This paper explores the integration of advanced cryptographic techniques for secure computation in data spaces to enable secure and trusted data sharing, which is essential for the evolving data economy. In addition, the paper examines the role of data intermediaries, as outlined in the EU Data Governance Act, in data spaces and specifically introduces the idea of trustless intermediaries that do not have access to their users' data. Therefore, we exploit the introduced secure computation methods, i.e. Secure Multi-Party Computation (MPC) and Fully Homomorphic Encryption (FHE), and discuss the security benefits. Overall, we identify and address key challenges for integration, focusing on areas such as identity management, policy enforcement, node selection, and access control, and present solutions through real-world use cases, including air traffic management, manufacturing, and secondary data use. Furthermore, through the analysis of practical applications, this work proposes a comprehensive framework for the implementation and standardization of secure computing technologies in dynamic, trustless data environments, paving the way for future research and development of a secure and interoperable data ecosystem.

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