Abstract
We propose a new computational problem and call it the twin bilinear Diffie-Hellman inversion (BDHI) problem. Inspired by the technique proposed by Cash, Kiltz and Shoup, we have developed a new trapdoor test which enables us to prove that the twin BDHI problem is at least as hard as the ordinary BDHI problem even in the presence of a decision oracle that recognizes a solution to the problem. The relation between the two problems implies that many of the cryptographic constructions based on ordinary BDHI problem can be improved with a tighter security reduction. As one such application, we present a new variant of Sakai-Kasahara Identity-Based Encryption (SK-IBE) with a simple and efficient security proof in the random oracle model, under the computational BDHI problem. We also present a new Identity-Based Key Encapsulation Mechanism (ID-KEM) based on SK-IBE, which has a better security analysis than previous results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abdalla, M., Bellare, M., Rogaway, P.: The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 143–158. Springer, Heidelberg (2001)
Barreto, P.S.L.M., Libert, B., McCullagh, N., Quisquater, J.-J.: Efficient and provably-secure identity-based signatures and signcryption from bilinear maps. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 515–532. Springer, Heidelberg (2005)
Bellare, M., Ristenpart, T.: Simulation without the Artificial Abort: Simplified Proof and Improved Concrete Security for Waters’ IBE Scheme. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 407–424. Springer, Heidelberg (2009)
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)
Bentahar, K., Farshim, P., Malone-Lee, J., Smart, N.P.: Generic Constructions of Identity-Based and Certificateless KEMs. Cryptology ePrint Archive, Report 2005/058 (2005), http://eprint.iacr.org/
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)
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)
Boneh, D., Franklin, M.K.: Identity-Based Encryption from theWeil Pairing. SIAM Journal on Computation 32, 586–615 (2003)
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)
Cash, D., Kiltz, E., Shoup, V.: The Twin Diffie-Hellman Problem and Applications. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 127–145. Springer, Heidelberg (2008)
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)
Chen, L., Cheng, Z., Malone-Lee, J., Smart, N.P.: An Efficient ID-KEM Based On The Sakai-Kasahara Key Construction. In: IEE Proceedings of Information Security, pp. 19–26 (2006)
Cheng, Z.: Simple SK-ID-KEM unpublished notes (2005), http://www.cs.mdx.ac.uk/staffpages/m_cheng/link/simple-sk-kem.pdf
Cheng, Z., Chen, L.: On security proof of McCullagh-Barreto’s key agreement protocol and its variants. IJSN 2(3/4), 251–259 (2007)
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)
Cramer, R., Shoup, V.: Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack. SIAM Journal on Computing 33, 167–226 (2001)
Diffie, W., Hellman, M.E.: New Directions in Cryptograpgy. IEEE Transactions on Infomation Theory 22(6), 644–654 (1976)
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)
Gentry, C.: Practical Identity-Based Encryption Without Random Oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445–464. Springer, Heidelberg (2006)
Libert, B., Quisquater, J.J.: Identity based encryption without redundancy. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 285–300. Springer, Heidelberg (2005)
McCullagh, N., Barreto, P.S.L.M.: A New Two-Party Identity-Based Authenticated Key Agreement. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 262–274. Springer, Heidelberg (2005)
Sakai, R., Kasahara, M.: ID based Cryptosystems with Pairing on Elliptic Curve. Cryptology ePrint Archive, Report 2003/054 (2003), http://eprint.iacr.org/
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, Y., Chen, L. (2011). The Twin Bilinear Diffie-Hellman Inversion Problem and Applications. In: Rhee, KH., Nyang, D. (eds) Information Security and Cryptology - ICISC 2010. ICISC 2010. Lecture Notes in Computer Science, vol 6829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24209-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-24209-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24208-3
Online ISBN: 978-3-642-24209-0
eBook Packages: Computer ScienceComputer Science (R0)