Cryptanalysis and fixed of short signature scheme without random oracle from bilinear parings

We first analyze the security of a short signature scheme without random oracles called ZCSM scheme and point out that it cannot support unforgeable under the chosen message and public key attacks. We also propose a new signature scheme without random oracle using bilinear pairing that is existentially unforgeable under a chosen message attack. The security of the proposed scheme de-pends on a complexity assumption called the k+1 square roots inverse assumption. The proposed scheme has the same signature length with the previous short signature scheme where it fixes the ZCSM scheme's deficiency.