1) Homomorphic encryption allows processing of encrypted data without decrypting it first, enabling secure computations on outsourced data in cloud computing. 2) A homomorphic encryption scheme is proposed that uses a large integer ring as the plaintext space and a single key for encryption and decryption, providing confidentiality even when a non-trusted cloud server processes encrypted data. 3) The scheme could enable applications like private queries to a search engine, private information retrieval from databases, and secure electronic voting by allowing computations on encrypted data.