The paper introduces a short group signature scheme that is approximately the size of a standard RSA signature while maintaining the same level of security. The scheme is based on the Strong Diffie-Hellman (SDH) assumption and a new assumption called the Decision Linear assumption in bilinear groups. The authors prove the security of their system in the random oracle model using a variant of the security definition for group signatures proposed by Bellare, Micciancio, and Warinschi. The scheme is flexible and can be extended to include features such as revocation and strong exculpability. The length of the group signature is under 200 bytes, making it suitable for applications like Trusted Computing and Vehicle Safety Communications.The paper introduces a short group signature scheme that is approximately the size of a standard RSA signature while maintaining the same level of security. The scheme is based on the Strong Diffie-Hellman (SDH) assumption and a new assumption called the Decision Linear assumption in bilinear groups. The authors prove the security of their system in the random oracle model using a variant of the security definition for group signatures proposed by Bellare, Micciancio, and Warinschi. The scheme is flexible and can be extended to include features such as revocation and strong exculpability. The length of the group signature is under 200 bytes, making it suitable for applications like Trusted Computing and Vehicle Safety Communications.