Cryptanalysis and Improvement of HIBS without Random Oracle

At Eurocrypt´02, Horwitz and Lynn first introduced the concept of HIBS. Till now, many HIBS schemes have been proposed. Recently (2011), Yang et al.´s proposed a hierarchical identity based signature (HIBS) scheme based on computational Diffie-Hellman (CDH) assumption in the standard model. They claimed that their scheme has more secure and more efficient than the existing HIBS schemes. However, we give an attack to their scheme to show that their scheme is insecure and an attacker can forge private key for any identity. And we also propose an improvement method.