| Abstract: | Design of secure and efficient public‐key encryption schemes under weaker computational assumptions has been regarded as an important and challenging task. As far as ElGamal‐type encryption schemes are concerned, some variants of the original ElGamal encryption scheme based on weaker computational assumption have been proposed: Although security of the ElGamal variant of Fujisaki‐Okamoto public‐key encryption scheme and Cramer and Shoup's encryption scheme is based on the Decisional Diffie‐Hellman Assumption (DDH‐A), security of the recent Pointcheval's ElGamal encryption variant is based on the Computational Diffie‐Hellman Assumption (CDH‐A), which is known to be weaker than DDH‐A. In this paper, we propose new ElGamal encryption variants whose security is based on CDH‐A and the Elliptic Curve Computational Diffie‐Hellman Assumption (EC‐CDH‐A). Also, we show that the proposed variants are secure against the adaptive chosen‐ciphertext attack in the random oracle model. An important feature of the proposed variants is length‐efficiency which provides shorter ciphertexts than those of other schemes. |
