Abstract
This paper proposes a new generalized ElGamal public key encryption scheme based on a new Diffie-Hellman problem, so-called EDDH problem, which DDH problem can be reduced to. This scheme is one-way if and only if ECDH assumption holds and it is semantically secure in the standard model if and only if EDDH assumption holds. Since EDDH assumption still holds for generic bilinear groups, this encryption scheme adds to the growing toolkit of provable security primitives that can be used by the protocol designer looking to build complex secure systems with a sound basis.
Project supported by the nature science foundation of China (No. 60573043; 60773175; 60773003).
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References
Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Brands, S.: An efficient off-line electronic cash system based on the representation problem. CWI Technical Report, CS-R9323 (1993)
Cramer, R., Shoup, V.: Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack. SIAM J. of Computing 33, 167–226 (2003)
Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inform. Theory 22(6), 644–654 (1976)
ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans. Inform. Theory 31(4), 469–472 (1985)
Fujisaki, E., Okamoto, T.: How to enhance the security of public-key encryption at minimum cost. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol. 1560, pp. 53–68. Springer, Heidelberg (1999)
Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)
Joux, A., Nguyen, K.: Separating Decision Diffie-Hellman from Diffie-Hellman in cryptographic groups. J. Cryptology 16(4), 239–247 (2003)
Lidl, R., Niederreiter, H.: Introduction to finite fields and their applications. Cambridge University Press, Cambridge (1986)
Maze, G., Monico, C., Rosenthal, J.: A public key cryptosystem based on actions by semigroups. In: Proceedings of the 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, p. 484 (2002)
Maze, G., Monico, C., Rosenthal, J.: Public key cryptography based on simple modules over simple rings. In: Proceedings of the 2002 Mathematical Theory of Networks and System, pp. 8–16. University of Notre Dame, Notre Dame (2002)
Menezes, A.J., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press Series on Discrete Mathematics and its Applications. CRC Press, Boca Raton (1997)
Schacham, H.: A Cramer-Shoup encryption scheme from the linear assumption and from progressively weaker linear variants, http://eprint.iacr.org/2007/074.pdf
Shoup, V.: Lower bounds for discrete logarithms and related problems. In: McCurley, K.S., Ziegler, C.D. (eds.) Advances in Cryptology 1981 - 1997. LNCS, vol. 1440, pp. 256–266. Springer, Heidelberg (1999)
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Huang, H., Yang, B., Zhu, S., Xiao, G. (2008). Generalized ElGamal Public Key Cryptosystem Based on a New Diffie-Hellman Problem. In: Baek, J., Bao, F., Chen, K., Lai, X. (eds) Provable Security. ProvSec 2008. Lecture Notes in Computer Science, vol 5324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88733-1_1
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DOI: https://doi.org/10.1007/978-3-540-88733-1_1
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