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Data sharing opportunities are everywhere, but privacy concerns and regulatory constraints often prevent organizations from fully realizing their value. A private data federation tackles this challenge by enabling secure querying across multiple privately held data stores where only the final results are revealed to anyone. We investigate optimizing relational queries evaluated under secure multiparty computation, which provides strong privacy guarantees but at a significant performance cost. We present Alchemy, a query optimization framework that generalizes conventional optimization techniques to secure query processing over circuits, the most popular paradigm for cryptographic computation protocols. We build atop VaultDB, our open-source framework for oblivious query processing. Alchemy leverages schema information and the query's structure to minimize circuit complexity while maintaining strong security guarantees. Our optimization framework builds incrementally through four synergistic phases: (1) rewrite rules to minimize circuits; (2) cardinality bounding with schema metadata; (3) bushy plan generation; and (4) physical planning with our fine-grained cost model for operator selection and sort reuse. While our work focuses on MPC, our optimization techniques generalize naturally to other secure computation settings. We validated our approach on TPC-H, demonstrating speedups of up to 2 OOM.