New Compact CCA Secure Elgamal Scheme in the Random Oracle Model

Chosen ciphertext security (CCA security) is a very important security notion for public key encryption. Until now, there are numerous ways to construct CCA secure public key encryption (PKE) or key encapsulation mechanism (KEM) schemes. In this paper, we propose a new CCA secure Elgmal scheme, which is proved secure in the random oracle based on the CDH assumption, has almost no additional overhead compared with the traditional IND-CPA secure Elgamal scheme, except one more modular exponentiation for the decryption. To the best of our knowledge, this is the first scheme which runs almost like the basic Elgsmal scheme but with CCA security.