Skip to main content
SpringerLink
Log in

On Pairing-Based Cryptosystems

  • Conference paper
Progress in Cryptology - VIETCRYPT 2006 (VIETCRYPT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4341))

Included in the following conference series:

Abstract

The pairing technique that uses the (Weil and Tate) pairings over elliptic (or hyperelliptic) curves represents a great breakthrough in cryptography. This paper surveys this new trend in cryptography, and emphasizes the design of efficient cryptographic primitives that are provably secure in the standard model (i.e., without the random oracle model).

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. Ateniese, G., Camenisch, J., de Medeiros, B., Hohenberger, S.: Practical Group Signatures without Random Oracles, IACR ePrint Archive, 2005/385 (2005), http://eprint.iacr.org/2005/385

  2. Balasubramanian, R., Koblitz, N.: The Improbability that an Elliptic Curve Has Subexponential Discrete Log Problem under the Menezes-Okamoto-Vanstone Algorithm. J. Cryptology 11, 141–145 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Barreto, P.: The Pairing-Based Crypto Lounge, http://paginas.terra.com.br/informatica/paulobarreto/pblounge.html

  4. Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations Among Notions of Security for Public-Key Encryption Schemes. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 26–45. Springer, Heidelberg (1998)

    Google Scholar 

  5. Bellare, M., Rogaway, P.: Random Oracles are Practical: a Paradigm for Designing Efficient Protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, CCS 1993, pp. 62–73. ACM, New York (1993)

    Chapter  Google Scholar 

  6. Bellare, M., Rogaway, P.: The Exact Security of Digital Signatures: How to Sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)

    Google Scholar 

  7. Boldyreva, A.: Threshold Signature, Multisignature and Blind Signature Schemes 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 

  8. 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 

  9. Boneh, D., Boyen, X.: Short Signatures Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Boneh, D., Boyen, X.: Secure Identity Based Encryption Without Random Oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443–459. Springer, Heidelberg (2004)

    Google Scholar 

  11. Boneh, D., Boyen, X., Halevi, S.: Chosen Ciphertext Secure Public Key Threshold Encryption Without Random Oracles. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 226–243. Springer, Heidelberg (2006), http://crypto.stanford.edu/~dabo/abstracts/threshold.html

    Chapter  Google Scholar 

  12. Boneh, D., Franklin, M.: Identity-Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001); Journal version in SIAM Journal of Computing, 32(3), pp. 586–615 (2003)

    Chapter  Google Scholar 

  13. 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 

  14. Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Boyen, X., Mei, Q., Waters, B.: Direct Chosen Ciphertext Security from Identity-Based Techniques. In: Proceedings of the 12th ACM Conference on Computer and Communications Security, CCS 2005, ACM, New York (2005), Full version available at: http://www.cs.stanford.edu/~xb/ccs05/

    Google Scholar 

  16. Boyen, X., Waters, B.: Compact Group Signatures Without Random Oracles, IACR ePrint Archive, 2005/381 (2005), http://eprint.iacr.org/2005/381

  17. Chen, L., Cheng, Z.: Security Proof of Sakai-Kasahara’s Identity-Based Encryption Scheme. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol. 3796, pp. 442–459. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Cheon, J.H.: Security Analysis of the Strong Diffie-Hellman Problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Camenisch, J., Lysyanskaya, A.: A Signature Scheme with Efficient Protocols. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  20. Camenisch, J., Lysyanskaya, A.: Signature Schemes and Anonymous Credentials from Bilinear Maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004)

    Google Scholar 

  21. Canetti, R., Halevi, S., Katz, J.: A Forward-Secure Public-Key Encryption Scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003), Full version available at: http://eprint.iacr.org/2003/083

    Chapter  Google Scholar 

  22. 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), Full version available at: http://eprint.iacr.org/2003/182

    Chapter  Google Scholar 

  23. Cramer, R., Shoup, V.: A Practical Public Key Cryptosystem Provably Secure against Adaptive Chosen Ciphertext Attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)

