Skip to main content
Springer Nature Link
Log in

Key-Private Proxy Re-encryption under LWE

  • Conference paper
Progress in Cryptology – INDOCRYPT 2013 (INDOCRYPT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8250))

Included in the following conference series:

Abstract

Proxy re-encryption (PRE) is a highly useful cryptographic primitive whereby Alice and Bob can endow a proxy with the capacity to change ciphertext recipients from Alice to Bob, without the proxy itself being able to decrypt, thereby providing delegation of decryption authority. Key-private PRE (KP-PRE) specifies an additional level of confidentiality, requiring pseudo-random proxy keys that leak no information on the identity of the delegators and delegatees.

In this paper, we propose a CPA-secure PK-PRE scheme in the standard model (which we then transform into a CCA-secure scheme in the random oracle model). Both schemes enjoy highly desirable properties such as uni-directionality and multi-hop delegation.

Unlike (the few) prior constructions of PRE and KP-PRE that typically rely on bilinear maps under ad hoc assumptions, security of our construction is based on the hardness of the standard Learning-With-Errors (LWE) problem, itself reducible from worst-case lattice hard problems that are conjectured immune to quantum cryptanalysis, or “post-quantum”.

Of independent interest, we further examine the practical hardness of the LWE assumption, using Kannan’s exhaustive search algorithm coupling with pruning techniques. This leads to state-of-the-art parameters not only for our scheme, but also for a number of other primitives based on LWE published the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Ateniese, G., Benson, K., Hohenberger, S.: Key-private proxy re-encryption. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 279–294. Springer, Heidelberg (2009), Full version at http://eprint.iacr.org/2008/463

  3. Ateniese, G., Fu, K., Green, M., Hohenberger, S.: Improved proxy re-encryption schemes with applications to secure distributed storage. ACM Trans. Inf. Syst. Secur. 9(1), 1–30 (2006)

    Article  Google Scholar 

  4. Banaszczyk, W.: New bounds in some transference theorems in the geometry of numbers. Mathematische Annalen 296(1), 625–635 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Banaszczyk, W.: Inequalities for convex bodies and polar reciprocal lattices in ℝn. Discrete & Computational Geometry 13(1), 217–231 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Denning, D.E., Pyle, R., Ganesan, R., Sandhu, R.S., Ashby, V. (eds.) ACM Conference on Computer and Communications Security, pp. 62–73. ACM Press, New York (1993)

    Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical gapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  9. Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehlé, D.: Classical hardness of learning with errors. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) STOC, pp. 575–584. ACM (2013)

    Google Scholar 

  10. Canetti, R., Hohenberger, S.: Chosen-ciphertext secure proxy re-encryption. In: Ning, P., di Vimercati, S.D.C., Syverson, P.F. (eds.) ACM Conference on Computer and Communications Security, pp. 185–194. ACM (2007)

    Google Scholar 

  11. T. D. S. Challenge, http://www.latticechallenge.org/svp-challenge/

  12. Dawson, E. (ed.): CT-RSA 2013. LNCS, vol. 7779. Springer, Heidelberg (2013)

    MATH  Google Scholar 

  13. Deng, R.H., Weng, J., Liu, S., Chen, K.: Chosen-ciphertext secure proxy re-encryption without pairings. In: Franklin, M.K., Hui, L.C.K., Wong, D.S. (eds.) CANS 2008. LNCS, vol. 5339, pp. 1–17. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. J. Cryptology 26(1), 80–101 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gama, N., Nguyen, P.Q., Regev, O.: Lattice enumeration using extreme pruning. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 257–278. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Hanaoka, G., Kawai, Y., Kunihiro, N., Matsuda, T., Weng, J., Zhang, R., Zhao, Y.: Generic construction of chosen ciphertext secure proxy re-encryption. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 349–364. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Hohenberger, S., Rothblum, G.N., Shelat, A., Vaikuntanathan, V.: Securely obfuscating re-encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 233–252. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Isshiki, T., Nguyen, M.H., Tanaka, K.: Proxy re-encryption in a stronger security model extended from CT-RSA2012. In: Dawson [12], pp. 277–292

