Skip to main content
SpringerLink
Log in

Distributed Private-Key Generators for Identity-Based Cryptography

  • Conference paper
Security and Cryptography for Networks (SCN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6280))

Included in the following conference series:

Abstract

An identity-based encryption (IBE) scheme can greatly reduce the complexity of sending encrypted messages. However, an IBE scheme necessarily requires a private-key generator (PKG), which can create private keys for clients, and so can passively eavesdrop on all encrypted communications. Although a distributed PKG has been suggested as a way to mitigate this key escrow problem for Boneh and Franklin’s IBE scheme, the security of this distributed protocol has not been proven. Further, a distributed PKG has not been considered for any other IBE scheme.

In this paper, we design distributed PKG setup and private key extraction protocols for three important IBE schemes; namely, Boneh and Franklin’s BF-IBE, Sakai and Kasahara’s SK-IBE, and Boneh and Boyen’s \(\mbox{BB}_1\)-IBE. We give special attention to the applicability of our protocols to all possible types of bilinear pairings and prove their IND-ID-CCA security in the random oracle model against a Byzantine adversary. Finally, we also perform a comparative analysis of these protocols and present recommendations for their use.

An extended version of this paper is avaiable [1].

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. Kate, A., Goldberg, I.: Asynchronous Distributed Private-Key Generators for Identity-Based Cryptography. Cryptology ePrint Archive, Report 2009/355 (June 2010), http://eprint.iacr.org/2009/355

  2. Shamir, A.: Identity-Based Cryptosystems and Signature Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  3. Boneh, D., Franklin, M.K.: Identity-Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Joye, M., Neven, G.: Identity-Based Cryptography. Cryptology and Information Security Series, vol. 2. IOS Press, Amsterdam (2008)

    Google Scholar 

  5. Feldman, P.: A Practical Scheme for Non-interactive Verifiable Secret Sharing. In: FOCS 1987, pp. 427–437 (1987)

    Google Scholar 

  6. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure Distributed Key Generation for Discrete-Log Based Cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999)

    Google Scholar 

  7. Kate, A., Zaverucha, G.M., Goldberg, I.: Pairing-Based Onion Routing. In: PETS 2007, pp. 95–112 (2007)

    Google Scholar 

  8. Abdalla, M., Catalano, D., Fiore, D.: Verifiable Random Functions from Identity-Based Key Encapsulation. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 554–571. Springer, Heidelberg (2010)

    Google Scholar 

  9. Boyen, X.: A Tapestry of Identity-based Encryption: Practical Frameworks Compared. IJACT 1(1), 3–21 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Geisler, M., Smart, N.P.: Distributing the Key Distribution Centre in Sakai-Kasahara Based Systems. In: Parker, M.G. (ed.) Cryptography and Coding. LNCS, vol. 5921, pp. 252–262. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Sakai, R., Kasahara, M.: ID based Cryptosystems with Pairing on Elliptic Curve. Cryptology ePrint Archive, Report 2003/054 (2003)

    Google Scholar 

  12. Al-Riyami, S.S., Paterson, K.G.: Certificateless Public Key Cryptography. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 452–473. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Lee, B., Boyd, C., Dawson, E., Kim, K., Yang, J., Yoo, S.: Secure key issuing in ID-based cryptography. In: ACSW Frontiers 2004, pp. 69–74 (2004)

    Google Scholar 

  14. Gangishetti, R., Gorantla, M.C., Das, M., Saxena, A.: Threshold key issuing in identity-based cryptosystems. Computer Standards & Interfaces 29(2), 260–264 (2007)

    Article  Google Scholar 

  15. Chunxiang, X., Junhui, Z., Zhiguang, Q.: A Note on Secure Key Issuing in ID-based Cryptography. Technical report (2005), http://eprint.iacr.org/2005/180

