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Technology is being used increasingly for lowering the trust barrier in domains where collaboration and cooperation are necessary, but reliability and efficiency are critical due to high stakes. An example is an industrial marketplace where many suppliers must participate in production while ensuring reliable outcomes; hence, partnerships must be pursued with care. Online marketplaces like Xometry facilitate partnership formation by vetting suppliers and mediating the marketplace. How- ever, such an approach requires that all trust be vested in the middleman. This centralizes control, making the system vulnerable to being biased toward specific providers. The use of blockchains is now being explored to bridge the trust gap needed to support decentralizing marketplaces, allowing suppliers and customers to interact more directly by using the information on the blockchain. A typical scenario is the need to preserve privacy in certain interactions initiated by the buyer (e.g., protecting a buyer’s intellectual property during outsourcing negotiations). In this work, we initiate the formal study of matching between suppliers and buyers when buyer-privacy is required for some marketplace interactions and make the following contributions. First, we devise a formal security definition for private interactive matching in the Universally Composable (UC) Model that captures the privacy and correctness properties expected in specific supply chain marketplace interactions. Second, we provide a lean protocol based on any programmable blockchain, anonymous group signatures, and public-key encryption. Finally, we implement the protocol by instantiating some of the blockchain logic by extending the BigChainDB blockchain platform.