    Google Scholar 

  20. Kannan, R.: Improved algorithms for integer programming and related lattice problems. In: Johnson, D.S., Fagin, R., Fredman, M.L., Harel, D., Karp, R.M., Lynch, N.A., Papadimitriou, C.H., Rivest, R.L., Ruzzo, W.L., Seiferas, J.I. (eds.) STOC, pp. 193–206. ACM (1983)

    Google Scholar 

  21. Libert, B., Vergnaud, D.: Unidirectional chosen-ciphertext secure proxy re-encryption. IEEE Transactions on Information Theory 57(3), 1786–1802 (2011)

    Article  MathSciNet  Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. Liu, M., Nguyen, P.Q.: Solving BDD by enumeration: An update. In: Dawson [12], pp. 293–309

    Google Scholar 

  24. Micciancio, D., Regev, O.: Lattice-based cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 147–191. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  25. Rckert, M., Schneider, M.: Estimating the security of lattice-based cryptosystems. Cryptology ePrint Archive, Report 2010/137 (2010), http://eprint.iacr.org/

  26. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) STOC, pp. 84–93. ACM (2005)

    Google Scholar 

  27. Schnorr, C.-P.: Lattice reduction by random sampling and birthday methods. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  28. Seo, J.W., Yum, D.H., Lee, P.J.: Comments on “unidirectional chosen-ciphertext secure proxy re-encryption”. IEEE Transactions on Information Theory 59(5), 32–56 (2013)

    Article  MathSciNet  Google Scholar 

  29. Shao, J.: Anonymous ID-based proxy re-encryption. In: Susilo, W., Mu, Y., Seberry, J. (eds.) ACISP 2012. LNCS, vol. 7372, pp. 364–375. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  30. Shao, J., Cao, Z., Liu, P.: SCCR: a generic approach to simultaneously achieve cca security and collusion-resistance in proxy re-encryption. Security and Communication Networks 4(2), 122–135 (2011)

    Article  Google Scholar 

  31. Shao, J., Liu, P., Cao, Z., Wei, G.: Multi-use unidirectional proxy re-encryption. In: ICC, pp. 1–5. IEEE (2011)

    Google Scholar 

  32. Shao, J., Liu, P., Wei, G., Ling, Y.: Anonymous proxy re-encryption. Security and Communication Networks 5(5), 439–449 (2012)

    Article  Google Scholar 

  33. Shao, J., Liu, P., Zhou, Y.: Achieving key privacy without losing cca security in proxy re-encryption. Journal of Systems and Software 85(3), 655–665 (2012)

    Article  Google Scholar 

  34. Wang, L., Wang, L., Mambo, M., Okamoto, E.: New identity-based proxy re-encryption schemes to prevent collusion attacks. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 327–346. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  35. Weng, J., Chen, M.-R., Yang, Y., Deng, R.H., Chen, K., Bao, F.: CCA-secure unidirectional proxy re-encryption in the adaptive corruption model without random oracles. SCIENCE CHINA Information Sciences 53(3), 593–606 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NICT, Japan

    Yoshinori Aono, Le Trieu Phong & Lihua Wang

  2. Queensland University of Technology, Australia

    Xavier Boyen

Authors
  1. Yoshinori Aono
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xavier Boyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Le Trieu Phong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lihua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. R.C. Bose Centre for Cryptology and Security, Indian Statistical Institute, 203 B.T. Road, 700 108, Kolkata, India

    Goutam Paul

  2. EPFL - I&C - LASEC, INF 24, Station 14, 1015, Lausanne, Switzerland

    Serge Vaudenay

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Aono, Y., Boyen, X., Phong, L.T., Wang, L. (2013). Key-Private Proxy Re-encryption under LWE. In: Paul, G., Vaudenay, S. (eds) Progress in Cryptology – INDOCRYPT 2013. INDOCRYPT 2013. Lecture Notes in Computer Science, vol 8250. Springer, Cham. https://doi.org/10.1007/978-3-319-03515-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03515-4_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03514-7

  • Online ISBN: 978-3-319-03515-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics