Abstract
IND-CCA secure public key encryption schemes based on the CDH assumption in the standard model use a hardcore function as a key derivation function for a shared key. Therefore, many secret and public key size are necessary for sending a sufficiently long shared key. Yamada et al. [17,16] and Haralambiev et al. [12] proposed efficient public key encryption schemes based on the CDH assumption. Moreover, they proposed a method that drastically reduces the secret and the public key sizes by using a bilinear map, and they also proposed IND-CCA secure public key encryption based on the bilinear DH assumption. Unfortunately, many secret and public key sizes are still necessary in general cyclic groups that lack known efficient bilinear map.
In this paper, we propose a compact public key scheme based on the CDH assumption in the standard model. The public and secret key sizes are trivially reduced by sending several block of the ciphertext. By using batch verification, our scheme succeeded in reducing the ciphertext size compared with that in the case of the trivially extended scheme. To prove IND-CCA security of our scheme, we define a new computational assumption, namely, the extended hashed strong twin Diffie-Hellman assumption. Moreover, we construct an extended trapdoor test to simulate a decisional oracle, and prove that if the CDH assumption holds and the hash function is the hardcore function for DH key, then the extended hashed strong twin DH assumption also holds. Our reducing technique is also applicable to other schemes [17,16,15] based on the CDH assumption.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bellare, M., Garay, J.A., Rabin, T.: Fast batch verification for modular exponentiation and digital signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)
Boneh, D.: The decision Diffie-Hellman problem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 48–63. Springer, Heidelberg (1998)
Boneh, D., Shparlinski, I.E.: On the unpredictability of bits of the elliptic curve Diffie–Hellman scheme. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 201–212. Springer, Heidelberg (2001)
Boneh, D., Venkatesan, R.: Hardness of computing the most significant bits of secret keys in Diffie-Hellman and related schemes. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 129–142. 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)
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.: 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)
Fiat, A.: Batch RSA. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 175–185. Springer, Heidelberg (1990)
Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: STOC, pp. 25–32 (1989)
Hanaoka, G., Kurosawa, K.: Efficient chosen ciphertext secure public key encryption under the computational Diffie-Hellman assumption. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 308–325. Springer, Heidelberg (2008)
Haralambiev, K., Jager, T., Kiltz, E., Shoup, V.: Simple and efficient public-key encryption from computational Diffie-Hellman in the standard model. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 1–18. Springer, Heidelberg (2010)
Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)
Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004), http://eprint.iacr.org/
Wee, H.: Efficient chosen-ciphertext security via extractable hash proofs. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 314–332. Springer, Heidelberg (2010)
Yamada, S., Kawai, Y., Hanaoka, G., Kunihiro, N.: Public key encryption schemes from the (B)CDH assumption with better efficiency. IEICE Transactions 93-A(11), 1984–1993 (2010)
Yamada, S., Kawai, Y., Hanaoka, G., Kunihiro, N.: Public key encryption schemes from the (B)CDH assumption with shorter keys. In: SCIS 2010, 1A1-5 (2010) (in Japanese)
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
Hanatani, Y., Muratani, H., Yonemura, T. (2011). Toward Compact Public Key Encryption Based on CDH Assumption via Extended Twin DH Assumption. In: Boyen, X., Chen, X. (eds) Provable Security. ProvSec 2011. Lecture Notes in Computer Science, vol 6980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24316-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-24316-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24315-8
Online ISBN: 978-3-642-24316-5
eBook Packages: Computer ScienceComputer Science (R0)