Attribute-based signature (ABS), which enables users sign messages with any predicate of their attributes issued from an attribute authority, is useful in many important applications such as anonymous authentication and attribute-based messaging systems. However, the signature computational costs scale with the complexity of the predicate has attested to the message, which makes signature a possible bottleneck for some applications. To address this problem, we propose a new on/offline scheme for ABS that splits the computation for these algorithms into two phases: a preparation phase that does the vast majority of the work to sign a message before it knows the message and the predicate has attested to the message. The second phase can then rapidly assemble an ABS signature when the specifics become known. We note that unknown message and predicate make ABS significantly more challenging. This scheme is especially suitable for resource constrained environment. When the resource is ample, we can do the offline phase. And when it is limited, online phase can be done rapidly without much resource.