    Google Scholar 

  24. Cramer, R., Shoup, V.: Signature Schemes Based on the Strong RSA Assumption. ACM TISSEC 3(3), 161–185 (2000); Extended abstract in: Proc. 6th ACM CCS (1999)

    Article  Google Scholar 

  25. Cramer, R., Shoup, V.: Universal Hash Proofs and a Paradigm for Adaptive Chosen Ciphertext Secure Public-Key Encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  26. Dodis, Y., Yampolskiy, A.: A Verifiable Random Function with Short Proofs and Keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 416–431. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  27. Fischlin, M.: The Cramer-Shoup Strong-RSASignature Scheme Revisited. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 116–129. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  28. Gentry, C.: Practical Identity-Based Encryption Without Random Oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  29. Gentry, C., Silverberg, A.: Hierarchical Identity-Based Cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548–566. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  30. Goldwasser, S., Micali, S., Rivest, R.: A Digital Signature Scheme Secure against Adaptive Chosen-Message Attacks. SIAM J. Computing 17(2), 281–308 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  31. Joux, A.: One Round Protocol for Tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000); Journal version in Journal of Cryptology, 17(4), pp. 263–276 (2004)

    Chapter  Google Scholar 

  32. Kiltz, E.: Direct Chosen-Ciphertext Secure Identity-Based Encryption in the Standard Model with Short Ciphertexts, IACR ePrint Archive, 2006/122 (2006), http://eprint.iacr.org/2006/122

  33. Koblitz, N., Menezes, A.: Pairing-Based Cryptography at High Security Levels, IACR ePrint Archive, 2005/076 (2005), http://eprint.iacr.org/2005/076

  34. Menezes, A., Okamoto, T., Vanstone, S.: Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field. IEEE Transactions on Information Theory 39, 1639–1646 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  35. Miller, V.: The Weil Pairing, and its Efficient Calculation. Journal of Cryptology 17(4) (2004)

    Google Scholar 

  36. Miyaji, A., Nakabayashi, M., Takano, S.: New Explicit Conditions of Elliptic Curve Traces for FR-reduction. IEICE Trans. Fundamentals, E84-A(5) (2001)

    Google Scholar 

  37. Okamoto, T.: Efficient Blind and Partially Blind Signatures Without Random Oracles. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 80–99. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  38. Sakai, R., Kasahara, M.: ID Based Cryptosystems with Pairing on Elliptic Curve, IACR ePrint Archive, 2003/054 (2003), http://eprint.iacr.org/2003/054

  39. Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems Based on Pairings. In: Symposium on Cryptography and Information Security, SCIS 2000, Japan (2000)

    Google Scholar 

  40. 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 

  41. Verheul, E.: Self-Blindable Credential Certificates from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 533–551. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  42. Waters, B.: Efficient Identity-Based Encryption Without Random Oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005), www.eprint.iacr.org/2004/180

    Chapter  Google Scholar 

  43. Zhang, F., Chen, X., Susilo, W., Mu, Y.: A New Short Signature Scheme Without Random Oracles from Bilinear Pairings, IACR ePrint Archive, 2005/386 (2005), http://eprint.iacr.org/2005/386

Download references

Author information

Authors and Affiliations

  1. NTT Laboratories, Nippon Telegraph and Telephone Corporation, 1-1 Hikarino-oka, Yokosuka, 239-0847, Japan

    Tatsuaki Okamoto

Authors
  1. Tatsuaki Okamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Département d’Informatique, École Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 05, France

    Phong Q. Nguyen

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Okamoto, T. (2006). On Pairing-Based Cryptosystems. In: Nguyen, P.Q. (eds) Progress in Cryptology - VIETCRYPT 2006. VIETCRYPT 2006. Lecture Notes in Computer Science, vol 4341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11958239_4

Download citation

  • DOI: https://doi.org/10.1007/11958239_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68799-3

  • Online ISBN: 978-3-540-68800-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation