Possibility of decryption speed-up by parallel processing in CCA secure hashed ElGamal.

In order to prove the ElGamal CCA(Chosen Ciphertext Attack) security in the random oracle model, it is necessary to use the group where ICDH(Interactive Computational Diffie Hellman) assumption holds. Until now, only bilinear group with complex algebraic structure has been known as the ICDH group. In this paper, we introduce the ICDH group with simple algebraic structure.