arXiv:2610.12535v1 Announce Type: new Abstract: Privacy-preserving order matching enables traders to discover and execute compatible orders while limiting disclosure of sensitive trading information. Existing systems span financial markets and blockchain-based asset exchanges and employ diverse market structures, privacy mechanisms, and trust assumptions, making their privacy guarantees difficult to compare. We present a systematization of privacy-preserving order matching covering 22 protocol families. We organize the order lifecycle into four phases: order representation and submission, order discovery and collection, order-matching, and settlement, and characterize each phase by protected and exposed information, access roles, privacy mechanisms, and trust assumptions. Our analysis shows that privacy is not a single protocol-level property: protecting selected order attributes or individual phases does not necessarily prevent leakage elsewhere in the lifecycle. We identify recurring trade-offs among privacy, functionality, trust, and verifiability, highlighting the challenge of achieving end-to-end privacy across the complete order lifecycle.