A new convertible group signature scheme on the basis of dual complexities

The development of digital signature provides a new field for cryptology. Chaum and van Heyet apply digital signature to group signature. The research of group digital signature is booming because group digital signature fits e-commerce very well. Although some literature has strong theoretical rationale, criticism cannot be waived because a good digital signature has to pass some rigid thresholds as follows: anonymity, unlinkability, protection, and trace-ability. Lately, Chen and Liu make use of zero knowledge and focus on faster computation time than does Camenisch. However, the development of Chen and Liu is on the basis of the Lucas cryptosystem suffering from the questioning by Bleichenbacher because the Lucas cryptosystem has the Laih's fold problem. This paper is to advance a new group digital signature scheme that can be free from the problem implicit in the Lucas cryptosystem by improving the Chen and Liu scheme. The new crypto scheme we provide in this paper is not only protected by dual complexities which can be safer while under a situation of being invaded but also possessed with the advantage of faster computation.