The Internet of Production (IoP) envisions the interconnection of previously isolated CPS in the area of manufacturing across institutional boundaries to realize benefits such as increased profit margins and product quality as well as reduced product development costs and time to market. This interconnection of CPS will lead to a plethora of new dataflows, especially between (partially) distrusting entities. In this paper, we identify and illustrate these envisioned inter-organizational dataflows and the participating entities alongside two real-world use cases from the production domain: a fine blanking line and a connected job shop. Our analysis allows us to identify distinct security and privacy demands and challenges for these new dataflows. As a foundation to address the resulting requirements, we provide a survey of promising technical building blocks to secure inter-organizational dataflows in an IoP and propose next steps for future research. Consequently, we move an important step forward to overcome security and privacy concerns as an obstacle for realizing the promised potentials in an Internet of Production.