This chapter explores critical aspects of privacy computing in federated recommendation systems. It provides an overview of homomorphic encryption, discussing partial and full homomorphism alongside their advantages and limitations. Key techniques in differential privacy, such as additive noise and randomized response, are evaluated for effectiveness. Secure multi-party computation is discussed with methods like Secret Sharing (SS) and Garbled Circuit. The chapter also addresses attack vectors, including poisoning and inference attacks, and strategies for Byzantine resilience. This analysis aims to strengthen privacy-preserving techniques in federated learning environments.