This paper proposes an identity-based signature scheme using gap Diffie-Hellman (GDH) groups. The scheme is proven secure against existential forgery under adaptively chosen message and ID attacks in the random oracle model, assuming the hardness of the computational Diffie-Hellman problem (CDHP). Using GDH groups derived from bilinear pairings, the scheme shares the same system parameters as the ID-based encryption scheme (BF-IBE) by Boneh and Franklin, and is as efficient as BF-IBE. Combining the signature scheme with BF-IBE provides a complete solution for an ID-based public key system, offering an alternative to certificate-based PKIs when efficient key management and moderate security are required. The scheme is based on GDH groups, where the decisional Diffie-Hellman problem (DDHP) is solvable, but the computational Diffie-Hellman problem (CDHP) is hard. The scheme uses a master key to generate private keys for users, and a signature is created by signing a message with the user's private key. The signature is verified by checking if the resulting tuple satisfies the Diffie-Hellman condition. The scheme provides stronger non-repudiation than previous ID-based schemes, as the secret can be shared among multiple parties through a threshold scheme. The scheme is secure under the assumption that CDHP is hard. The security proof reduces the problem to a game where an adversary attempts to forge a signature. If the adversary succeeds, it implies that CDHP can be solved. The scheme is efficient and can be implemented using elliptic curves with bilinear pairings, such as the Weil pairing. The performance of the scheme is compared to BF-IBE, showing that verification is the most expensive operation, while signing is the least expensive. The scheme is secure against adaptively chosen message and ID attacks, and can be used in applications requiring simple key management and built-in key recovery.This paper proposes an identity-based signature scheme using gap Diffie-Hellman (GDH) groups. The scheme is proven secure against existential forgery under adaptively chosen message and ID attacks in the random oracle model, assuming the hardness of the computational Diffie-Hellman problem (CDHP). Using GDH groups derived from bilinear pairings, the scheme shares the same system parameters as the ID-based encryption scheme (BF-IBE) by Boneh and Franklin, and is as efficient as BF-IBE. Combining the signature scheme with BF-IBE provides a complete solution for an ID-based public key system, offering an alternative to certificate-based PKIs when efficient key management and moderate security are required. The scheme is based on GDH groups, where the decisional Diffie-Hellman problem (DDHP) is solvable, but the computational Diffie-Hellman problem (CDHP) is hard. The scheme uses a master key to generate private keys for users, and a signature is created by signing a message with the user's private key. The signature is verified by checking if the resulting tuple satisfies the Diffie-Hellman condition. The scheme provides stronger non-repudiation than previous ID-based schemes, as the secret can be shared among multiple parties through a threshold scheme. The scheme is secure under the assumption that CDHP is hard. The security proof reduces the problem to a game where an adversary attempts to forge a signature. If the adversary succeeds, it implies that CDHP can be solved. The scheme is efficient and can be implemented using elliptic curves with bilinear pairings, such as the Weil pairing. The performance of the scheme is compared to BF-IBE, showing that verification is the most expensive operation, while signing is the least expensive. The scheme is secure against adaptively chosen message and ID attacks, and can be used in applications requiring simple key management and built-in key recovery.