IP traceback plays an important role in cyber investigation processes, where the sources and the traversed paths of packets need to be identified. It has a wide range of applications, including network forensics, security auditing, network fault diagnosis, and performance testing. Despite a plethora of research on IP traceback, the Internet is yet to see a large-scale practical deployment of traceback. Some of the major challenges that still impede an Internet-scale traceback solution are, concern of disclosing Internet Service Provider (ISP's) internal network topologies (in other words, concern of privacy leak), poor incremental deployment, and lack of incentives for ISPs to provide traceback services. In this paper, we argue that cloud services offer better options for the practical deployment of an IP traceback system. We first present a novel cloud-based traceback architecture, which possesses several favorable properties encouraging ISPs to deploy traceback services on their networks. While this makes the traceback service more accessible, regulating access to traceback service in a cloud-based architecture becomes an important issue. Consequently, we address the access control problem in cloud-based traceback. Our design objective is to prevent illegitimate users from requesting traceback information for malicious intentions (such as ISPs topology discovery). To this end, we propose a temporal token-based authentication framework, called FACT, for authenticating traceback service queries. FACT embeds temporal access tokens in traffic flows, and then delivers them to end-hosts in an efficient manner. The proposed solution ensures that the entity requesting for traceback service is an actual recipient of the packets to be traced. Finally, we analyze and validate the proposed design using real-world Internet data sets.