This paper presents a fully functional identity-based encryption (IBE) scheme based on the Weil pairing. The scheme provides chosen ciphertext security in the random oracle model under the assumption of a variant of the computational Diffie-Hellman problem on elliptic curves. The IBE system allows the public key to be an arbitrary string, eliminating the need for certificate management. The system is built using a bilinear map between two groups, with the Weil pairing as an example. The scheme is secure against adaptive chosen ciphertext attacks and allows for efficient key distribution and revocation. The paper also discusses applications of IBE, including key revocation, delegation of decryption keys, and the construction of an ElGamal encryption scheme with built-in key escrow. The security of the IBE system is based on the Weil Diffie-Hellman assumption, which is a natural analogue of the computational Diffie-Hellman problem on elliptic curves. The paper also explores extensions of the IBE system, including the use of other curves and pairings, and the distribution of the master key among multiple parties. The IBE system is shown to imply a public key signature scheme, and the paper concludes with a discussion of open problems and future research directions.This paper presents a fully functional identity-based encryption (IBE) scheme based on the Weil pairing. The scheme provides chosen ciphertext security in the random oracle model under the assumption of a variant of the computational Diffie-Hellman problem on elliptic curves. The IBE system allows the public key to be an arbitrary string, eliminating the need for certificate management. The system is built using a bilinear map between two groups, with the Weil pairing as an example. The scheme is secure against adaptive chosen ciphertext attacks and allows for efficient key distribution and revocation. The paper also discusses applications of IBE, including key revocation, delegation of decryption keys, and the construction of an ElGamal encryption scheme with built-in key escrow. The security of the IBE system is based on the Weil Diffie-Hellman assumption, which is a natural analogue of the computational Diffie-Hellman problem on elliptic curves. The paper also explores extensions of the IBE system, including the use of other curves and pairings, and the distribution of the master key among multiple parties. The IBE system is shown to imply a public key signature scheme, and the paper concludes with a discussion of open problems and future research directions.