Cryptanalysis and Improvement on a Digital Signature Scheme without using One-way Hash and Message Redundancy

Digital signature schemes based on public-key cryptosystems generally permit existential forgery, except the schemes are equipped with some message formatting mechanisms, such as using hash functions or padding redundancies. In 2004, Chang et al. proposed a new digital signature scheme, and claimed the scheme without using any hash function or padding any redundancy can resist forgery attacks. However, many attacks on Chang et al. ´s scheme were presented. Kang et al. also gave an effective improvement to resist these forgery attacks. In this letter, we gave a further improvement to shorten the signed signature. Our improvement keeps the security of Kang et al. ´s scheme and makes it more efficient in computation and communication.