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. Once the group secret key of a group member is found stolen, he will be revoked and can not sign documents any more. 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 physicallysecure device that stores a "master key". Our scheme has secure and random-access key updates. The exposure of up to t of the N time periods, chosen adaptively by the adversary, still keeps any period that was not exposed secure. Our scheme supports selective revocation, i.e. only revoking the user?s signing ability for some periods that were exposed, which is appropriate for the key-insulated group signature scheme.