The paper presents the first efficient Identity-Based Encryption (IBE) scheme that is fully secure without random oracles. The authors first introduce their IBE construction and prove its security by reducing it to the decisional Bilinear Diffie-Hellman (BDH) problem. They also show that their techniques can be used to build a new signature scheme that is secure under the computational Diffie-Hellman assumption without random oracles. The IBE scheme is based on an algebraic method similar to Boneh and Boyen's but with a modification in the evaluation of the private key, which is crucial for achieving full security. The paper includes a detailed security proof, complexity assumptions, and an efficient implementation. Additionally, it discusses the extension of the IBE scheme to a hierarchical identity-based encryption scheme and its application to achieving CCA-security. The authors also describe a signature scheme derived from the IBE scheme, which is secure under the computational Diffie-Hellman assumption. The paper concludes by highlighting two open problems: finding an efficient IBE system with short public parameters and achieving a tight reduction in security for IBE systems.The paper presents the first efficient Identity-Based Encryption (IBE) scheme that is fully secure without random oracles. The authors first introduce their IBE construction and prove its security by reducing it to the decisional Bilinear Diffie-Hellman (BDH) problem. They also show that their techniques can be used to build a new signature scheme that is secure under the computational Diffie-Hellman assumption without random oracles. The IBE scheme is based on an algebraic method similar to Boneh and Boyen's but with a modification in the evaluation of the private key, which is crucial for achieving full security. The paper includes a detailed security proof, complexity assumptions, and an efficient implementation. Additionally, it discusses the extension of the IBE scheme to a hierarchical identity-based encryption scheme and its application to achieving CCA-security. The authors also describe a signature scheme derived from the IBE scheme, which is secure under the computational Diffie-Hellman assumption. The paper concludes by highlighting two open problems: finding an efficient IBE system with short public parameters and achieving a tight reduction in security for IBE systems.