  16. Goyal, V.: Reducing Trust in the PKG in Identity Based Cryptosystems. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 430–447. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Boldyreva, A.: Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Wang, H., Zhang, Y., Feng, D.: Short Threshold Signature Schemes Without Random Oracles. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 297–310. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Boyen, X., Martin, L.: Identity-Based Cryptography Standard (IBCS) (Version 1), Request for Comments (RFC) 5091 (2007), http://www.ietf.org/rfc/rfc5091.txt

  20. Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Applied Mathematics 156(16), 3113–3121 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Blake, I., Seroussi, G., Smart, N.P. (eds.): Advances in Elliptic Curve Cryptography. London Mathematical Society Lecture Note Series, vol. 317, pp. 183–252 (2005)

    Google Scholar 

  22. Chatterjee, S., Menezes, A.: On Cryptographic Protocols Employing Asymmetric Pairings - The Role of Ψ Revisited. CACR 2009-34 (2009), http://www.cacr.math.uwaterloo.ca/techreports/2007/cacr2009-34.pdf

  23. Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)

    Google Scholar 

  24. Pedersen, T.P.: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)

    Google Scholar 

  25. Chaum, D., Pedersen, T.P.: Wallet Databases with Observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)

    Google Scholar 

  26. Joux, A., Nguyen, K.: Separating Decision Diffie-Hellman from Computational Diffie-Hellman in Cryptographic Groups. Journal of Cryptology 16(4), 239–247 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. Kate, A., Goldberg, I.: Distributed Key Generation for the Internet. In: ICDCS 2009, pp. 119–128 (2009)

    Google Scholar 

  28. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure Distributed Key Generation for Discrete-Log Based Cryptosystems. Journal of Cryptology 20(1), 51–83 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  29. Canetti, R., Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Adaptive Security for Threshold Cryptosystems. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 98–115. Springer, Heidelberg (1999)

    Google Scholar 

  30. Joux, A.: A One Round Protocol for Tripartite Diffie-Hellman. In: ANTS-IV, pp. 385–394 (2000)

    Google Scholar 

  31. Mitsunari, S., Sakai, R., Kasahara, M.: A New Traitor Tracing. IEICE Transactions E85-A(2), 481–484 (2002)

    Google Scholar 

  32. Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  33. Bar-Ilan, J., Beaver, D.: Non-Cryptographic Fault-Tolerant Computing in Constant Number of Rounds of Interaction. In: PODC 1989, pp. 201–209 (1989)

    Google Scholar 

  34. Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: STOC 1988, pp. 1–10 (1988)

    Google Scholar 

  35. Cachin, C., Kursawe, K., Lysyanskaya, A., Strobl, R.: Asynchronous Verifiable Secret Sharing and Proactive Cryptosystems. In: ACM CCS 2002, pp. 88–97 (2002)

    Google Scholar 

  36. Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and Fact-Track Multiparty Computations with Applications to Threshold Cryptography. In: PODC 1998, pp. 101–111 (1998)

    Google Scholar 

  37. Shamir, A.: How to Share a Secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  38. Boyen, X.: General Ad Hoc Encryption from Exponent Inversion IBE. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 394–411. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  39. Chen, L., Cheng, Z.: Security Proof of Sakai-Kasahara’s Identity-Based Encryption Scheme. In: IMA Int. Conf., pp. 442–459 (2005)

    Google Scholar 

  40. Joux, A.: The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 20–32. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Canada

    Aniket Kate & Ian Goldberg

Authors
  1. Aniket Kate
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ian Goldberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. AT&T Labs Research, Florham Park, NJ, USA

    Juan A. Garay

  2. Dipartimento di Informatica ed Applicazioni, Università di Salerno, via Ponte don Melillo, 84084, Fisciano, (SA), Italy

    Roberto De Prisco

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kate, A., Goldberg, I. (2010). Distributed Private-Key Generators for Identity-Based Cryptography. In: Garay, J.A., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2010. Lecture Notes in Computer Science, vol 6280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15317-4_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15317-4_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15316-7

  • Online ISBN: 978-3-642-15317-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation