Signing a digital signature without using one-way hash functions and message redundancy schemes

In 2000, Shieh et al. proposed some multisignature schemes based on a new digital signature scheme to satisfy the special requirements of the mobile system. In these schemes, one-way hash functions and message redundancy schemes are not used. Later, Hwang and Li indicated that Shieh et al.'s digital signature scheme suffers from the forgery attacks. They also claimed that message redundancy schemes should still be used to resist some attacks. In this letter, we show another attack on Shieh et al.'s signature scheme and propose a secure digital signature scheme, where neither one-way hash functions nor message redundancy schemes are employed.