Although employing blockchain in supply chain management (SCM) can provide benefits in numerous aspects such as traceability, transparency, and more, using public blockchain for SCM may compromise the privacy of the supply chain participants and their business secrets. In this paper, we review recent papers that integrate blockchain with SCM and the papers that propose privacy-preserving approaches for public blockchain. Then, we identify the problem in the existing solutions. Additionally, we present an outline of a framework that enables entities in a supply chain to upload their data records anonymously. This framework preserves unlinkability when transferring product ownership. The proposed scheme allows data auditors, who can be the end customers of a supply chain, to access a product's history and verify the authenticity of the data while preserving the privacy of the data uploader. We demonstrate that supply chain data records follow a directed acyclic graph (DAG), similar to the data structure that maintains data records in version control systems (VCS). Hence, this insight could make the framework applicable for anonymous version control systems based on blockchain.