The paper presents two efficient Identity-Based Encryption (IBE) systems that are secure against selective identity attacks without relying on random oracles. The first system extends to a secure Hierarchical IBE (HIBE) without random oracles, while the second system is more efficient and based on a new assumption called Decision Bilinear Diffie-Hellman Inversion (BDHI). Both systems are proven secure under their respective assumptions, and the paper also discusses the construction of efficient CCA2-secure public key systems using these IBE systems. The paper concludes by highlighting the ongoing challenge of constructing fully secure IBE systems against adaptive identity attacks without random oracles.The paper presents two efficient Identity-Based Encryption (IBE) systems that are secure against selective identity attacks without relying on random oracles. The first system extends to a secure Hierarchical IBE (HIBE) without random oracles, while the second system is more efficient and based on a new assumption called Decision Bilinear Diffie-Hellman Inversion (BDHI). Both systems are proven secure under their respective assumptions, and the paper also discusses the construction of efficient CCA2-secure public key systems using these IBE systems. The paper concludes by highlighting the ongoing challenge of constructing fully secure IBE systems against adaptive identity attacks without random oracles.