005)Google Scholar
  4. 4.
    Ateniese, G., Fu, K., Green, M., Hohenberger, S.: Improved proxy re-encryption schemes with applications to secure distributed storage. In: ACM TISSEC, pp. 29–43 (2006)Google Scholar
  5. 5.
    Banaszczyk, W.: New bounds in some transference theorems in the geometry of numbers. Mathematische Annalen 296(1), 625–635 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Blaze, M., Bleumer, G., Strauss, M.J.: Divertible protocols and atomic proxy cryptography. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 127–144. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    Canetti, R., Hohenberger, S.: Chosen-ciphertext secure proxy re-encryption. In: Proc. of ACM-CCS 2007, pp. 185–194. ACM Press (2007)Google Scholar
  8. 8.
    El Gamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  9. 9.
    Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009)Google Scholar
  10. 10.
    Green, M., Ateniese, G.: Identity-based proxy re-encryption. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 288–306. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press (1994)Google Scholar
  12. 12.
    Libert, B., Vergnaud, D.: Unidirectional chosen-ciphertext secure proxy re-encryption. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 360–379. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. In: SIAM J. on Computing, pp. 372–381 (2004)Google Scholar
  14. 14.
    Peikert, C.: An efficient and parallel gaussian sampler for lattices. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 80–97. Springer, Heidelberg (2010)CrossRefGoogle 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)CrossRefGoogle Scholar
  16. 16.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93. ACM Press (2005)Google Scholar
  17. 17.
    Vershynin, R.: Introduction to the non-asymptotic analysis of random matrices (2011),
  18. 18.
    Xagawa, K.: Cryptography with Lattices. PhD thesis, Tokyo Institute of Technology (2010),

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Elena Kirshanova
    • 1
  1. 1.Horst Görtz Institute for IT-Security, Faculty of MathematicsRuhr University BochumGermany

Personalised recommendations