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.
Similar content being viewed by others
References
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).
Bellare M., Rogaway P.: Entity authentication and key distribution. In: Stinson D.R. (ed.) CRYPTO’93, LNCS 773, pp. 232–249. Springer-Verlag (1994).
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).
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).
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).
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).
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/.
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).
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).
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).
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).
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).
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/.
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).
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/.
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/.
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).
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).
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).
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).
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).
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).
Lee W.-B., Liao K.-C.: Constructing identity-based cryptosystems for discrete logarithm based cryptosystems. J. Netw. Comput. Appl. 27, 191–199 (2004).
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).
Maurer U., Yacobi Y.: Non-interactive public-key cryptography. In: Davies D.W. (ed.) EUROCRYPT91, LNCS 547, pp. 498–507. Springer-Verlag (1991).
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).
Maurer U.M., Yacobi Y.: A non-interactive public-key distribution system. Des. Codes Cryptogr. 9(3), 305–316 (1996).
Menezes A.J., van Oorschot P.C., Vanstone S.A.: Handbook of Applied Cryptography. CRC Press (1997).
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/.
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).
Paillier P.: Public-key cryptosystems based on composite-degree residuosity. In: Stern J. (ed.) EUROCRYPT99, LNCS 1592, pp. 223–238. Springer-Verlag (1999).
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.
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).
Sakai R., Ohgishi K., Kasahara M.: Cryptosystems based on pairing over elliptic curve.In: 2001 Symposium on Cryptography and Information Security (SCIS2001), January (2001).
Shamir A.: Identity-based cryptosystems and signature schemes. In: Blakley G.R., Chaum D. (eds.) CRYPTO84, LNCS 196, pp. 47–53. Springer-Verlag (1985).
Teske E.: An elliptic curve trapdoor system. J. Cryptol. 19(1), 115–133 (2006).
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).
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).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by S. Galbraith.
Rights 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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-009-9278-y