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This lecture covers the concept of homomorphic encryption, a technique that allows computation on encrypted data without decrypting it. It explains the security of data in transit and at rest, the need for confidentiality in data processing, and the application of homomorphic encryption in secure statistics computation. The lecture delves into the definition, security, and practical considerations of homomorphic encryption, including noise management and bootstrapping. It also discusses the history of homomorphic encryption, different types of homomorphic encryption schemes, and the implementation of lattice-based cryptosystems. The lecture concludes with the potential of homomorphic encryption in ensuring data security and the ongoing research in this field.