Skip to main content
SpringerLink
Log in

Key-Dependent Message Security for Division Function: Discouraging Anonymous Credential Sharing

  • Conference paper
Provable Security (ProvSec 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6980))

Included in the following conference series:

Abstract

Key-dependent message (KDM) security means that the encryption scheme remains secure even encrypting f(sk), where f is an efficient computable function chosen by the adversary and sk = sk 1, ⋯ , sk n are private keys. We concentrate on a special case that the function f is a division function. Namely, the messages of the form sk i /sk j are encrypted. We prove that if a public key encryption (PKE) scheme is IND-CPA (chosen plaintext attacks) secure and has the properties of public-key blinding and secret-key homomorphism, then it is KDM secure for division function (KDM-div secure). For concrete scheme, we show that the hybrid ElGamal scheme is KDM-div secure based on the decisional Diffie-Hellman (DDH) assumption in the standard model. We show that KDM-div secure scheme is useful in the design of anonymous credential systems.

Supported by the National Natural Science Foundation of China (No.61070171), the National Basic Research Program of China(973 project) (No.2007CB311201) and the Postdoctoral Science Foundation of China (No.20100480514).

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

Access this chapter

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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Micali, S., Rackoff, C., Sloan, R.: The notion of security for probabilistic cryptosystems. SIAM J. on Computing (April 1988)

    Google Scholar 

  2. Camenisch, J., Lysyanskaya, A.: Efficient non-transferable anonymous credential system with optional anonymity revocation. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 93–118. Springer, Heidelberg (2001)

    Google Scholar 

  3. Black, J., Rogaway, P., Shrimpton, T.: Encryption-Scheme Security in the Presence of Key-Dependent Messages. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 62–75. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Backes, M., Pfitzmann, B., Scedrov, A.: Key-dependent message security under active attacks - brsim/uc-soundness of symbolic encryption with key cycles. In: CSF, pp. 112–124. IEEE Computer Society, Los Alamitos (2007)

    Google Scholar 

  5. Halevi, S., Krawczyk, H.: Security under key-dependent inputs. In: Ning, P., De Capitani di Vimercati, S., Syverson, P.F. (eds.) ACM Conference on Computer and Communications Security, pp. 466–475. ACM, New York (2007)

    Google Scholar 

  6. Hofheinz, D., Unruh, D.: Towards Key-Dependent Message Security in the Standard Model. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 108–126. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Boneh, D., Halevi, S., Hamburg, M., Ostrovsky, R.: Circular-Secure Encryption from Decision Diffie-Hellman. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 108–125. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  8. Backes, M., Dürmuth, M., Unruh, D.: OAEP Is Secure under Key-Dependent Messages. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 506–523. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Camenisch, J., Chandran, N., Shoup, V.: A Public Key Encryption Scheme Secure against Key Dependent Chosen Plaintext and Adaptive Chosen Ciphertext Attacks. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 351–368. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Haitner, I., Holenstein, T.: On the (Im)Possibility of key dependent encryption. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 202–219. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  12. Brakerski, Z., Goldwasser, S., Kalai, Y.: Black-box circular-secure encryption beyond affine functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 201–218. Springer, Heidelberg (2011), http://eprint.iacr.org

    Chapter  Google Scholar 

  13. Barak, B., Haitner, I., Hofheinz, D., Ishai, Y.: Bounded Key-Dependent Message Security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 423–444. Springer, Heidelberg (2010), http://eprint.iacr.org/

    Chapter  Google Scholar 

  14. Brakerski, Z., Goldwasser, S.: Circular and Leakage Resilient Public-Key Encryption Under Subgroup Indistinguishability (or: Quadratic Residuosity Strikes Back). In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010), http://eprint.iacr.org

    Chapter  Google Scholar 

  15. Applebaum, B.: Key-Dependent Message Security: Generic Amplification and Completeness. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 527–546. Springer, Heidelberg (2011), http://eprint.iacr.org

    Chapter  Google Scholar 

  16. Malkin, T., Teranishi, I., Yung, M.: Efficient Circuit-Size Independent Public Key Encryption with KDM Security. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 507–526. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Bellare, M., Keelveedhi, S.: Authenticated and misuse-resistant encryption of key-dependent data. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 610–629. Springer, Heidelberg (2011), http://eprint.iacr.org/2011/269

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Xianhui Lu, Bao Li & Haixia Xu

  2. School of Information, Guangdong Ocean University, Zhanjiang, 524088, China

    Qixiang Mei

Authors
  1. Xianhui Lu
    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. Qixiang Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haixia Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Palo Alto Research Center, 94304, Palo Alto, CA, USA

    Xavier Boyen

  2. School of Telecommunications Engineering, Xidian University, 710071, Xi’an, China

    Xiaofeng Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lu, X., Li, B., Mei, Q., Xu, H. (2011). Key-Dependent Message Security for Division Function: Discouraging Anonymous Credential Sharing. In: Boyen, X., Chen, X. (eds) Provable Security. ProvSec 2011. Lecture Notes in Computer Science, vol 6980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24316-5_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24316-5_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24315-8

  • Online ISBN: 978-3-642-24316-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation