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This lecture covers the legal aspects, security, and privacy in the context of homomorphic encryption. It explains the legislative bases, laws, and organizations related to this topic. The instructor discusses the use of elliptic curves, operations, and notations in homomorphic encryption. The lecture also delves into encoding and decoding numbers into points, as well as the concept of aggregated keys. It explores the practical applications of homomorphic encryption, such as multi-party homomorphic encryption and the challenges of securely decrypting aggregated results. The lecture concludes with a detailed explanation of how a researcher can choose, encrypt, and aggregate data using homomorphic encryption techniques.