The paper introduces the concept of Public Key Encryption with Keyword Search (PEKS), which allows a user to encrypt data using a public key and enable a third party to search for specific keywords in the encrypted data without learning any other information about the content. The authors define the security requirements for PEKS and present two constructions: one based on a variant of the Computational Diffie-Hellman problem and another based on general trapdoor permutations. The first construction is semantically secure under the assumption that the underlying public key encryption system is secure, while the second construction is efficient but has a limited number of searchable keywords. The paper also discusses the relationship between PEKS and Identity-Based Encryption (IBE), showing that PEKS implies IBE but the converse is not currently known.The paper introduces the concept of Public Key Encryption with Keyword Search (PEKS), which allows a user to encrypt data using a public key and enable a third party to search for specific keywords in the encrypted data without learning any other information about the content. The authors define the security requirements for PEKS and present two constructions: one based on a variant of the Computational Diffie-Hellman problem and another based on general trapdoor permutations. The first construction is semantically secure under the assumption that the underlying public key encryption system is secure, while the second construction is efficient but has a limited number of searchable keywords. The paper also discusses the relationship between PEKS and Identity-Based Encryption (IBE), showing that PEKS implies IBE but the converse is not currently known.