In group signature schemes, the user?s group secret key is often stored on insecure devices e.g. mobile phones that are likely to be compromised by an adversary. To mitigate the damage of key exposure in group signature schemes, we proposed a key-insulated group signature scheme. The group secret key stored on an insecure device is refreshed at discrete time periods via interaction with a physically-secure device that stores a "master key". Our scheme has secure and random-access key updates. The exposure of up to t of the T time periods, chosen adaptively by the adversary, still keeps any period that was not exposed secure. Our scheme also adopts method of Verifier-Local Revocation (VLR) and supports backward unlinkability, i.e. previously signed signatures remain valid, anonymous and unlinkable even after the signer is revoked.