Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Security

IWSEC 2015: Advances in Information and Computer Security pp 193–210Cite as

Improved Efficiency of MP12

  • Conference paper
  • First Online:

  • 1041 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9241))

Abstract

MP12 (proposed by Micciancio and Peikert in Eurocrypt 2012) presented a chosen ciphertext secure public key encryption (PKE) scheme based on the learning with errors (LWE) problem. In this paper, we improve the efficiency of the scheme and give two sets of parameters. In both sets of parameters, the size of secret key is \(O(\log q)\) times less than the scheme in MP12. Furthermore, in the second case of \(p=O(n)\), we can decrease the message expansion rate from \(O(\log q)\) to O(1). The main ideas in our scheme are we can hide the message by the knapsack LWE assumption and embed the message into the error item.

This research is supported by the National Nature Science Foundation of China (No. 61379137 and No. 61272040), the National Basic Research Program of China (973 project) (No. 2013CB338002), and IIE’s Cryptography Research Project (No. Y4Z0061D03).

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. 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)

    Chapter  Google Scholar 

  2. Alperin-Sheriff, J., Peikert, C.: Circular and KDM security for identity-based encryption. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 334–352. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boneh, D., Katz, J.: Improved efficiency for CCA-secure cryptosystems built using identity-based encryption. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 87–103. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, ITCS 2012, pp. 309–325. ACM, New York (2012)

    Google Scholar 

  6. Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehlé, D.: Classical hardness of learning with errors. In: STOC, pp. 575–584 (2013)

    Google Scholar 

  7. Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Kiltz, E., Masny, D., Pietrzak, K.: Simple chosen-ciphertext security from low-noise LPN. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 1–18. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  11. Micciancio, D., Mol, P.: Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 465–484. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. O’Neill, A., Peikert, C., Waters, B.: Bi-deniable public-key encryption. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 525–542. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  14. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: STOC, pp. 333–342 (2009)

    Google Scholar 

  15. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In; STOC, pp. 187–196 (2008)

    Google Scholar 

  16. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93 (2005)

    Google Scholar 

  17. Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Vershynin, R.: Introduction to the non-asymptotic analysis of random matrices (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Fuyang Fang, Bao Li, Xianhui Lu & Xiaochao Sun

  2. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, 100093, China

    Fuyang Fang, Bao Li, Xianhui Lu & Xiaochao Sun

  3. University of Chinese Academy of Sciences, Beijing, China

    Fuyang Fang & Xiaochao Sun

Authors
  1. Fuyang Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xianhui Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaochao Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fuyang Fang .

Editor information

Editors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Keisuke Tanaka

  2. Internet Initiative Japan Inc., Tokyo, Japan

    Yuji Suga

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Fang, F., Li, B., Lu, X., Sun, X. (2015). Improved Efficiency of MP12. In: Tanaka, K., Suga, Y. (eds) Advances in Information and Computer Security. IWSEC 2015. Lecture Notes in Computer Science(), vol 9241. Springer, Cham. https://doi.org/10.1007/978-3-319-22425-1_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22425-1_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22424-4

  • Online ISBN: 978-3-319-22425-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation