ID-based online/offline signature from pairings

Even, Goldreich and Micali introduced the notion of online/offline signature in 1989. Their scheme splits the signature generation algorithm into two phases: the offline and the online phases. Before the actual message is ready, the signing algorithm runs the offline phase which performs most of the computations. Once the signing message is available, the signing algorithm executes the online phase and produces the final signature with little costs. The goal of this type of schemes is to reduce the time signature generation preprocessing. Online/offline signatures are useful in settings where signatures need to be produced with few operations, either when the device performing the signature is not computationally powerful. This method can be applied to online transactions in e-commerce. One could pre-compute the offline phase´s operations when the banks sent their customers financial bank cards with chip. Then, we use the online procedure to complete an electronic transaction. We utilize ID-based bilinear pairing to propose an efficient online/offline signature. The security of our scheme is related to the computational Diffie-Hellman assumption in the random oracle model. Our schemes have extremely low computation cost so are particularly suitable for devices with limited computing capabilities such as smart cards or mobile devices.