As a typical fast public key cryptosystem, HCC (Hyper-elliptic Curves Cryptosystem) provides efficient asymmetric algorithms for cryptography schemes. In the paper, we presented an improved authenticated encryption scheme based on HCC as a prototype of signcryption scheme. In the scheme, data encryption and signature generation can be achieved in a single formula and signature verifying protocol is also the decryption algorithm. Therefore, the scheme achieves secret message transmission and authentication simultaneously in one protocol. The scheme renders effective secrecy protection for message receiver; the attack on the authenticated signature and random parameters via the cipher-text is computationally infeasible. The designing strategy of message recovery signature reinforces the security and reliability of authenticated encryption and greatly improves its efficiency for software and hardware application. As a generalization of the authenticated encryption scheme, we presented a signcryption scheme based on HCC. The scheme makes full use of the superiority of fast asymmetric cryptosystem and effectively improves the application efficiency of signcryption for integrated environment.