A note on the security proof of yet another forward secure signature from bilinear pairings

In the 8th Annual International Conference on Information Security and Cryptology, D. L. Vo and K. Kim proposed yet another forward secure signature from bilinear pairings. They claimed that their signature allows unlimited times of key update and is provably forward secure assuming CDH problem is hard. In this paper, we point out the security analysis of this scheme is not correct. Therefore, their scheme couldn´t achieve the unlimited key update ability they claimed under the condition of provable security. Assuming that the proof of forward security is right in their scheme, we can give the improved theorem and its proof.