Skip to main content
SpringerLink
Log in

On the relations between non-interactive key distribution, identity-based encryption and trapdoor discrete log groups

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

This paper investigates the relationships between identity-based non-interactive key distribution (ID-NIKD) and identity-based encryption (IBE). It provides a new security model for ID-NIKD, and a construction that converts a secure ID-NIKD scheme satisfying certain conditions into a secure IBE scheme. This conversion is used to explain the relationship between the ID-NIKD scheme of Sakai, Ohgishi and Kasahara and the IBE scheme of Boneh and Franklin. The paper then explores the construction of ID-NIKD and IBE schemes from general trapdoor discrete log groups. Two different concrete instantiations for such groups provide new, provably secure ID-NIKD and IBE schemes. These schemes are suited to applications in which the Trusted Authority is computationally well-resourced, but clients performing encryption/decryption are highly constrained.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balfanz D., Durfee G., Shankar N., Smetters D., Staddon J., Wong H.-C.: Secret handshakes from pairing-based key agreements. In: Proceedings of the 2003 IEEE Symposium on Security and Privacy, pp. 180–196. IEEE Computer Society Press (2003).

  2. Bellare M., Rogaway P.: Entity authentication and key distribution. In: Stinson D.R. (ed.) CRYPTO’93, LNCS 773, pp. 232–249. Springer-Verlag (1994).

  3. Bellare M., Canetti R., Krawczyk H.: A modular approach to the design and analysis of authentication and key exchange protocols. In: 30th STOC, pp. 419–428. ACM Press (1998).

  4. Bentahar K., Farshim P., Malone-Lee J., Smart N.P.: Generic constructions of identity-based and certificateless KEMs. J. Cryptol. 21(2), 178–199 (2008).

    Article  MATH  Google Scholar 

  5. Blake-Wilson S., Johnson D., Menezes A.: Key agreement protocols and their security analysis. In: Darnell M. (ed.) Cryptography and Coding, 6th IMA International Conference, LNCS 1355, pp. 30–45. Springer-Verlag (1997).

  6. Boneh D., Franklin M.: Identity-based encryption from the Weil pairing. In: Kilian J. (ed.) CRYPTO 2001, LNCS 2139, pp. 213–229. Springer-Verlag (2001).

  7. Boneh D., Gentry C., Hamburg M.: Space-efficient identity based encryption without pairings. In: 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2007), pp. 647–657. IEEE Computer Society (2007). Full version available at Cryptology ePrint Archive, Report 2007/177. http://eprint.iacr.org/.

  8. Boyd C., Mao W., Paterson K.G.: Key agreement using statically keyed authenticators. In: Jakobsson M., et al. (eds.) ACNS 2004, LNCS 3089, pp. 248–262. Springer-Verlag (2004).

  9. Canetti R., Krawczyk H.: Analysis of key-exchange protocols and their use for building secure channels. In: Pfitzmann B. (ed.) EUROCRYPT 2001, LNCS 2045, pp. 453–474. Springer-Verlag (2001).

  10. Cavallar S., Dodson B., Lenstra A.K., Lioen W.M., Montgomery P.L., Murphy B., te Riele H., Aardal K., Gilchrist J., Guillerm G., Leyland P.C., Marchand J., Morain F., Muffett A., Putnam C., Putnam C., Zimmermann P.: Factorization of a 512-Bit RSA modulus. In: Preneel B. (ed.) EUROCRYPT 2000, LNCS 1807, pp. 1–18. Springer-Verlag (2000).

  11. Cocks C.: An identity based encryption scheme based on quadratic residues. In: Honary B. (ed.) Cryptography and Coding, 8th IMA International Conference, LNCS 2260, pp. 360–363. Springer-Verlag (2001).

  12. Dent A.W., Galbraith S.D.: Hidden pairings and trapdoor DDH groups. In: Hess F., Pauli S., Pohst M. (eds.) Algorithmic Number Theory: 7th International Symposium (ANTS VII), LNCS 4076, pp. 436–451. Springer-Verlag (2006).

  13. Dupont R., Enge A.: Provably secure non-interactive key distribution based on pairings. Discrete Appl. Math. 154(2), 270–276 (2006). See also cryptology ePrint archive, report 2002/136 (2002). http://eprint.iacr.org/.

  14. Galbraith S., Hess F., Smart N.P.: Extending the GHS Weil descent attack. In: Knudsen L. (ed.) EUROCRYPT 2002, LNCS 2332, pp. 29–44. Springer-Verlag (2002).

  15. Galbraith S.D., Paterson K.G., Smart N.P.: Pairings for cryptographers. Discrete Appl. Math. 156, 3113–3121 (2008). Available from cryptology ePrint archive: report 2006/165 (2006). http://eprint.iacr.org/.

  16. Gentry C., Peikert C., Vaikuntanathan V.: Trapdoors for hard lattices and new cryptographic constructions. In: Ladner R.E., Dwork C. (eds.) Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 197–206, ACM (2008). Full version available from cryptology ePrint archive: report 2007/432 (2007). http://eprint.iacr.org/.

  17. Gordon D.M.: Designing and detecting trapdoors for discrete log cryptosystems. In: Brickell E.F. (ed.) CRYPTO’92, LNCS 740, pp. 66–75. Springer-Verlag (1993).

