A new type of authenticated encryption schemes is proposed.It first combines signature with message recovery schemes and symmetric encryption schemes together.This type of schemes has the following two characteristics:the commitment value of the signature is only recoverable by an intended receiver

so the value also can be used as a shared symmetric key of symmetric encryption and acts as "two birds one stone".The validity of the received message is verified by comparing the recovered message from the signature with the decrypted message instead of using Hash or Redundancy functions in traditional method.Therefore

the proposed scheme is an authenticated encryption without using Hash functions or Redundancy functions.