ID-based cryptosystems (IBCs) allow the use of publicly identifiable information in public encryption keys, which reduces the overhead of certificate management and eliminates the need for a certificate authority in the public-key infrastructure. Up to now, bilinear pairing technology is usually used in ID-based paradigms. However, it is expensive in computation time and is unsuitable for mobile networks. Over recent years, the evolution of mobile devices has seen them transformed from a voice communication device to a daily life information ...