Method of constructing elliptic curve authenticated encryption scheme

An elliptic curve authenticated encryption scheme with message recovery is proposed and its security is also analyzed. In accordance with this scheme, the more general signature equation of the proposed scheme is presented. Accordingly, the method of constructing elliptic curve authenticated encryption scheme is described, including the method of choosing the parameters of signature equation. Then the two forgery attacks with known plaintext is discussed respectively. The results indicate that some schemes can resist the imitating attacks and some cannot.