A number of previous papers explored the notion of identity-based group signature. We present a generic construction of identity-based group signatures. ]Our construction is based on the Naor transformation of a identity-based signature out of an identity-based encryption, adjusted to hierarchical identity-based encryption. We identify sufficient conditions on the underlying HIBE so that the scheme that results from our transformation meets our security definitions. Finally, we suggest a couple of extensions enabled by our construction, one of which is to hierarchical identity-based group signatures.