  18. Heng S.-H., Kurosawa K.: k-resilient identity-based encryption in the standard model. In: Okamoto T. (ed.) CT-RSA 2004, LNCS 2964, pp. 67–80. Springer-Verlag (2004).

  19. Hühnlein D., Jacobson Jr. M.J., Weber D.: Towards practical non-interactive public-key cryptosystems using non-maximal imaginary quadratic orders. Des. Codes Cryptogr. 39(3), 281–299 (2003).

    Article  Google Scholar 

  20. Kitagawa T., Yang P., Hanaoka G., Zhang R., Watanabe H., Matsuura K., Imai H.: Generic transforms to acquire CCA-security for identity based encryption: the cases of FOpkc and REACT. In: Batten L.M., Safavi-Naini R. (eds.) ACISP 2006, LNCS 4058, pp. 348–359. Springer-Verlag (2006).

  21. Kügler D., Maurer M.: A Note on the Weakness of the Maurer-Yacobi Squaring Method. Technical Report TI-15/99. Department of Computer Science, Technical University of Darmstadt, Darmstadt, Germany (1999).

  22. Kunihiro N., Abe W., Ohta K.: Maurer-Yacobi ID-based key distribution revisited. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 89(5), 1421–1424 (2006).

    Google Scholar 

  23. Lee W.-B., Liao K.-C.: Constructing identity-based cryptosystems for discrete logarithm based cryptosystems. J. Netw. Comput. Appl. 27, 191–199 (2004).

    Article  Google Scholar 

  24. Lim C.H., Lee P.J.: Modified Maurer-Yacobi’s scheme and its applications. In: Seberry J., Zheng Y. (eds.) ASIACRYPT92, LNCS 718, pp. 308–323. Springer-Verlag (1992).

  25. Maurer U., Yacobi Y.: Non-interactive public-key cryptography. In: Davies D.W. (ed.) EUROCRYPT91, LNCS 547, pp. 498–507. Springer-Verlag (1991).

  26. Maurer U., Yacobi Y.: A remark on a non-interactive public-key distribution system. In: Rueppel R.A. (ed.) EUROCRYPT92, LNCS 658, pp. 458–460. Springer-Verlag (1993).

  27. Maurer U.M., Yacobi Y.: A non-interactive public-key distribution system. Des. Codes Cryptogr. 9(3), 305–316 (1996).

    MATH  MathSciNet  Google Scholar 

  28. Menezes A.J., van Oorschot P.C., Vanstone S.A.: Handbook of Applied Cryptography. CRC Press (1997).

  29. Murakami Y., Kasahara M.: Murakami-Kasahara ID-based key sharing scheme revisited—in comparison with Maurer-Yacobi schemes. Cryptology ePrint archive, report 2005/306 (2005). http://eprint.iacr.org/.

  30. Okamoto T., Uchiyama S.: Security of an identity-based cryptosystem and the related reductions. In: Nyberg K. (ed.) EUROCRYPT98, LNCS 1403, pp. 546–560. Springer-Verlag (1998).

  31. Paillier P.: Public-key cryptosystems based on composite-degree residuosity. In: Stern J. (ed.) EUROCRYPT99, LNCS 1592, pp. 223–238. Springer-Verlag (1999).

  32. Rivest R.: Controlled algebras and GIIs. Talk given at IPAM Workshop on “Securing Cyberspace: Applications and Foundations of Cryptography and Computer Security”, October (2006). Available from http://www.ipam.ucla.edu/publications/scws1/scws1_6243.ppt.

  33. Sakai R., Ohgishi K., Kasahara M.: Cryptosystems based on pairing. In: The 2000 Symposium on Cryptography and Information Security, Okinawa, Japan, January, pp. 26–28 (2000).

  34. Sakai R., Ohgishi K., Kasahara M.: Cryptosystems based on pairing over elliptic curve.In: 2001 Symposium on Cryptography and Information Security (SCIS2001), January (2001).

  35. Shamir A.: Identity-based cryptosystems and signature schemes. In: Blakley G.R., Chaum D. (eds.) CRYPTO84, LNCS 196, pp. 47–53. Springer-Verlag (1985).

  36. Teske E.: An elliptic curve trapdoor system. J. Cryptol. 19(1), 115–133 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  37. Tseng Y.-M., Jan J.-K.: ID-based cryptographic schemes using a non-interactive public-key distribution system. In: ACSAC 1998, pp. 237–243. IEEE Computer Society (1998).

  38. Yang P., Kitagawa T., Hanaoka G., Zhang R., Matsuura K., Imai H.: Applying Fujisaki-Okamoto to identity-based encryption. In: Fossorier M., et al. (eds.) AAECC 2006, LNCS 3857, pp. 183–192. Springer- Verlag (2006).

Download references

Author information

Authors and Affiliations

  1. Information Security Group, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    Kenneth G. Paterson & Sriramkrishnan Srinivasan

Authors
  1. Kenneth G. Paterson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sriramkrishnan Srinivasan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kenneth G. Paterson.

Additional information

Communicated by S. Galbraith.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paterson, K.G., Srinivasan, S. On the relations between non-interactive key distribution, identity-based encryption and trapdoor discrete log groups. Des. Codes Cryptogr. 52, 219–241 (2009). https://doi.org/10.1007/s10623-009-9278-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-009-9278-y

Keywords

Mathematics Subject Classification (2000)

Search

Navigation