This paper presents two efficient Identity-Based Encryption (IBE) systems that are selectively identity secure without the random oracle model. Selective identity security is a weaker security model than the standard IBE security model, where the adversary must commit to the identity it intends to attack in advance, rather than adaptively choosing it. The authors construct two IBE systems that are provably secure under the Decision Bilinear Diffie-Hellman (Decision BDH) assumption and the Decision Bilinear Diffie-Hellman Inversion (Decision BDHI) assumption, respectively. The first IBE system is based on the Decision BDH assumption and extends to an efficient selective identity secure Hierarchical IBE (HIBE) without random oracles. The second IBE system is based on the Decision BDHI assumption and is more efficient than the first. Both systems are shown to be chosen ciphertext secure (CCA2) without random oracles, with the second system having performance comparable to the Cramer-Shoup system based on the Decision Diffie-Hellman (DDH) assumption. The paper also discusses the security of these systems under the selective identity model, where the adversary is not allowed to issue decryption queries. It shows that any selective identity, chosen plaintext IBE system can be converted into a chosen ciphertext secure public key system. The authors also extend their IBE systems to handle arbitrary identities by hashing them using a collision-resistant hash function. The paper concludes that the problem of constructing a fully secure IBE system against adaptive identity attacks without random oracles remains open. The authors hope that this work will contribute to resolving this open problem.This paper presents two efficient Identity-Based Encryption (IBE) systems that are selectively identity secure without the random oracle model. Selective identity security is a weaker security model than the standard IBE security model, where the adversary must commit to the identity it intends to attack in advance, rather than adaptively choosing it. The authors construct two IBE systems that are provably secure under the Decision Bilinear Diffie-Hellman (Decision BDH) assumption and the Decision Bilinear Diffie-Hellman Inversion (Decision BDHI) assumption, respectively. The first IBE system is based on the Decision BDH assumption and extends to an efficient selective identity secure Hierarchical IBE (HIBE) without random oracles. The second IBE system is based on the Decision BDHI assumption and is more efficient than the first. Both systems are shown to be chosen ciphertext secure (CCA2) without random oracles, with the second system having performance comparable to the Cramer-Shoup system based on the Decision Diffie-Hellman (DDH) assumption. The paper also discusses the security of these systems under the selective identity model, where the adversary is not allowed to issue decryption queries. It shows that any selective identity, chosen plaintext IBE system can be converted into a chosen ciphertext secure public key system. The authors also extend their IBE systems to handle arbitrary identities by hashing them using a collision-resistant hash function. The paper concludes that the problem of constructing a fully secure IBE system against adaptive identity attacks without random oracles remains open. The authors hope that this work will contribute to resolving this open problem.