This paper presents a short group signature scheme based on the Strong Diffie-Hellman (SDH) assumption and a new assumption in bilinear groups called the Decision Linear assumption. The scheme provides signatures that are approximately the size of a standard RSA signature with the same security level. The group signature allows members of a group to sign messages while keeping their identities secret. A third party can trace the signature if needed, and the system supports revocation of signing keys without affecting the signing ability of other members. The scheme is constructed using a zero-knowledge proof of knowledge (ZKPK) of an SDH problem, converted into a group signature via the Fiat-Shamir heuristic. The security of the scheme is proven in the random oracle model using a variant of the security definition for group signatures proposed by Bellare, Micciancio, and Warinschi. The group signature is efficient and short, with a signature length under 200 bytes, suitable for applications such as privacy-preserving attestation and vehicle safety communications. The scheme is also flexible, allowing for the addition of features such as revocation and strong exculpability. The system is based on bilinear groups and uses a new assumption in bilinear groups called the Linear assumption. The security of the scheme relies on the hardness of the SDH problem and the Decision Linear problem in bilinear groups. The scheme is proven to be correct, fully traceable, and CPA-fully anonymous. The system is efficient, with signature generation requiring no pairing computations and verification requiring a single pairing.This paper presents a short group signature scheme based on the Strong Diffie-Hellman (SDH) assumption and a new assumption in bilinear groups called the Decision Linear assumption. The scheme provides signatures that are approximately the size of a standard RSA signature with the same security level. The group signature allows members of a group to sign messages while keeping their identities secret. A third party can trace the signature if needed, and the system supports revocation of signing keys without affecting the signing ability of other members. The scheme is constructed using a zero-knowledge proof of knowledge (ZKPK) of an SDH problem, converted into a group signature via the Fiat-Shamir heuristic. The security of the scheme is proven in the random oracle model using a variant of the security definition for group signatures proposed by Bellare, Micciancio, and Warinschi. The group signature is efficient and short, with a signature length under 200 bytes, suitable for applications such as privacy-preserving attestation and vehicle safety communications. The scheme is also flexible, allowing for the addition of features such as revocation and strong exculpability. The system is based on bilinear groups and uses a new assumption in bilinear groups called the Linear assumption. The security of the scheme relies on the hardness of the SDH problem and the Decision Linear problem in bilinear groups. The scheme is proven to be correct, fully traceable, and CPA-fully anonymous. The system is efficient, with signature generation requiring no pairing computations and verification requiring a single pairing.