Abstract
Non-interactive key exchange (NIKE) is a fundamental but much-overlooked cryptographic primitive. It appears as a major contribution in the ground-breaking paper of Diffie and Hellman, but NIKE has remained largely unstudied since then. In this paper, we provide different security models for this primitive and explore the relationships between them. We then give constructions for secure NIKE in the Random Oracle Model based on the hardness of factoring and in the standard model based on the hardness of a variant of the decisional Bilinear Diffie Hellman Problem for asymmetric pairings. We also study the relationship between NIKE and public key encryption (PKE), showing that a secure NIKE scheme can be generically converted into an IND-CCA secure PKE scheme. Our conversion also illustrates the fundamental nature of NIKE in public key cryptography.
Chapter PDF
Similar content being viewed by others
References
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory 22(6), 644–654 (1976)
Çapar, Ç., Goeckel, D., Paterson, K.G., Quaglia, E.A., Towsley, D., Zafer, M.: Signal-flow-based analysis of wireless security protocols. Information and Computation (to appear)
Dodis, Y., Katz, J., Smith, A., Walfish, S.: Composability and On-Line Deniability of Authentication. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 146–162. Springer, Heidelberg (2009)
Boyd, C., Mao, W., Paterson, K.G.: Key Agreement Using Statically Keyed Authenticators. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 248–262. Springer, Heidelberg (2004)
Jakobsson, M., Sako, K., Impagliazzo, R.: Designated Verifier Proofs and Their Applications. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 143–154. Springer, Heidelberg (1996)
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)
Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: The 2000 Symposium on Cryptography and Information Security, pp. 26–28 (2000)
Dupont, R., Enge, A.: Provably secure non-interactive key distribution based on pairings. Discrete Applied Mathematics 154(2), 270–276 (2006)
Gennaro, R., Halevi, S., Krawczyk, H., Rabin, T., Reidt, S., Wolthusen, S.D.: Strongly-Resilient and Non-interactive Hierarchical Key-Agreement in MANETs. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 49–65. Springer, Heidelberg (2008)
Paterson, K.G., Srinivasan, S.: On the relations between non-interactive key distribution, identity-based encryption and trapdoor discrete log groups. Des. Codes Cryptography 52(2), 219–241 (2009)
Bellare, M., Rogaway, P.: Entity Authentication and Key Distribution. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 232–249. Springer, Heidelberg (1994)
Shoup, V.: On formal models for secure key exchange (version 4) (1999)
Bellare, M., Pointcheval, D., Rogaway, P.: Authenticated Key Exchange Secure against Dictionary Attacks. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 139–155. Springer, Heidelberg (2000)
Canetti, R., Krawczyk, H.: Analysis of Key-Exchange Protocols and Their Use for Building Secure Channels. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 453–474. Springer, Heidelberg (2001)
Krawczyk, H.: HMQV: A High-Performance Secure Diffie-Hellman Protocol. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 546–566. Springer, Heidelberg (2005)
Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma. In: Juels, A., Wright, R.N., di Vimercati, S.D.C. (eds.) ACM Conference on Computer and Communications Security, pp. 390–399. ACM (2006)
Ristenpart, T., Yilek, S.: The Power of Proofs-of-Possession: Securing Multiparty Signatures against Rogue-Key Attacks. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 228–245. Springer, Heidelberg (2007)
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)
Lu, S., Ostrovsky, R., Sahai, A., Shacham, H., Waters, B.: Sequential Aggregate Signatures and Multisignatures Without Random Oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 465–485. Springer, Heidelberg (2006)
Hofheinz, D., Kiltz, E.: The Group of Signed Quadratic Residues and Applications. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 637–653. Springer, Heidelberg (2009)
Hofheinz, D., Jager, T., Kiltz, E.: Short Signatures from Weaker Assumptions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 647–666. Springer, Heidelberg (2011)
Krawczyk, H., Rabin, T.: Chameleon signatures. In: NDSS (2000)
Chatterjee, S., Sarkar, P.: Generalization of the Selective-ID Security Model for HIBE Protocols. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 241–256. Springer, Heidelberg (2006)
ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory 31(4), 469–472 (1985)
Freire, E.S.V., Hofheinz, D., Kiltz, E., Paterson, K.G.: Non-interactive key exchange. Cryptology ePrint Archive, Report 2012/xxx (2012), http://eprint.iacr.org/
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM Journal on Computing 18(1), 186–208 (1989)
Fischlin, R., Schnorr, C.P.: Stronger security proofs for RSA and Rabin bits. Journal of Cryptology 13(2), 221–244 (2000)
Hofheinz, D., Kiltz, E.: Practical Chosen Ciphertext Secure Encryption from Factoring. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 313–332. Springer, Heidelberg (2009)
Galindo, D.: Boneh-Franklin Identity Based Encryption Revisited. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 791–802. Springer, Heidelberg (2005)
Barreto, P.S.L.M., Naehrig, M.: Pairing-Friendly Elliptic Curves of Prime Order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol. 3897, pp. 319–331. Springer, Heidelberg (2006)
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 (2003)
Joux, A.: A One Round Protocol for Tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 International Association for Cryptologic Research
About this paper
Cite this paper
Freire, E.S.V., Hofheinz, D., Kiltz, E., Paterson, K.G. (2013). Non-Interactive Key Exchange. In: Kurosawa, K., Hanaoka, G. (eds) Public-Key Cryptography – PKC 2013. PKC 2013. Lecture Notes in Computer Science, vol 7778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36362-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-36362-7_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36361-0
Online ISBN: 978-3-642-36362-7
eBook Packages: Computer ScienceComputer Science (R0)