Abstract
In this paper, we present a new public key encryption scheme which is proven chosen-ciphertext (CCA) secure under the decisional Diffie-Hellman (DDH) assumption. The main motivation behind this scheme is to clarify the essential mechanism for yielding CCA-security from the DDH assumption. The structure and security proof of our scheme is simple, and it is likely that even non-experts can immediately understand them with ease. We consider that our scheme is helpful for convincing a wide range of users (including developers and students who are just starting to study CCA-secure encryption) how the Cramer-Shoup cryptosystem and its variants work.
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References
Abe, M., Gennaro, R., Kurosawa, K., Shoup, V.: Tag-KEM/DEM: a new framework for hybrid encryption and a new analysis of Kurosawa-Desmedt KEM. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 128–146. Springer, Heidelberg (2005)
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., Shparlinski, I.: 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., Hofheinz, D., Kiltz, E.: A twist on the Naor-Yung paradigm and its application to efficient CCA-secure encryption from hard search problems. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 146–164. Springer, Heidelberg (2010)
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)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: Proc. of STOC 1991, pp. 542–552 (1991)
Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: Proc. of STOC 1989, pp. 25–32 (1989)
Hanaoka, G., Imai, H., Ogawa, K., Watanabe, H.: Chosen ciphertext secure public key encryption with a simple structure. In: Matsuura, K., Fujisaki, E. (eds.) IWSEC 2008. LNCS, vol. 5312, pp. 20–33. Springer, Heidelberg (2008)
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)
Hofheinz, D., Kiltz, E.: Secure hybrid encryption from weakened key encapsulation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 553–571. Springer, Heidelberg (2007)
Kurosawa, K., Desmed, Y.: A new paradigm of hybrid encryption scheme. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 426–442. Springer, Heidelberg (2004)
Kiltz, E., Mohassel, P., O’Neill, A.: Adaptive trapdoor functions and chosen-ciphertext security. In: Eurocrypt 2010. LNCS, vol. 6110, pp. 673–692. Springer, Heidelberg (2010)
Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput. 17(2), 373–386 (1988)
Myers, S., Shelat, A.: Bit encryption is complete. In: Proc. of FOCS 2009, pp. 607–616 (2009)
Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Proc. of STOC 1990, pp. 427–437 (1990)
Okamoto, T., Pointcheval, D.: The gap-problems: a new class of problems for the security of cryptographic schemes. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 104–118. Springer, Heidelberg (2001)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Proc. of STOC 2008, pp. 187–196 (2008)
Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)
Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)
Shoup, V.: Using hash functions as a hedge against chosen ciphertext attack. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 275–288. Springer, Heidelberg (2000)
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Yamada, S., Hanaoka, G., Kunihiro, N. (2010). Toward an Easy-to-Understand Structure for Achieving Chosen Ciphertext Security from the Decisional Diffie-Hellman Assumption. In: Heng, SH., Kurosawa, K. (eds) Provable Security. ProvSec 2010. Lecture Notes in Computer Science, vol 6402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16280-0_16
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DOI: https://doi.org/10.1007/978-3-642-16280-0_16
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