Affiliations: Department of Industrial Education and Technology, National Changhua University of Education, No. 1, Jin-De Road, Changhua City, Taiwan, R.O.C., e-mail: tychang@cc.ncue.edu.tw | Department of Computer Science & Information Engineering, Asia University, 1500, Lioufeng Rd., Wufeng, Taichung, Taiwan, R.O.C., e-mail: mshwang@mail.cyut.edu.tw | Department of Information Management, National Dong Hwa University, 1, Sec. 2, Da Hsueh Rd., Shou-Feng, Hualien, Taiwan, R.O.C., e-mail: wpyang@mail.ndhu.edu.tw
Note: [] Corresponding author.
Abstract: Hwang et al. proposed an ElGamal-like scheme for encrypting large messages, which is more efficient than its predecessor in terms of computational complexity and the amount of data transformation. They declared that the resulting scheme is semantically secure against chosen-plaintext attacks under the assumptions that the decision Diffie–Hellman problem is intractable. Later, Wang et al. pointed out that the security level of Hwang et al.'s ElGamal-like scheme is not equivalent to the original ElGamal scheme and brings about the disadvantage of possible unsuccessful decryption. At the same time, they proposed an improvement on Hwang et al.'s ElGamal-like scheme to repair the weakness and reduce the probability of unsuccessful decryption. However, in this paper, we show that their improved scheme is still insecure against chosen-plaintext attacks whether the system is operated in the quadratic residue modulus or not. Furthermore, we propose a new ElGamal-like scheme to withstand the adaptive chosen-ciphertext attacks. The security of the proposed scheme is based solely on the decision Diffie–Hellman problem in the random oracle model.
