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.