The group signature schemes were proposed by Chaum and van Heyst for
the first time.  A group signature scheme allows a group member to
anonymously sign a message on behalf of the group and anyone can
verify whether or not the signature was created by some 
(unknown) member of the group.
But in case of dispute or necessity, the
group manager can reveal the signer's identity.  At present,
Group signature scheme based on RSA signature is proposed.
However this scheme is
disadvantageous in that the signature length is long.
On the other hand, as an alternative,
Group signature scheme with bilinear maps is proposed.  The group
signature scheme with bilinear maps is advantageous in that
computational cost of verification is efficient and signature length
is short.  However, the current bilinear-map-based group signature 
schemes
are suffering from much computational cost of  verification
dependent on the number revoked members.

Here we propose the group signature scheme indepent
of the number of revoked members.  Our scheme divides members into sub 
groups to reduce
the cost of signature verification which depends on the number of
revoked member in one sub-group.
By using the proposed
scheme, cost of signature verification depends on the number of
revoked members who belong to the sub-group.