Public key Encryption with Keyword Search (PEKS) has emerged as a solution for the receiver to securely search the sender’s encrypted data on the cloud. However, the PEKS scheme is threatened by the Keyword Guessing Attack (KGA), which leaks the receiver’s keyword privacy. To resist KGA, researchers have inherited the authentication mechanism into the PEKS system (PAEKS) but also forbid using one trapdoor to search all sender’s encrypted data. In this paper, we explore the KGA problem from grouping senders and propose the notion of Identity-based Group Encryption with Keyword Search (IBGEKS), which leverages Identity-based cryptography to securely search encrypted data. Compared with the PAEKS scheme, the IBGEKS scheme can search the sender’s ciphertexts within the same group established by the receiver via one receiver’s trapdoor. For security, we analyze the KGA problem and propose ciphertexts, identities, and trapdoors indistinguishability for IBGEKS. The evaluation depicts that the IBGEKS has competitive algorithm performance with other SA-PEKS and PAEKS schemes and has superior search performance on the Enron email dataset.