Explore a research talk on multi-party private set union (mPSU) protocols that addresses scalability challenges in secure computation. Learn about the limitations of existing symmetric key encryption (SKE)-based and public key encryption (PKE)-based mPSU approaches, which fail to efficiently utilize computational resources and leave participants idle during protocol execution. Discover a unified framework for designing efficient mPSU protocols and examine PULSE (Parallel mPSU for Large-Scale Entities), a novel PKE-based solution that enables parallel computation across all parties without idle time. Understand how PULSE maintains security even when up to n-1 semi-honest parties are corrupted, and review performance benchmarks showing 1.91 to 3.57× speedup improvements compared to state-of-the-art protocols for 8 parties across various set sizes. Gain insights into how parallel processing can significantly enhance efficiency in multi-party secure computation scenarios, particularly as the number of participating entities increases.