The paper proposes a fully functional identity-based encryption (IBE) scheme that achieves chosen ciphertext security in the random oracle model, assuming a variant of the computational Diffie-Hellman problem on elliptic curves. The scheme is based on the Weil pairing and includes precise definitions for secure IBE systems. The authors discuss several applications of IBE, such as key revocation and delegation of decryption keys. They also provide a detailed security analysis, including a proof that the scheme is one-way IBE if the Weil Diffie-Hellman assumption holds. The paper describes the basic IBE scheme and its extension to achieve chosen ciphertext security using the Fujisaki-Okamoto transformation. Additionally, it explores extensions like distributed Private Key Generator (PKG) and working in subgroups, and introduces an ElGamal encryption scheme with built-in key escrow. The paper concludes with a discussion on open problems and future research directions.The paper proposes a fully functional identity-based encryption (IBE) scheme that achieves chosen ciphertext security in the random oracle model, assuming a variant of the computational Diffie-Hellman problem on elliptic curves. The scheme is based on the Weil pairing and includes precise definitions for secure IBE systems. The authors discuss several applications of IBE, such as key revocation and delegation of decryption keys. They also provide a detailed security analysis, including a proof that the scheme is one-way IBE if the Weil Diffie-Hellman assumption holds. The paper describes the basic IBE scheme and its extension to achieve chosen ciphertext security using the Fujisaki-Okamoto transformation. Additionally, it explores extensions like distributed Private Key Generator (PKG) and working in subgroups, and introduces an ElGamal encryption scheme with built-in key escrow. The paper concludes with a discussion on open problems and future research directions.