In practical applications, the forward security and public verifiability are very important to cryptography. An authenticated signcryption without using Hash and Redundancy functions is analyzed in this paper, and the result indicates that the scheme does not possess the characters of forward security and public verifiability. Modified schemes are proposed respectively according to each character mentioned above, and theoretically proved. By adopting the modified schemes, the original scheme's defects of non- forward-security or non-public-verifiability are overcome, and the computational cost and communication overhead are not increased.